text:
Talk:Earl Dodge

Some background on the 2003-2004 Prohibition quarrels
Since the above note indicates that the biography should be altered, I thought that some additional information might be of use.

In the summer of 2003, Dodge called a private meeting in his house in Lakewood, Colorado, from which he excluded a number of Party members. The Prohibition Party's membership had not approved this private meeting. Dodge and six other people, including two daughters, met in his living room. The group nominated him for president and Howard Lydick for vice president. One of those present was Leroy J. Pletten, the secretary of the executive committee, who later "switched sides" as the controversy widened, upon being informed of Dodge's having refused disfavored members notice of the meeting and of the right to attend. Dodge and Pletten are not related.

The party's membership as a whole immediately objected to Dodge's private meeting. The membership as a whole called the Convention due that year, to be held in Tennessee. This full membership Convention occurred in the fall of 2003. At this meeting, new officers were chosen for the executive committee, and Dodge was asked to give an account of the party funds and Storms collection. Chronicler3 11:56, 12 August 2006 (UTC)

The historic Party learned that Dodge had secretly incorporated a new Party, calling it the "National Prohibition Party" to distinguish it from the original Party (founded in 1869). However, to the unsuspecting subscribers, Dodge continued using the historic name, over the objections of the historic Party.

Huh?
Is this a joke? No joke, Dodge and his people seceded, set up a DIFFERENT competing party that they called the "National Prohibition Party." They knew, of course, they could raise no funds with that, so to outsiders, they pretended no change had occurred! and that Dodge remained Chairman of the historic Party. This is as though, in history, Jefferson Davis had pretended he was President of the United States, not Lincoln! -- not just a lie but an ultra-whopper of a lie! Yes, Dodge's lying was so extreme you might think that revealing the truth is a "joke," but truth is stranger than fiction (a joke).

Questions? Ask them through Wikinews
Hello,

I'm Nick Moreau, an accredited reporter for Wikinews. I'm co-ordinating our 2008 US Presidential election interviews. We will be interviewing as many candidates as possible, from the Democrats, Republicans, and other parties/independents.

I'll be sending out requests for interviews to the major candidates very soon, but I want your input, as people interested in American politics: what should I ask them?

Please go to any of these three pages, and add a question.

 * n:Wikinews:Story preparation/US 2008/Democratic Party
 * n:Wikinews:Story preparation/US 2008/Republican Party
 * n:Wikinews:Story preparation/US 2008/Third Party or Independent

Questions? Don't ask them here, I'll never see them. Either ask them on the talk page of any of these three pages, or<EMAIL_ADDRESS>e-mail me].

Thanks, Nick --  Zanimum 19:44, 19 July 2007 (UTC)

recent deletion
The recent derogatory paragraphs appear to me to be presenting the assertions of the non-Dodge faction as fact.

The second "citation" link is, in fact, to a web page maintained by said faction. Somehow, I don't think that counts as a valid citation. I mean, I could easily create a web page containing wild accusations against some other person - would it be legit if I cited that page in support of similar statements on Wikipedia?

Meanwhile, the first link appears to point to a page which was written by the person who added the derogatory paragraphs. If I understand correctly, this is considered to be spamming. If I don't understand correctly, I welcome correction from anyone who is knowledgeable on the subject.

At any rate, that's why I deleted the paragraphs in question. If they're added again, I'll delete them again, until the poster tires of the cycle, or one of us is blocked from making such changes, or someone can persuade me that mere repetition of the other faction's assertions is considered legitimate.

Caldodge 04:16, 16 November 2007 (UTC)

Conflict of interest
Earl Dodge's son has taken it upon himself to censor information in his father's wikipedia biography. In so doing, he is in violation of Wikipedia policy. His threat to engage in a revert war with anyone who dares to present information he considers deragatory or otherwise unacceptable also appears to be in violation of Wikipedia policy.David Justin 16:02, 16 November 2007 (UTC)

Reference tag
Following the posting of the tag calling for more references on November 8, the reference density has increased from one per 162 words to one per 25 words. Therefore, I have removed that tag.David Justin (talk) 13:59, 17 November 2007 (UTC)

not a threat
Sorry, Professor Hanson aka "David Justin", but I didn't declare war. I did say I'd delete your items which merely parrot the other faction's claims (with one exception, every non-Wikipedia link you added is a pointer to that faction's web site). I don't consider unsubstantiated allegations motivated by political considerations to be "information".

In addition, I see no citation for your claim that "divisiveness may continue because of the Amondson faction’s contention that the Dodge family controls most of the assets held by the party and its foundations". Who says "divisiveness may continue"? Are you quoting a member of the other faction? If so, who? Or is this simply your speculation, given your antipathy toward all temperance organizations? At any rate, I also don't believe the editorial comments of a biased party count as "information".

I'm not a Party member, and haven't been for years. But I know the Dodge family has no desire to "control" the party, and I'd say that knowledge has more validity than your biased uninformed speculations.

So, again, I'll keep deleting your crap until 1) you tire of this game, or 2) you or I are blocked from making such changes, or 3) someone persuades me that the other faction's claims are valid (you could do this if you cited real evidence, rather than playing "Polly wants a cracker" for Pletten and his bunch).

Caldodge (talk) 18:33, 17 November 2007 (UTC)

an alternative course for David J. Hanson
Professor Hanson,

One alternative for you would be to post your crap on the Prohibition Party page. I promise not to revert any claims you put there. Of course, I may also post counter-claims on that page, and let people see both sides of the story, instead of the one-sided story you are repeating over and over.

Caldodge (talk) 18:36, 17 November 2007 (UTC)

Professor Hanson (aka "David Justin") conflict of interest
Professor Hanson has an obvious conflict of interest, too. He believes that moderate drinking is healthier than abstinence, and consequently has written numerous derogatory items about temperance organizations (as well as organizations which simply want people to not drink while they're driving).

It's obvious to me that his continuous reposting of the other Prohibition faction's claims is simply another way to attack a temperance leader, advancing Professor Hanson's cause.

 * Hi Caldodge- Writing about ones father necessarily constitutes a conflict of interest according to Wikipedia guidelines. However, writing about something or someone and having a point of view (as does everyone) does not. Thanks. David Justin (talk) 22:02, 20 November 2007 (UTC)

Professor Hanson's latest error
Professor Justin was apparently ignorant of the date of the Earl Dodge quote on politics1.com.

A check with the Internet Wayback machine [] shows the "fair and objective" quote dates back to 2000, and therefore CANNOT be a reference to the "divisive events" of 2003. That is why I removed the quote - it falsely implies his agreement the description of those events.

I added what I've been told is the real motivation of anti-Dodge faction (i.e., compromising prohibition goals). I didn't do so in some partisan spirit, since I've been a Republican since 1994.

Regarding "Dodge faction does not refute these allegations", Dad felt that what he _did_ was more important than what people said about him (believing God would judge his actions), so he was not in the habit of defending himself publicly (or, most of the time, privately).

And I know from discussions with Mom just how much Dad sacrificed to keep the party afloat in recent years, as well as when the party faced financial disaster in 1960. No, there are no citations available for this fact, since it wasn't published in any news story.

Caldodge (talk) 12:16, 20 November 2007 (UTC)

 * Hi Caldodge- I don’t believe your father’s quote regarding the accuracy of Politics1.com is misleading. By letting his comments stand, he is reasonably presumed to have acknowledged the accuracy of the material in question.

 * However, it is unacceptable to add, as you have, numerous statements based on hearsay and other non-verifiable sources. Even though you have a clear conflict of interest, I don’t doubt your integrity or the veracity of these statements. Nevertheless,  their inclusion is inconsistent with Wikipedia policy. Thanks. David Justin (talk) 22:02, 20 November 2007 (UTC)

Professor Hanson's request for citations
Since Professor Hanson's "citations" consist almost entirely of links to the pagss of the anti-Dodge faction (with an occasional link to an article which merely mentions the fact that there _is_ a party schism), I'm assuming that similar links to the pro-Dodge's faction would also count as suitable citations.

I'll discuss this with the prohibition.org webmaster, to see what pages I can create which will then be used as citations.

 * Hi Caldodge- That would be most useful. It’s important that both sides of the issue be presented as well as possible. Thanks for your efforts. David Justin (talk) 01:13, 23 November 2007 (UTC)

Meanwhile, I'm curious about Professor Hanson's obsession with repeatedly posting the anti-Dodge faction's allegations. Is his motivation simply a desire to denigrate all temperance organizations? Does he have some unmentioned conflict with Earl Dodge? Or does he have an undisclosed relationship with the anti-Dodge faction?

As one of Earl Dodge's sons, I trust my motivation is obvious. What is your motivation, Professor Hanson?

 * Hi again Caldodge - I regret that I never met or communicated with your father. From the obituaries and related news, he appears to have been a man with a magnetic personality with whom even strangers could easily relate, who loved his family, and who largely devoted his life to the cause of prohibition to which he was so deeply committed. Even some in the opposing faction considered him to be their friend and he seems not to have spoken ill of anyone regardless of their beliefs about alcohol.

 * My motivation is to help present a balanced encyclopedia entry for the man who was truly “Mr. Prohibition.” No encyclopedia entry about George Washington would be balanced without a discussion of his slave-holding, nor of Jefferson without attention to his apparently illegitimate offspring, nor of Nixon without an explication of Watergate, nor of Clinton without  consideration of the Monica Lewinsky affair.

 * A man of your father’s stature deserves more than a superficial “puff-piece” and an encyclopedia entry demands it. Best regards,David Justin (talk) 01:13, 23 November 2007 (UTC)

<IP_ADDRESS> (talk) 04:57, 22 November 2007 (UTC)

Sorry - I forgot to log in before adding this section. Caldodge (talk) 05:34, 22 November 2007 (UTC)

 * I have been with the Amondson faction since 2004, and I have never heard of him by either name. I did take a look at his website once and realized that I agreed with the "neo-prohibitionist" agenda completely.Chronicler3 (talk) 11:12, 22 November 2007 (UTC) Earl Dodge was NEVER "Mr. Prohibition." In fact, in his last years, he tried to destroy the historic 1869 Prohibition Party both organizationally and in court, by pretending that it was a new group just formed in Septmber 2003!  He ran against the historic Party, using his new secessionaist group which he called the "National Prohbition Party" as his vehicle.

restored "sudden"
I restored the "sudden" adjective because the death WAS sudden - unexpected by anybody.

Dad had a heart attack in 1984, and septuple bypass surgery in 1999, but to all appearances seemed to be healthy enough for his age (unlike my wife's grandparents, both of whom had an obvious decline in health for months before their deaths) —Preceding unsigned comment added by Caldodge (talk • contribs) 18:55, 29 November 2007 (UTC)

SmokeDoctor, reveal yourself
Instead of hiding behind a phony name, why don't you post your real identity?

Frankly, based on your additions, I'm guessing you're another of David J Hanson's sock puppets. But it would be nice to know for sure.

Come out from under your rock, and let people know who you really are.

Caldodge (talk) 15:19, 7 July 2008 (UTC)

Who are you, "Exofreeze"?
So you restored comments from the phony "SmokeDoctor" "due to neutrality bias"?

Who are you, Exofreeze? What's your bias? Or are you just another sock puppet of David J. Hanson? —Preceding unsigned comment added by Caldodge (talk • contribs) 14:54, 1 August 2008 (UTC)

There is nothing to 'reveal'. You seem to think that only people related to David Hanson would disagree with you. I am a university student who has been writing a paper on political parties that either are not impactful during election processes (such as the Prohibitionists) or actually split votes (such as the Green party). I have no bias either way, nor am I related to any of those in question.

Now whether or not you agree with me or not is not important. The fact is there is a neutrality bias once you, the son of the person in question, take it upon yourself to censor this page in any way you see fit. It does not take a student or a 'sock puppet' (as you call them) to understand this.

Your attitude in attacking anyone who edits this page is proof enough of a neutrality bias - and it is the readers' right to know this when they come to your fathers page.

Exofreeze (talk) 01:45, 4 August 2008 (UTC)

You have no bias? Then why are you hiding behind an alias? Why are you adding language which is not in the cited pages ("new secessionist party")? How is it that my comments based on personal experience (Dad paying for many party expenses out of his own pocket, for example) are considered a "neutrality bias", while text derived from the opposing faction is not so?

All we have is your word that you aren't a sock puppet (the term is a well-known one at Wikipedia (and other sites) - not something _I_ made up). For all I know, you could be Leroy Pletten (a man who has been described as "a nut" by people in the opposing faction) or (more likely) David Hanson.

I'm not afraid to list my real name, and let readers know where I'm coming from, so they can use that knowledge in judging the veracity of my comments. Meanwhile, you hide behind an alias, so the readers have no idea as to who you really are, or where you're coming from. I'll let that difference speak for itself.

Caldodge (talk) 11:55, 21 August 2008 (UTC)

Debating with you is pointless, since you can claim anything I say is made up. My name is Anthony and I live in Texas, at the time I visited this site I was attending UTD. The fact that you assume anyone on this page who disagrees with you is in league with some anti-earl dodge party is simply insane. I am sorry that you have people who you believe are slandering your father, but do you really think every person who comes here is out to get him? Luckily, by your lack of recent edits, it seems you have moved on to live your own life - just as I graduated and moved on past the class I was taking that led me to dealing with you. Your profile page is missing, so I gather you were banned from the site. Wikipedia became a better place on that day.

Exofreeze (talk) 19:01, 5 November 2008 (UTC)

2008 candidate?
Considering he died last year why is he in this category? If this has been dealt with already I apologize.--T. Anthony (talk) 04:47, 23 August 2008 (UTC)

Dodge's symptoms of mental disorder
This is something that came out in the lawsuit that Earl Dodge and his group of secessionists caused against the historic Prohibition organization. Information was provided to the historic group to the effect that when Dodge would periodically be caught stealing, that he would use an apparent insanity defense. For the full text of the affidavit filed under oath, see http://medicolegal.tripod.com/wagneraffidavit.pdf

This above was added by Leroy Pletten, the ringleader of the anti-Dodge faction of the Prohibition Party. The reader may find this information useful in judging the veracity of the information. - Caldodge (talk) 21:01, 27 August 2008 (UTC)

Dodge's secession and setting up a corporation
This is another fact that came out in Court. It came out when Dodge was being cross-examined by the judge. Dodge admitting incorporating the group. He did this in Colorado in September 2003. Dodge was enraged when the historic group by majority vote refused to re-elect him. So Dodge and his minority -- like Confederates -- seceded, set up their own Party, which they named the "National Prohibition Party." For background, see the Court hearing transcript, at http://medicolegal.tripod.com/transcript011607.doc

The incorporation paper itself has a Colorado file number, #<PHONE_NUMBER>3. The document is posted online at the State of Colorado site, http://www.sos.state.co.us/biz/BusinessEntityDetail.do?quitButtonDestination=BusinessEntityResults&nameTyp=ENT&masterFileId=20031285653&entityId2=20031285653&srchTyp=ENTITY&fileId=20031285653  Note that Dodge, to give himself the Chairmanship for life, specified NO voting by the members! He had been voted out, he wanted to make sure his new Party could never vote him out!

Given that you're citing documents from a site controlled by Leroy Pletten (the ringleader of the anti-Dodge faction) - and that those documents appear to NOT have any links within that web site, I feel safe in assuming you're actually Leroy Pletten, the fellow who took control of said faction.

That makes it a little more obvious 1) why you persist in kicking a dead man, and 2) why you resort to aliases, so people won't see that YOU are also subject to the charge of "neutrality bias".

So, Leroy, are you also "ExoFreeze"? What other pseudonyms are you using here? Inquiring minds want to know!

Caldodge (talk) 14:37, 26 August 2008 (UTC)

Is Calvin Dodge's paranoia showing? pretending that somebody named Leroy Pletten controls the above sites including the State of Colorado site!! :)  More likely, the Governor or Secretary of State of Colorado controls the Colorado site!

It is significant that Calvin Dodge does not deny the truth of any of the statements in the Court Transcript, the Wagner Affidavit, nor the State of Colorado website. He just denounces somebody, "ExoFreeze," or whomever! :) Implies his awareness of his father's guilt as charged!

No, I didn't, Leroy. And if you read my comments CAREFULLY, you'll see they're referring to the phony user "SmokeDoctor" (since THAT user is the one posting links to files on your website).

But since lying appears to be your stock-in-trade, it's not surprising that you'd claim that I said something which I didn't. medicolegal.tripod.com IS under your control, and citing your web site to back up your comments is generally considered to be bad form on Wikipedia (just ask David J Hanson). The Colorado document does state that Dad would have control of the party name (in Colorado, at least), but that is probably a reaction to his belief that you conned others into giving you control of the rest of the party. You weren't the first person who wanted the Party for his own uses - just the most successful one.

I don't KNOW the "truth" of the Wagner Affidavit, but since it was apparently created after your tenure in the Party (as mentioned in that court transcript), it wouldn't surprise me that you could con Wagner into creating it for your benefit. I DO know that Dad had plenty of happy customers, and their comments after his death gave us a good idea as to how much they respected and trusted him.

The negative remarks about Dad in the Court Transcript are all from YOU (assuming you're the "Mr. Plutten" in the transcript). Again, citing yourself is not exactly considered good form here.

I'm curious, Leroy. Dad's been dead for 9 months now. Now that Howard Lydick is also dead, it seems likely the entire party will be under your control, and ready for you to run it into the ground. So why this continued vendetta against Dad? Why does the Prohibition Party Wikipedia page devote 80% of its space to the 2003 secession, instead of documenting the effects of Prohibition, and mentioning the great leaders like Homer Rodeheaver, etc.?

Dad is beyond your reach now, so I find it curious to see you wasting your time on making frequent additions to his web page. If your motivation is truly to advance the Party's cause, I think your time would be better spent on Party work, rather than spitting on the man who devoted 55 years of his life to the Party.

Caldodge (talk) 17:02, 27 August 2008 (UTC)

External links modified
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External links modified
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title: Talk:Earl Dodge


text:
Hantabad

Hantabad (, also Romanized as Ḩanţābād; also known as Handābād and Khantābād) is a village in Rivand Rural District, in the Central District of Nishapur County, Razavi Khorasan Province, Iran. At the 2006 census, its population was 39, in 10 families.

source: wikimedia

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Hantabad


text:
Linux Guide/CD Burning

Burning CDs and DVDs with K3B
K3B (k3b.org) is a CD and DVD burner for Linux. Technically, it is a front-end for some of the commands given in the "using the console" section below.

K3B requires KDE (see also KDE how-to) to run.

Burning CDs and DVDs with Brasero
Brasero (gnome.org) is a popular GTK+ CD burning software. It is part of the GNOME project.

Burning CDs and DVDs using xcdroast
xcdroast is an alternative front end to cdrtools, which does not require KDE. Similarly to K3B and other such programs, it acts as a front end to automate commands which would normally be entered from the console.

1. Make an ISO Image
An ISO Image is a file which contains all the data required on the CD or DVD - that is, all the files plus the directory structure. An ISO file is about the same size as all the files it is created from.

There are several ISO formats available,

To make the ISO in Linux, use 'mkisofs. mkisofs has many options to control how to handle CD and DVD creation - these include how linux-style filenames are converted to work for Windows and Apple Mac, and options for creation of a boot-cd. However, the standard command is:

 * mkisofs -r -o

The easiest way to make an CD/DVD image is to copy all the files required in a new directory, such as "myproject". Then just run the command mkisofs -r -o /tmp/myimage.iso myproject to create the image. The image size should not be larger than the size of the CD (~ 700MB) or DVD (~ 4.4GB).

Note also that the FAT32 file system can only manage files of less than 4GB (which is less than the maximum DVD size)

2. Identify a CD drive
To burn the CD or DVD, we'll use cdrecord. The following command lists all the CD-R and DVD-R drives. and provides an address (a SCSI-style address) cdrecord -scanbus

3. Burn the CD
Burn the CD or DVD with: cdrecord -v speed=2 dev=  [blank=fast] -data  Use blank=fast to clear all data from a CD-RW. cd_image is the ISO file created in step 1.

Example: cdrecord -v speed=2 dev=0,6,0 -data /tmp/myimage.iso

Creation of Video DVDs
For DVDs to work in a DVD player, the movies and file structure must be very specific. A guide to creating a DVD video is given at VideoLan Wiki - see Making a DVD Video with VLC.

title: Linux Guide/CD Burning


text:
Wikijunior:Big Cats/Puma

The Puma or Mountain Lion is a rather large cat, though it is classified as a smaller cat by scientists. Like smaller cats, pumas cannot roar though they can muster a very startling snarl or a piercing cry. In some places, these cats are also called cougars, catamounts, painted cats, panthers or painters. Scientists call them Puma concolor.

According to an old Mayan legend, all the animals of the jungle once looked the same until the gods offered to make them look different. The jaguar asked, "Let me be spangled with stars," and it was so. He was pleased with his gift and showed it to the puma. Not to be outdone, the puma asked the gods that he be as splendid as the jaguar, and it was so. Pleased with himself the puma went out to hunt. Unfortunately, he fell and rolled in the dust which clung to his still-wet design. For this foolishness he and all pumas afterwards went through life the color of the earth.

Where do pumas live?
Pumas are widely spread in North, Central and South America. They can be seen in a variety of habitats including deserts, swamps and forests from northern British Columbia all the way down to the southern end of the Andes mountain range. Pumas were driven out of the eastern half of North America by human pressure; a small population remains in Florida and occasionally there are puma sightings in other eastern states. The puma's habitat looks mostly green or yellow depending on where they are in the world.

What do pumas look like?
Most pumas are a light brown color, with black-tipped ears and tail. The pumas that live closest to the Equator are the smallest, and increase in size in populations closer to the poles. (This sort of size increase is seen in tigers too. The smallest ones live in the tropics, the largest Siberian tigers live far to the north where winters are very cold.)  The endangered Florida Panther is the smallest of the Pumas. Like many other cats, they can retract their sharp claws into their paws, which have four toes. The largest male pumas can be as big as eight feet (2.4 meters) long, and females can be as large as seven feet (2.1 meters). The males weigh in a bit less than the average adult human at about 150 pounds (70 kilograms), with females weighing even less at 75 pounds (35 kilograms) or less.

Although pumas do not have a bright pattern, there are distinct black "tearstains" on their upper lips and a vivid white fur around the mouth that emphasizes facial expressions. Although cougars cannot roar, when they growl their "business end" looks rather intimidating, helped along by the markings.

What do pumas eat, and how do they catch their prey?
Pumas mostly eat large animals like deer. Because the puma can run very fast, as much as 45 mph (72.42 km/h), and because they can jump 30 ft (10 m) forward from a standing position, they can very easily catch slower animals. Pumas can jump 18 ft (6 m) straight up and can climb onto rocks and up trees to hunt. Their bite is very strong, much stronger than a strong dog's bite, and their largest teeth are about twice the size of a large dog's teeth.

Pumas have a very powerful hunting instinct, and have sometimes been known to chase and catch humans on bicycles. A favorite food for pumas is the deer, but they will also eat smaller animals. In areas where pumas and people live close together, pumas have hunted dogs and cats for food, but they usually do not hunt people for food. If you are around a puma, it is better not to run fast or to ride a bicycle, because their instinct is to chase, catch and kill running animals.

On January 8, 2004 a puma killed and partly ate a mountain biker in Whiting Ranch Wilderness Park, in Orange County, California, but attacks on humans are rare.

Stay safe around pumas
These are good safety ideas for areas where pumas live:

 * Never hike alone, Pumas are more likely to attack people who are alone than in a group.
 * If you see a puma, do not run, because their instinct might make them chase you. Instead, stand and face the animal, and look into its eyes. Stand tall, raise your arms, and make yourself look large. The puma will think you are a giant and run away. If it comes toward you, scare it away by shouting, waving your arms, or throwing things.

 * Do not turn away from the puma; do not crouch down or do anything that would make you seem like an animal. If you or someone in your group is attacked, fight back by throwing stones, hitting or kicking. Pumas have been chased away by using rocks, sticks, garden tools and bare hands.  The best place to hit a puma is on the nose.

 * Watch around you when in an area where pumas might be. Like other cats, they like to spring out from a hiding place and attack their prey from behind.

 * Don't go hiking with your pet in areas with pumas, because any animal (even a dog) can make a puma want to chase and kill it, because of the "chase reflex" that pumas have. Also, the puma might be attracted to your pet's food.

Fun facts

 * Female pumas call to potential mates with a piercing cry that sounds much like a high pitched scream. Every year some panicked people call the police to report an "attack" in progress.

For more information
Next Topic: Lynx and bobcats
 * Wikipedia: Puma

ca:Viquijúnior:Grans felins/Puma Wikijunior Großkatzen/ Puma fr:Wikijunior:Les félins/Les pumas Wikijunior Grandi felini/Puma zh:Wikijunior:大猫/美洲狮

title: Wikijunior:Big Cats/Puma


text:
Swimming at the 2019 African Games – Men's 4 × 100 metre medley relay

The Men's 4 × 100 metre medley relay competition of the 2019 African Games was held on 24 August 2019.

Records
Prior to the competition, the existing world and championship records were as follows.

The following new records were set during this competition.

Final
The final was started on 24 August.


text:
User:MikaylaS2000/sandbox

Humans are fairly susceptible to illusions, regardless of our innate ability to process complex stimuli. Confirmation bias is believed to be largely responsible for the inaccurate judgments that we make when evaluating information, given that humans typically interpret and recall information that appeals to their own biases. Amongst these misinterpretations, known as illusions, falls the category of auditory illusions. Auditory illusions are false perceptions of a real sound or outside stimulus. These false perceptions are the equivalent of an optical illusion: the listener hears either sounds which are not present in the stimulus, or sounds that should not be possible given the circumstance on how they were created. The brain uses multiple senses simultaneously to process information, however, spatial processing of stimuli is handled by the visual sense, whereas temporal processing of stimuli is handled by the auditory sense. The auditory and visual experiences differ in that auditory is non-spatial and is much less detailed than visual. Auditory illusions highlight areas where the human ear and brain, as organic survival tools, differentiate from perfect audio receptors; this shows that it is possible for a human being to hear something that is not there and be able to react to the sound they supposedly heard. When someone is experiencing an auditory illusion, their brain is falsely interpreting its surroundings and distorting their perception of the world around them. While illusions may offer amusement, it is important to understand the important insights they bring to our understanding of how the brain processes both auditory and visual stimuli.

Sounds that are found in words are called embedded sounds, and these sounds are the cause of some auditory illusions. In order to prevent hearing echo created by perceiving multiple sounds coming from different spaces, our auditory system relates the sounds as being from one source. A person's perception of a word can be influenced by the way they see the speaker's mouth move, even if the sound they hear is unchanged. For example, if someone is looking at two people saying "far" and "bar", the word they will hear will be determined by who they look at. If these sounds are played in a loop, the listener will be able to hear different words inside the same sound. People with brain damage can be more susceptible to auditory illusions and they can become more common for that person.

Composers have long been using the spatial components of music to alter the overall sound experienced by the listener. One of the more common methods of sound synthesis is the use of combination tones. Combination tones are illusions that are not physically present as sound waves, but rather, they are created by one's one neuromechanics. According to Purwins, auditory illusions have been used effectively by various composers such as Beethoven (Leonore Overture), Berg (Wozzeck), Krenek (Spiritus Intelligentiae, Sanctus), Ligeti (Études), Violin Concerto, Double Concerto, for flute, oboe and orchestra), Honegger (Pacific 231), and Stahnke (Partota 12).

title: User:MikaylaS2000/sandbox


text:
Talk:Don Cherry (singer)

Requested move

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: article moved as proposed Armbrust The Homunculus 04:35, 23 October 2013 (UTC)

Don Cherry (singer and golfer) → Don Cherry (singer) – Per WP:DAB, disambiguators should be concise and non-unique. This is the only article that describes a (singer and golfer). I'm not too familiar with golf, but it looks like this person only barely meets WP:NGOLF (he "played in" Masters Tournaments, and I don't know if that constitutes "making the cut"; the Canadian Amateur Championship probably is good enough). Browsing the article, references, and authority files, it's clear he was best known as a singer first. Don Cherry (golfer) should be a redirect, and would be my second choice for the title. BDD (talk) 18:31, 16 October 2013 (UTC)

 * I have no problem with the move, but he certainly meets WP:NGOLF: 1) three Walker Cups, 4) Canadian Amateur, 5) 9th in 1960 U.S. Open, 7 cuts in 9 Masters. Tewapack (talk) 18:50, 16 October 2013 (UTC)

 * Weak support. We should avoid compound disambiguations wherever possible. He does meet the notability standards for golf players, though, if only barely. <IP_ADDRESS> (talk) 18:56, 16 October 2013 (UTC)
 * Support as a means of simplifying. I don't know if there's a way to tell whether he was better known for singing or for golf, but a cursory investigation suggests there are more sources for his music career than his golf career.--Cúchullain t/ c 19:18, 16 October 2013 (UTC)
 * Support per nom. In ictu oculi (talk) 22:59, 16 October 2013 (UTC)
 * Support. John Davies (swimmer) is another fun one along these lines. A redirect from the second area of fame should do fine. bd2412  T 17:37, 17 October 2013 (UTC)

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title: Talk:Don Cherry (singer)


text:
Talk:Plasticity (physics)

untitled
This page is very bad. The description of plasticity here is simplistic if not wrong. The fact that stress and strain are **tensors** is overlooked. I think it should in particular start with the plastic yield stress, so as to give some insights on how it works). I have added a couple of info myself, but the litterature on plasticity is enormous. Kachanov's book is a good start. Herve661

Clays
Hi, The article seems good ... up to a point as to me it seems a little biased towards metal. Can anyone expand it to include that most famous group of plastic materials: clays

Regards,

Andy

 * Be bold! It sounds like you know something about clays so why not contribute yourself. --cfp 19:40, 11 August 2006 (UTC)

 * In this case, boldness might not be rewarded...in the technical terms in which this article was written, clays are brittle materials that display no plasticity at room temperature. Just try making a permanent bend in an individual clay particle, or in a sintered piece of pottery!  You'll need a very high-temperature forge, much hotter than would be needed to work titanium.  A suspension of clay in water will deform permanently, but plasticity is a property of solids, not liquids.--Joel 06:00, 11 August 2007 (UTC)

Plastic deformation is a property of the material, not a property of the applied stress. Normal stresses can cause plastic behavior. The most common measure of static material properties is a tensile test.

Effective stress
The current link out to effective stress doesn't seem appropriate given the current contents of the linked article. —DIV (<IP_ADDRESS> (talk) 07:52, 9 January 2009 (UTC))

Contradicts other Wikipedia article
Clay - "Clay is a naturally occurring material composed primarily of fine-grained minerals, which show plasticity through a variable range of water content, and which can be hardened when dried and/or fired." —Preceding unsigned comment added by <IP_ADDRESS> (talk) 01:51, 24 March 2010 (UTC)

 * I've removed the contradictory examples from the intro in this article. Thanks for the heads up. Wizard191 (talk) 17:07, 30 March 2010 (UTC)

Merge from Creep (deformation)
These 2 articles appear to be both on the exact same topic and we don't need 2 articles that are so much the same. Blackbombchu (talk) 20:05, 9 March 2015 (UTC)

Creep is continued deformation at a constant load at a high temperature. Plasticity is the permanent deformation of a material at ever-increasing loads. They're two different physical phenomena and should not be merged. — Preceding unsigned comment added by <IP_ADDRESS> (talk) 14:45, 19 March 2015 (UTC)

Plasticity is the fundamental property and creep is a special case that varies with temperature. They are miles apart and deserve separate pages. — Preceding unsigned comment added by <IP_ADDRESS> (talk) 14:06, 6 May 2015 (UTC)

title: Talk:Plasticity (physics)


text:
Kabrastan

Kabrastan is a 1988 low budget Hindi horror film directed and produced by Mohan Bhakri. This film was released on 10 June 1988.

Plot
William D'Souza wanted to become a doctor and creates a miraculous surgery involving a heart transplant. One day a patient required a heart transplant but needed a fresh heart. He murdered one innocent person and transplanted his heart to his patient. After he succeeded, the dead body wanted to take revenge and started murdering one by one the doctor's family.

Cast

 * Hemant Birje as Rocky D'Souza
 * Amjad Khan as Napoleon D'Costa
 * Javed Khan as Mike
 * Kunika as Kitty
 * Raza Murad as William D'Souza
 * Jagdeep as Hitler
 * Huma Khan as Madhumati
 * Satish Kaul as Inspector
 * Kamna
 * Daljeet Kaur
 * Ram Mohan as Priest
 * Birbal as Butler
 * Ved Goswami
 * Sunil Dhawan

title: Kabrastan


text:
Microprocessors

Syllabus
EE 311

Lectures
Introduction to Microprocessor Hardware

It is evidently impossible to attempt to review in detail the very many different types of processor and processor hardware available today and therefore this course will necessarily deal with either (and mainly) general principles which can be quickly particularised to most systems, or with some specific examples mainly aimed at our specific system. I do hope however to discuss some other systems as they are relevant to our lectures and for variety.

Definitions

Before we go further, a word on terminology - a "bit" (binary digit) is a single logical entity and may either be TRUE or FALSE, or 0 or 1 for short. A "byte" is conventionally 8 bits and we designate for this course bit 0 to be the least-significant bit and bit 7 to be the most significant. Please note that this is not universal and some people do it the other way around. A "word" is a collection of bits and may or may not be an integer number of bytes long. It needs a qualifier such as "16-bit word". In this course we will take the term "word" without a qualifier as a "16-bit word". There is a term for 4 bits called a "nibble" which is sometimes useful but not everybody recognizes it.

Simple Systems

A computer in general consists of a set of objects in some sort of network, each of which may itself be a computer. However, microprocessor systems tend to be a little simpler in that they have one Central Processor Unit (CPU), which bosses the operation, and other units which are its subordinates. Subordinates have however been known to revolt. The simplest diagram of a system is as follows: (Please note that this diagram has been drawn for simplicity, not for truth as we shall see later) The CPU fetches an entity from the memory by providing it with an address and receiving "data" back. Since the busses over which communication occurs are logical networks we can describe both the address and the "data" as either collections of logical signals or group them together as numbers. For the computer, the most logical number system is binary so that the computer fetches 10010001 from<PHONE_NUMBER>100000 (assuming 8-bit data and 16-bit address - see below). However this is not very convenient for us as we would tend to say that it fetches 145 from address 57504. In order to get the two systems (human and computer) to discuss things in a reasonably compact form, we compromise on hexadecimal notation where each group of 4 bits from the binary representation is represented by a single alphanumeric according to the value of the 4-bit number. 0-9 are the digits 0-9 and 10-15 are the letters A-F. Thus our fetch now becomes 91(h) from E0A0(h), using the (h) notation to eliminate any ambiguity. (There are many other ways of denoting hexadecimal notation - Turbo Pascal uses a "$" sign, eg $E0A0, and the C language uses "0x" as a leader, eg 0xE0A0) The advantages of hex notation are compactness, reasonable ease of arithmetic, and easy expansion to the binary where necessary (but hopefully not often). (There is also the octal system of notation which groups things together in threes but we shall not use that here) The entity that a computer fetches is a bit pattern, however, it may be interpreted by the system in various ways depending upon the "context", or in other words, what the CPU thought it was getting. Thus if a 6809 system fetches 4F(h), it may interpret that as CLRA (clear register A) if it was expecting an instruction, as data if it expected data, or as another part of an instruction if it is halfway through a multi-byte instruction. The most common way in which you expect "context" is as follows: Sitting at a computer thinking about a program you might want to look at the set of instructions you gave the compiler - that might be "prog.cpp" - so you "type prog.cpp" and expect to see text. The computer expects to get executable instructions for a program and so its "version" of the program is in "prog.exe". Now if you try "type prog.exe" you will be confused and if the computer tries to execute "prog.cpp" it will be confused. Both files are just collections of bits and bytes - they can even be said to represent that same thing - but you and the computer were going to interpret them in a particular context. All bit patterns are interpreted according to the context. We shall see later that even common numbers have at least three different representations depending upon the context (character, integer or real). In a normal machine, there is a differentiation in the designer's mind between code (that is, the program) and data which is the stuff the program acts on. However as we have seen above the distinction is in the designer's mind, not the computer's which will happily attempt to execute data as code and vice versa.

ROM, RAM and Other Memory

In order to prevent a run-away machine from modifying its program and in order to avoid reloading the program every time the thing is turned on some memory is designed as Read-Only Memory (ROM) in the sense that the computer is unable to change it. (There must be some ultimate way of changing it otherwise things get difficult.) Some read-only memory is sufficiently standard to warrant manufacturing "en masse", e.g. the dot patterns for an alpha-numeric display, but mostly the memory may be written by special equipment (Programmable, Read-Only Memory (PROM)) and may further be erasable by similarly specialized equipment (EPROM). Newer developments allow the machine to change the memory with difficulty (EEPROM). Thus a simple microprocessor system dedicated to a single task may have its program stored in EPROM and some RAM (Random Access Memory or more correctly Read-Write Memory) for use by the program. Languages and Other Issues Armed with our knowledge of hardware and our software "hooks", or bridges, we can conquer the world in a high-level language. Why not assembler or machine code? - Well the answer to that is that in a high-level language all the useful tools are available and the code is much more readable. Which is better? CLRA STA $0007 or A = 0 The rule of thumb I was taught was that a good programmer should produce about 100 lines of documented, tested code per day on average. Now 100 lines of C does much more than 100 lines of assembler so that productivity is higher. I gratefully dropped machine-code some years ago when I made this discovery. I have more recently been informed that the benchmark is now ten lines of code which has implications I don’t even want to think about!! Of course, the advent of graphical languages such as LabVIEW makes the computation of “lines of code/day” an extremely tenuous thing, but the principle still remains that the higher the level of the language, the more you can get done in a finite time. High-level languages isolate you from the machine architecture which makes the program somewhat portable - not wholly portable, but better than nothing.

Having said all that, I admit that there are a number of occasions when assembler code is important. These are: When the language won't support what you want to do Some languages can't support some operations. Interrupt handling routines are a case in point that can be handled effectively by very few languages. When there is a special instruction that is very useful A case in point is an instruction to reverse the bits in a word. This turns out to be handy in a Fourier transform routine, is lousy (and slow) to do in high-level language but is dandy if there is a machine instruction to do it. In this case, write a short (I said SHORT) piece of assembler code as a subroutine to do the job and flee back to high-level as soon as possible. When speed is of the essence and you can't go any faster the first defense for getting speed is to check out the algorithm for effectiveness. The second defense is to check out the coding for efficiency and the third defense is to buy the fastest machine possible. Only if all the above fails should you re-code the speed-critical portion of your code in the assembler again by putting it in a short (remember I said SHORT) subroutine. When doing DSP programming this is an exotic field, but one which we get into in the course. Since DSP programming is tricky and extremely speed-critical, but generally short - it is a candidate for assembler programming.

Reference books
Microprocessor Architecture Programming and Applications with the 8085 by Ramesh S Gaonkar

Online resources
"The course covers the design of real-time digital systems using microprocessor-based embedded controllers to design, debug, and construct several systems that illustrate and employ digital system design techniques. The content focuses on laboratory work. The lectures are used primarily for the introduction of examples, description of specific modules to be designed, and instruction in the hardware and high-level design tools to be employed."
 * https://ece4760.github.io/ - Cornell University's Digital Systems Design Using Microcontrollers taught by V. Hunter Adams

Learning projects
1. Design a microprocessor-based EPROM Programmer to program 2716. The EPROM can be programmed by applying 25V at VPP and 5V at OE pin. Initially, all data of EPROM will be 1's and the user should make the bits zero selectively. The bit parallel data is applied to the data output pins(D0-D7). The address for the EPROM is provided through the address pins. To program the address of each location to be programmed should be stable for 55ms. When address and data are stable, a 50ms active high pulse is applied to CE input.

title: Microprocessors


text:
File:BNA Records logo.gif

Rationale for BNA Records
The image shown here is claimed to be used under Fair-use in the above article:
 * 1) This image is unique and thus non-replaceable with a free alternative.
 * 2) The inclusion of this image adds significantly to the article because it is a primary means by which the subject may be identified.
 * 3) This image will not interfere with the copyright holder's ability to exploit its work.
 * 4) This image is being used for informational purposes in the context of a scholarly article.
 * 5) This image is not used in such a way that a reader might believe that the article is written or authorized by the copyright holder of the image.
 * 6) This image enhances the article in which it is displayed, as it provides a visual reference more useful to the reader than the textual description alone.
 * 7) This image is of low resolution and cannot be used to illegally reproduce its depiction.

title: File:BNA Records logo.gif


text:
nimmer

Etymology
From, equivalent to. Cognate with 🇨🇬, 🇨🇬.

Noun

 * 1) A petty thief.

Etymology
From, , , also , from , from either (equivalent to modern  + ) or  (equivalent to modern  + , compare 🇨🇬 from ), or maybe both. Cognate with 🇨🇬, 🇨🇬.

Adverb

 * 1) no more, no longer
 * 2) never again
 * 1) never again

Etymology
From, from. Equivalent to.

Adverb

 * 1)  never

Usage notes
Nimmer is rarer and nowadays considered much more formal than, excluding some compounds and set expressions.

Etymology
Perhaps originally, thus the same construct as 🇨🇬 and. According to others a dialectal contraction of, later remodelled according to.

Adverb

 * 1)  no more, no longer
 * 2)  never again
 * 3)  never, at no time
 * 1)  never, at no time

Usage notes

 * In northern Germany and many parts of central Germany, the word is used mainly in some set phrases such as . Otherwise, it sounds archaic or poetic. It is used more readily in southern Germany and Austria, meaning “no more” or “never again”. The original sense “never, at no time” is now rare.

title: nimmer


text:
Intelligence Intensification/Information Sifting

Working in the IT field I come across an unimaginable amount of data on a regular basis in just dealing with day-to-day issues. Any task is like that these days - and especially to someone who knows nothing of the task until it's presented.

The main thing to remember here is organization. The method you use to organize the data is not important - only that you stick to it for the most part. If something doesn't fit then you either change the item you're having a problem with...or you change your system of organization.

Ever watch a flock of birds? One thing you'll notice is that if you try to focus on all the birds at once you'll most likely get confused. If you focus on, say, one bird out of the flock, then you've mentally organized that one bird out of the flock. Guess what...if you keep adding birds out of the flock until you've looked at them all then you've organized the flock in your mind. Information in the day-to-day world is no different.

Breaking down information into chunks you can deal with is absolutely vital to understanding and remembering. After all, without training you couldn't recall a whole book from memory, right? But you could recall important parts of it. Eventually, if you keep adding to those parts then you would at some point recall the entire book. In another context, this techique has been known for roughly two millennia. Remember the Latin phrase divide et impera (divide and rule)?

Now, how this relates to sifting is most of the time pretty simple. Organize the data, but focus on the stuff you want. For instance if you want to observe only the red birds in the flock then focus on the color red. Sounds pretty easy right? Well...yes and no.

When dealing with large amounts of data you have to do a little estimation of chance up front.

What's that mean? Let's say your family bakes a pie with a ring in it for the holiday. Whoever gets the ring wins a prize. You really want that prize so you focus on the ring. Thus you ask some questions of yourself:

Does the ring have any special properties I can use to identify it?

Does the ring affect the piece of pie it's in in any way?

Is there anywhere in the pie I know the ring is not located?

Suppose the ring is copper and turns the pie green. Then you know that any piece of pie that is the normal color is less likely to have the ring in it.

That narrows your focus by a certain amount.

Suppose the ring is also pretty big, so the pie bulges where the ring is. Then you know that any flat piece of pie will not have the ring in it.

That narrows your focus again.

You keep going with this method until you've found the ring.

Some things that help this process:

''Learning to speed-read. There are plenty of courses out there for this.''

Good language skills for the materials you're searching.

''Frequent breaks. Spending too much time sifting often blurs your focus.''

Focus on one thing at a time. You get more done that way. Remember, sunlight spread out only warms things up, but sunlight focused on one place with a magnifying glass can burn holes in things.

Know what you want. Know what you are looking for. If you don't know, how will you know if you find it?

Delegate. Get people to help you. Parallel searching is helpful, as long as you make sure they know what they are looking for.

It's horribly cliche, but big mountains are just piles of pebbles stacked on top of each other. Information is the same...

Next
../Speed Reading/


text:
User:Kizer/Web Page/Flash

Flash
Part of the Web Page Wiki Project

Flash General Topics

 * Commonly used terms
 * Description of the Flash window
 * Description of Flash toolbars

Flash How To's

 * How to morph
 * How to mask
 * How to zoom
 * How to fade
 * How to tween

Flash Class Projects

 * TV Channel Project (uses alpha:color to create a fading effect to simulate a tv changing channels)
 * Masking Project (uses masks to reveal portions of a picture)
 * Think Project (uses tweening and alpha:color to rotate through thoughts on someone's mind)
 * Tracing Project (uses the line tool and curves to trace a logo)

title: User:Kizer/Web Page/Flash


text:
Introduction to Cartesian Geometry

Welcome to Introduction to Cartesian Geometry

In Cartesian or Analytic Geometry we will learn how to represent points, lines, and planes using the Cartesian Coordinate System, also called Rectangular Coordinate System. This can be applied to solve a broad range of problems from geometry to algebra and it will be very useful later on Calculus.

=Cartesian Coordinate System=

The foundations of Analytic Geometry lie in the search for describing geometric shapes by using algebraic equations. One of the most important mathematicians that helped to accomplish this task was René Descartes for whom the name is given to this exciting subject of mathematics.

The Coordinate System
For a coordinate system to be useful we want to give to each point an attribute that helps to distinguish and relate different points. In the Cartesian system we do that by describing a point using the intersection of two(2D Coordinates) or more(Higher Dimensional Coordinates) lines. Therefore a point is represented as P(x1,x2,x3,...,xn) in "n" dimensions.

2D Coordinates
You can look at a 2D Coordinate system as a system in which a point can be defined using two values. We do this by using two perpendicular and directed lines called the abscissa(x-axis) and the ordinate(y-axis). The point of intersection of these two lines is called the origin denoted O(0,0). Any point can be determined as P(x,y), where x is the value in the x-axis and y is the value in the y-axis.

=3d Coordinate Geometry=

The coordinate system in two dimensions uses values containing width and depth expressed as values of $$X$$ and/or $$Y.$$

Coordinate geometry in three dimensions adds the dimension of height, usually expressed as a value of $$Z.$$ The axes of $$X$$ and $$Y$$ usually represent the horizontal plane. The $$Z$$ axis is thus vertical or normal to the plane of $$X$$ and $$Y.$$

In three dimensional space a point is shown as $$(x_1, y_1, z_1)$$ where the 3 values locate the point relative to the origin along each of the $$X, Y, Z$$ axes respectively. The value $$(0, 0, 0)$$ is valid, usually the origin.

Within this page the values $$x_1, y_1, z_1$$ are all real numbers.

Examples of points in 3 dimensional space.
Points of 1 dimension

Each of the points in the diagram has exactly one dimension.

The point $$(10,\ 0,\ 0)$$ has only the dimension of width. It is on the $$X$$ axis.

The point $$(0,\ 12,\ 0)$$ has only the dimension of depth. It is on the $$Y$$ axis.

The point $$(0,\ 0,\ 13)$$ has only the dimension of height. It is on the $$Z$$ axis.

$$$$$$$$$$$$$$$$

Points of 2 dimensions

Each of the points in the diagram has exactly two dimensions.

The point $$(8,\ 6,\ 0)$$ has the dimensions of width and depth, no height.

The point $$(0,\ 12,\ 6)$$ has the dimensions of depth and height, no width.

The point $$11,\ 0,\ -7)$$ has the dimensions of width and height, no depth.

Points of 3 dimensions

Each of the points in the diagram has three dimensions.

Distance between 2 points

Consider the point $$Q\ (4, 3, 12).$$ What is the distance from point $$Q$$ to the origin?

Point $$P$$ is the projection of $$Q$$ on to the plane of $$X,Y.$$

Calculate length $$OP = \sqrt{4^2 + 3^2 }.$$

Then length $$OQ = \sqrt{(OP)^2 + 12^2 } = \sqrt{4^2 + 3^2 + 12^2 } = \sqrt{169} = 13.$$

Length $$OQ = \sqrt{x_1^2 + y_1^2 + z_1^2}.$$ In this case $$(x_1, y_1, z_1) = (4, 3, 12).$$

The general case:

For two points $$M\ (x_M, y_M, z_M)$$ and $$N\ (x_N, y_N, z_N)$$

the distance $$MN = \sqrt{(x_M - x_N)^2 + (y_M - y_N)^2 + (z_M - z_N)^2 }.$$

Length $$OQ$$ is the special case in which $$(x_N, y_N, z_N) = (0, 0, 0).$$

The distance $$MN$$ may be $$0$$ in which case $$M$$ and $$N$$ are the same point.

as 2 points
In the example above line $$OP$$ passes through the points $$O\ (0,0,0)$$ and $$P\ (4,3,0).$$

The line $$OP$$ may be defined by the two points $$O$$ and $$P$$ provided that the length $$OP$$ is non-zero.

Line $$OP = (O, P) = ((0,0,0),\ (4,3,0))$$

There are other ways to define a line. Add a descriptor to avoid confusion:

Line $$OP = (O, P) = ((0,0,0),\ (4,3,0),$$ '$$2$$points'$$)$$ where:

$$(x_O, y_O, z_O) = (0,0,0)$$ and $$(x_P, y_P, z_P) = (4,3,0).$$

Line $$PO = (P, O) = ((4,3,0),\ (0,0,0),$$ '$$2$$points'$$).$$

Similarly:

line $$PQ = (P, Q) = ((4,3,0),\ (4,3,12),$$ '$$2$$points'$$)$$

line $$QP = (Q, P) = ((4,3,12),\ (4,3,0),$$ '$$2$$points'$$)$$

line $$OQ = (O, Q) = ((0,0,0),\ (4,3,12),$$ '$$2$$points'$$)$$ and

line $$QO = (Q, O) = ((4,3,12),\ (0,0,0),$$ '$$2$$points'$$).$$

as point and 3 direction numbers
For information about direction numbers see Line_(Geometry).

Line $$OQ$$ above is defined by 2 points $$O\ (x_1,y_1,z_1)=(0,0,0)$$ and $$Q\ (x_2,y_2,z_2)=(4,3,12).$$

The direction numbers of line $$OQ = [A,B,C] = [x_2-x_1,y_2-y_1,z_2-z_1] = [4,3,12].$$

A line may be defined as $$((x_1,y_1,z_1),\ [A_1,B_1,C_1])$$ where:

$$(x_1,y_1,z_1)$$ is a known point on the line, and

$$[A_1,B_1,C_1]$$ are the direction numbers of the line.

In practice:

The programming language python, for example, recognizes  as a list and code can interpret these values as direction numbers.

Python recognizes  as a tuple and code can interpret these values as coordinates of a point.

In python a line may be defined as:

 * or

Line $$OQ$$ may be defined as $$((0,0,0), (4,3,12),$$ 'p&dn'$$).$$

Given a point on the line and the direction numbers of the line, any other point on the line may be established by introducing constant $$K.$$

On line $$((x_1,y_1,z_1),\ (A_1,B_1,C_1),$$ 'p&dn'$$)$$ any second point $$(x_2,y_2,z_2) = (x_1+KA_1, y_1+KB_1, z_1+KC_1)$$ and distance from $$(x_1,y_1,z_1)$$ to $$(x_2,y_2,z_2)$$

$$= \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$$

$$= \sqrt{(x_1+KA_1-x_1)^2 + (x_2+KB_1-y_1)^2 + (z_1+KC_1-z_1)^2}$$

$$= \sqrt{(KA_1)^2 + (KB_1)^2 + (KC_1)^2}$$

$$= K\sqrt{A_1^2 + B_1^2 + C_1^2}$$

It would be convenient if the value $$A_1^2 + B_1^2 + C_1^2$$ would $$= 1.$$

If $$A_1^2 + B_1^2 + C_1^2 == 1,$$ the values $$A_1, B_1, C_1$$ are the direction cosines of the line.

To convert direction numbers to direction cosines divide each direction number by $$\sqrt{A_1^2 + B_1^2 + C_1^2}.$$

$$(\frac{A_1}{\sqrt{A_1^2 + B_1^2 + C_1^2} })^2 + ( \frac{B_1}{\sqrt{A_1^2 + B_1^2 + C_1^2} }     )^2 + (  \frac{C_1}{\sqrt{A_1^2 + B_1^2 + C_1^2} }   )^2$$

$$= \frac{A_1^2}{A_1^2 + B_1^2 + C_1^2} + \frac{B_1^2}{A_1^2 + B_1^2 + C_1^2} + \frac{C_1^2}{A_1^2 + B_1^2 + C_1^2}$$

$$= \frac{A_1^2 + B_1^2 + C_1^2}{A_1^2 + B_1^2 + C_1^2} = 1.$$

If $$[A,B,C]$$ are the direction cosines of the line, any second point on the line exactly $$K$$ units from $$(x_1, y_1, z_1)$$ has coordinates $$(x_1 + KA, y_1+KB, z_1+KC).$$

While point $$(0,0,0)$$ is valid, direction numbers $$[A,B,C]=[0,0,0]$$ are not valid. For the group of direction numbers to be valid, at least one of $$A,B,C$$ must be non-zero.

Angle between two lines
In the diagram line $$OM$$ has direction numbers $$[A_1,B_1,C_1].$$ Point $$M$$ has coordinates $$(A_1,B_1,C_1).$$

Line $$ON$$ has direction numbers $$[A_2,B_2,C_2]$$ and point $$N$$ has coordinates $$(A_2,B_2,C_2).$$

Length $$OM = \sqrt{A_1^2 + B_1^2 + C_1^2}.$$

Length $$ON = \sqrt{A_2^2 + B_2^2 + C_2^2}.$$

Length $$MN = \sqrt{(A_1-A_2)^2 + (B_1-B_2)^2 + (C_1-C_2)^2}.$$

By the cosine rule $$MN^2 = ON^2 + OM^2 - 2\cdot OM\cdot ON\cdot\cos(\theta).$$

$$\cos(\theta) = \frac{MN^2 - ON^2 - OM^2}{- 2\cdot OM\cdot ON} = \frac{ON^2 + OM^2 - MN^2}{2\cdot OM\cdot ON}$$ $$= \frac{A_1\cdot A_2 + B_1\cdot B_2 + C_1\cdot C_2}{ \sqrt{A_1^2 + B_1^2 + C_1^2} \cdot \sqrt{A_2^2 + B_2^2 + C_2^2} }$$

If all values are direction cosines, $$\cos(\theta) = A_1\cdot A_2 + B_1\cdot B_2 + C_1\cdot C_2.$$

If $$\cos(\theta) == 0,$$ the lines are normal.

If $$\cos(\theta) == 1$$ or $$\cos(\theta) == -1,$$ the lines are parallel.

Angle between line and each axis:

Let a line have direction cosines $$[A_1,B_1,C_1].$$

Let $$X$$ axis have direction cosines $$[A_2,B_2,C_2] = [1,0,0].$$

Let $$\theta_X$$ be angle between line and $$X$$ axis.

$$\cos(\theta_X) = A_1\cdot 1 + B_1\cdot 0 + C_1\cdot 0 = A_1.$$

Hence the expression direction cosine. $$A_1$$ is the cosine of the angle between line and $$X$$ axis.

Similarly $$B_1$$ is cosine of angle between line and $$Y$$ axis and $$C_1$$ is cosine of angle between line and $$Z$$ axis.

Parallel lines:

Let one line have direction numbers $$[A,B,C]$$ and a second line have $$[KA,KB,KC].$$

$$\cos(\theta)$$ $$= \frac{A_1\cdot A_2 + B_1\cdot B_2 + C_1\cdot C_2}{ \sqrt{A_1^2 + B_1^2 + C_1^2} \cdot \sqrt{A_2^2 + B_2^2 + C_2^2} }$$ $$= \frac{A\cdot KA + B\cdot KB + C\cdot KC}{ \sqrt{A^2 + B^2 + C^2} \cdot K\sqrt{A^2 + B^2 + C^2} }$$ $$= \frac{K(A^2 + B^2 + C^2)}{ K(A^2 + B^2 + C^2 ) } = 1.$$

$$\theta = 0^\circ$$ and the lines are parallel.

Similarly, if the second line has direction numbers $$[-KA,-KB,-KC],\ \cos(\theta) = -1,\ \theta = 180^\circ$$ and the lines are parallel.

To verify that two lines are not parallel, check that $$|\cos(\theta)|$$ does not equal $$1.$$

If one line has direction numbers $$[A_1,B_1,C_1]$$ and the second line has direction numbers $$[A_2,B_2,C_2] = [KA_1,KB_1,KC_1]$$ then:

$$\frac{A_2}{A_1} = \frac{B_2}{B_1} = \frac{C_2}{C_1} = K$$

$$A_2B_1 = A_1B_2,\ B_2C_1 = B_1C_2,\ A_2C_1 = A_1C_2$$

The values $$B_1C_2 - C_1B_2,$$ $$C_1A_2 - A_1C_2,$$ $$A_1B_2 - B_1A_2$$ are the direction numbers of the normal to both lines. If the normal to both lines has direction numbers  the lines are parallel.

Normal to 2 lines
A line normal or perpendicular to two lines is normal to each line.

Before attempting to calculate the direction numbers of the normal, first verify that the two lines are not parallel.

Let the normal have direction numbers $$[A_1,B_1,C_1].$$

Let the 2 lines have direction numbers $$[A_2,B_2,C_2],\ [A_3,B_3,C_3].$$

Then:

$$A_1A_2 + B_1B_2 + C_1C_2 = 0\ \dots\ (1)$$ and

$$A_1A_3 + B_1B_3 + C_1C_3 = 0\ \dots\ (2)$$

$$(1)*C_3,\ A_1A_2C_3 + B_1B_2C_3 + C_1C_2C_3 = 0\ \dots\ (3)$$

$$(2)*C_2,\ A_1A_3C_2 + B_1B_3C_2 + C_1C_3C_2 = 0\ \dots\ (4)$$

$$(3)-(4),\ A_1(A_2C_3-A_3C_2) + B_1(B_2C_3 - B_3C_2) = 0\ \dots\ (5)$$

$$\frac{A_1}{B_1} = \frac{B_3C_2-B_2C_3}{A_2C_3-A_3C_2}\ \dots\ (6)$$

If divisor $$A_2C_3-A_3C_2 == 0,$$ $$\frac{B_1}{C_1} = \frac{C_3A_2-C_2A_3}{B_2A_3-B_3A_2}\ \dots\ (7)$$

If divisor $$B_2A_3-B_3A_2 == 0,$$ $$\frac{C_1}{A_1} = \frac{A_3B_2-A_2B_3}{C_2B_3-C_3B_2}\ \dots\ (8)$$

Provided that all inputs are valid, then at least one of $$[A_1,B_1,C_1]$$ must be non-zero and at least one of $$(6)$$ or $$(7)$$ or $$(8)$$ must be valid.

From $$(6), (7), (8)$$ above:

$$\frac{A_1}{B_3C_2 - B_2C_3} = \frac{B_1}{A_2C_3-A_3C_2} = \frac{C_1}{B_2A_3-B_3A_2}$$

Values of $$[A_1,B_1,C_1]$$ that satisfy this condition are:

$$[B_3C_2 - B_2C_3,\ A_2C_3-A_3C_2,\ B_2A_3-B_3A_2].$$

Proof:

Angle between $$[A_1,B_1,C_1]$$ and $$[A_2,B_2,C_2]:$$

$$\cos (\theta) = (B_3C_2 - B_2C_3)A_2 + (A_2C_3-A_3C_2)B_2 + (B_2A_3-B_3A_2)C_2$$ $$= B_3C_2A_2 - B_2C_3A_2 + A_2C_3B_2-A_3C_2B_2 + B_2A_3C_2-B_3A_2C_2$$ $$= B_3C_2A_2 - B_3A_2C_2 + A_2C_3B_2 - B_2C_3A_2 + B_2A_3C_2 - A_3C_2B_2$$ $$= 0$$

Therefore the two groups of direction numbers are normal.

Similarly it can be shown that the two groups of direction numbers $$(A_1,B_1,C_1)$$ and $$(A_3,B_3,C_3)$$ are normal.

The line normal to $$[A_2,B_2,C_2]$$ and $$[A_3,B_3,C_3]$$ has direction numbers:

$$A_1 = B_3C_2 - C_3B_2$$

$$B_1 = C_3A_2 - A_3C_2$$

$$C_1 = A_3B_2 - B_3A_2$$

Parallel input:

Let $$[A_3,B_3,C_3] = [KA_2,KB_2,KC_2]$$

Then $$A_1 = B_3C_2 - C_3B_2 = (KB_2)(C_2) - (KC_2)(B_2) = 0$$

If the two groups of direction numbers $$[A_2,B_2,C_2], [A_3,B_3,C_3]$$ are parallel, $$[A_1,B_1,C_1] = [0,0,0].$$

Normal to 1 line
If a given line has direction numbers then any of the following groups of direction numbers is normal to the given line:

For example:

If the given line has direction numbers arbitrary normals have direction numbers In this case only the groups  are valid.

If the given line has direction numbers arbitrary normals have direction numbers In this case all three groups of direction numbers are valid.

If the given line has direction numbers arbitrary normals have direction numbers In this case all three groups of direction numbers are valid. However, the groups are parallel.

Point and line
In the diagram line $$PQ$$ and point $$M$$ are well defined and $$\theta = \angle MPQ.$$$$$$$$$$

Point $$N$$ is on line $$PQ.$$

Line $$MN$$ is perpendicular to line $$PQ.$$

Calculate the coordinates of point $$N$$ and length $$MN.$$

Initial considerations:

 * Points $$M, P$$ may be the same point in which case points $$M,N,P$$ are the same point and lengths $$MN=NP=PM=0.$$

 * Point $$M$$ may be on line $$PQ$$ in which case lengths $$PM=PN$$ and length $$MN=0.$$

 * line $$MP$$ may be perpendicular to line $$PQ$$ in which case lengths $$MP=MN$$ and length $$PN=0.$$

Calculate direction cosines of line $$PQ$$: $$[A1,B1,C1].$$

Calculate direction cosines of line $$PM$$: $$[A2,B2,C2].$$

Calculate $$\cos(\theta).$$

Calculate length $$PM.$$

Calculate length $$PN = PM\cdot \cos(\theta).$$

Let point $$P$$ have coordinates $$(x_1,y_1,z_1)$$

Then point $$N = ( x_1+$$length$$PN*A1,\ y_1+$$length$$PN*B1,\ z_1+$$length$$PN*C1 ).$$

Calculate length $$MN.$$

By extending line PQ with constant K
Let line $$PN$$ be defined as

Let point $$N$$ have coordinates

Let point $$M$$ have coordinates

Then line $$MN$$ has direction numbers

Lines $$MN, PN$$ are normal. Therefore:

$$A(p+KA-s) + B(q+KB-t) + C(r+KC-u) = 0$$ and

$$K = \frac{As - Ap + Bt - Bq + Cu - Cr}{A^2 + B^2 + C^2}.$$

Use this value of $$K$$ to calculate the coordinates of point $$N$$ and the direction numbers of line $$MN.$$

Example:

is defined as

Point  has coordinates

Calculate coordinates of point  on   so that line is normal to

Distance between two parallel lines:

Let $$M$$ be a point on a line parallel to line $$PQ.$$

Distance between the two lines is length $$MN.$$

Points of closest approach
Points of closest approach are the 2 points at which the distance between 2 skew lines is minimum.

Let 2 lines be  and. Verify that the lines are not parallel.

Calculate point $$P_1$$ on    and  point $$P_2$$ on    so that line $$P_1P_2$$ is normal to   and line $$P_2P_1$$ is normal to

It's possible that length $$P_1P_2$$ may be zero in which case points $$P_1, P_2$$ are the same point and the lines intersect.

Let  be defined as point $$(p,q,r)$$ with direction numbers $$[A_1,B_1,C_1].$$

Let  be defined as point $$(s,t,u)$$ with direction numbers $$[A_2,B_2,C_2].$$

Calculate the direction numbers of the normal: $$[A_3,B_3,C_3].$$

Relative to  point $$P_1 = ( p+K_1\cdot A_1,\ q+K_1\cdot B_1,\ r+K_1\cdot C_1)$$

and point $$P_2 = ( p+K_1\cdot A_1+K_3\cdot A_3,\ q+K_1\cdot B_1+K_3\cdot B_3,\ r+K_1\cdot C_1+K_3\cdot C_3).$$

Relative to  point $$P_2 = ( s+K_2\cdot A_2,\ t+K_2\cdot B_2,\ u+K_2\cdot C_2)$$

Therefore:

$$p+K_1\cdot A_1+K_3\cdot A_3 = s+K_2\cdot A_2$$

$$q+K_1\cdot B_1+K_3\cdot B_3 = t+K_2\cdot B_2$$

$$r+K_1\cdot C_1+K_3\cdot C_3 = u+K_2\cdot C_2$$

or:

$$A_1\cdot K_1 - A_2\cdot K_2 + A_3\cdot K_3 + p - s = 0\ \dots\ (1)$$

$$B_1\cdot K_1 - B_2\cdot K_2 + B_3\cdot K_3 + q - t = 0\ \dots\ (2)$$

$$C_1\cdot K_1 - C_2\cdot K_2 + C_3\cdot K_3 + r - u = 0\ \dots\ (3)$$

This is a system of three equations with three unknowns: $$K_1, K_2, K_3.$$

If $$[A_3,B_3,C_3]$$ are direction cosines, $$K_3 =$$ length $$P_1P_2.$$

Example 1:

For function  see  "Solving_3_by_4"

Example 2:

Two lines are defined as:

and

Calculate the points of closest approach.

In this case, $$K_3 = 0$$ and the lines intersect at point $$(3,-5,11).$$

=The plane in 3 dimensions=

In two dimensions the point that is always equidistant from two fixed points is the line.

In three dimensions the point that is always equidistant from two fixed points is the plane.

Let point $$P_1$$ have coordinates $$(a,b,c).$$

Let point $$P_2$$ have coordinates $$(d,e,f).$$

Distance $$P_1P_2$$ must be non-zero.

Let point $$P_{xyz}$$ have coordinates $$(x,y,z).$$

Then length $$P_1 P_{xyz}$$ = length $$P_2 P_{xyz}.$$

$$(x-a)^2 + (y-b)^2 + (z-c)^2 = (x-d)^2 + (y-e)^2 + (z-f)^2$$

$$x^2 -2ax + a^2 + y^2 - 2by + b^2 + z^2 - 2cz + c^2 $$$$= x^2 -2dx + d^2 + y^2 - 2ey + e^2 + z^2 - 2fz + f^2$$

$$ -2ax + a^2 - 2by + b^2 - 2cz + c^2 =  -2dx + d^2 - 2ey + e^2  - 2fz + f^2$$

$$ -2ax - 2by - 2cz + a^2 + b^2 + c^2 =  -2dx - 2ey - 2fz + d^2  + e^2  + f^2$$

$$ 2(d-a)x + 2(e-b)y + 2(f-c)z + a^2 + b^2 + c^2 - (d^2  + e^2  + f^2)= 0 $$

This equation has the form $$Ax + By +Cz + D = 0$$ where:

$$A= 2(d-a);\ d-a = \frac{A}{2}$$

$$B= 2(e-b);\ e-b = \frac{B}{2}$$

$$C= 2(f-c);\ f-c = \frac{C}{2}$$

$$D = a^2 + b^2 + c^2 - (d^2 + e^2  + f^2)$$

Normal to the plane:
Line $$P_1P_2$$ is normal to the plane and it has direction numbers $$[d-a, e-b, f-c]$$ or $$[\frac{A}{2},\frac{B}{2},\frac{C}{2}].$$

When a plane is defined as $$Ax+By+Cz+D = 0,$$ the line normal to the plane has direction numbers $$[A,B,C].$$

Distances:
Distance $$P_1P_2 = \sqrt{(d-a)^2 +(e-b)^2 +(f-c)^2}$$ $$=\sqrt{    (\frac{A}{2})^2 +   (\frac{B}{2})^2 +  (\frac{C}{2})^2   }$$ $$= \frac{\sqrt{A^2 + B^2 + C^2}}{2}  $$

Distance from each point $$P_1,P_2$$ to plane $$= \frac{\sqrt{A^2 + B^2 + C^2}}{4} .$$

Consider the expression $$Ax + By + Cz + D.$$ Substitute $$(d,e,f)$$ or $$(a,b,c)$$ for $$(x,y,z).$$

$$Ad + Be + Cf + D = \frac{A^2 + B^2 + C^2}{4};$$ $$\frac{Ad+Be+Cf+D}{  \sqrt{A^2 + B^2 + C^2}     }$$$$   =\frac{\sqrt{A^2 + B^2 + C^2}}{4} $$

Let $$A_1 = \frac{A}{\sqrt{A^2 + B^2 + C^2} },$$ $$\ B_1 = \frac{B}{\sqrt{A^2 + B^2 + C^2} },$$ $$\ C_1 = \frac{C}{\sqrt{A^2 + B^2 + C^2} }.$$ $$\ D_1 = \frac{D}{\sqrt{A^2 + B^2 + C^2} }.$$

Then $$A_1d + B_1e + C_1f + D_1$$= distance from point $$(d,e,f)$$ to plane.

$$Aa + Bb + Cc + D = \frac{-(A^2 + B^2 + C^2)}{4}.$$

Similarly, $$A_1a + B_1b + C_1c + D_1$$= distance from point $$(a,b,c)$$ to plane with opposite sign.

When the values $$(A,B,C)$$ are all direction cosines, the distance from point $$(a,b,c)$$ to plane $$= Aa+Bb+Cc+D$$ with the sign of the result determined by the position of the point relative to the origin.

If on the same side of the plane as the origin, the sign of the result is the sign of D.

If on the side of the plane opposite to that of the origin, the sign of the result is the sign of -D.

To visualize the plane:
Think of the normal to the plane. The normal has direction numbers $$[A,B,C].$$ The plane is perpendicular to the normal.

Note which direction number or numbers are missing. The plane is parallel to the missing axes.

The plane $$x=4$$ is parallel to both $$Y,Z$$ axes.

The plane $$y=3$$ is parallel to both $$X,Z$$ axes.

The plane $$z=-2$$ is parallel to both $$X,Y$$ axes.

The plane $$3x - 4y + 7 = 0$$ is parallel to the $$Z$$ axis.

The plane $$3x - 4z = 7$$ is parallel to the $$Y$$ axis.

The plane $$3y - 4z = 7$$ is parallel to the $$X$$ axis.

The plane $$9x - 8y + 12z + 9 = 0$$ is not parallel to any axis.

By definition above
Given two points as above, the equation $$Ax + By + Cz + D = 0$$ may be calculated.

If this is too complicated, calculate the three direction numbers and the point midway between the two given points. Proceed as under "Point and direction numbers" below.

By point and direction numbers
A point and direction numbers usually define a line. In this case it is a special line, the line normal to the plane with the given point being a point in the plane.

Given $$((x_1,y_1,z_1),[A_1,B_1,C_1]):$$

The equation of the plane is $$A_1x + B_1y + C_1z + D = 0$$ where $$D = -(A_1x_1 + B_1y_1 + C_1z_1).$$

By three points
Verify that the three points form a real triangle with all sides non-zero.

From the three points produce two groups of direction numbers. Calculate the direction numbers of the normal to the two groups of direction numbers. Using any one of the points and the direction numbers of the normal proceed as under "Point and direction numbers" above.

Plane and line
Given a plane and a line in 3 dimensions some relevant questions are:

 * Is the line parallel to the plane? if so, what is distance from line to plane?

 * If not parallel, what is the point within the plane at which the line enters the plane?

Let the plane be defined as: $$Ax + By + Cz + D = 0.$$

Let the line be defined as point $$(x_1, y_1, z_1)$$ and direction numbers $$[A_1, B_1, C_1].$$

The point at which the line enters the plane is: $$(x_1 + KA_1, y_1+KB_1, z_1+KC_1).$$

These points satisfy the equation of the plane:

$$A(x_1 + KA_1) + B(y_1+KB_1) + C(z_1+KC_1) + D = 0$$

$$K = \frac{-(+ Ax_1 + By_1 + Cz_1 + D )}{AA1 + BB1 + CC1}.$$

The divisor $$AA1 + BB1 + CC1$$ is the top line of the equation for $$\cos \theta,$$ angle between two lines.

If $$\cos \theta == 0,$$ the angle between line and normal to the plane is $$90^\circ$$ and line is parallel to plane.

The point of intersection is: $$(x_1 + KA_1, y_1+KB_1, z_1+KC_1).$$

If the direction numbers $$[A_1, B_1, C_1]$$ are all direction cosines, distance from point to plane along the line is $$K.$$

For example:

In the diagram point $$P$$ has coordinates $$(8,11,-12).$$

Line $$PR$$ through $$P$$ has direction numbers $$[5,25,-7].$$

Point $$R$$ is within the plane $$9x + 12y + 8z +181 = 0.$$

What are the coordinates of point $$R$$?

With $$[ A, B, C ]$$ as direction cosines the coefficients of the plane $$= (A,B,C,D) = ( \frac{9}{17}, \frac{12}{17}, \frac{8}{17}, \frac{181}{17} ).$$

As direction cosines the direction numbers of the line $$= [A_1,B_1,C_1] = [ \frac{5}{\sqrt{699}}, \frac{25}{\sqrt{699}}, \frac{-7}{\sqrt{699}} ].$$

Using $$K = \frac{-(+ Ax_1 + By_1 + Cz_1 + D )}{AA_1 + BB_1 + CC_1} = \frac{-17}{0.643} = -26.4386,$$

The point of intersection $$=(x_1 + KA_1, y_1+KB_1, z_1+KC_1) = (3,-14,-5).$$

Provided that all values $$[A,B,C], [A_1,B_1,C_1]$$ are direction cosines,

$$-(+ Ax_1 + By_1 + Cz_1 + D ) =$$ length $$PQ$$ and $$AA_1 + BB_1 + CC_1 = \cos(\theta).$$

If the value of $$\angle \theta_1$$ is desired, $$\sin (\theta_1) = \cos(\theta).$$

Plane and point
Given a plane and a point in 3 dimensions some relevant questions are:

 * What is distance from point to plane?

 * What is the point within the plane at which the line through the point and normal to plane enters the plane?

Let the plane be defined as: $$Ax + By + Cz + D = 0.$$

Any line normal to the plane has direction numbers $$(A, B, C).$$

Let the point be defined as point $$(x_1, y_1, z_1).$$

Let  be defined as the line through point $$(x_1, y_1, z_1)$$ with direction numbers $$(A, B, C).$$

Ensure that the values $$(A, B, C)$$ are direction cosines.

Use the method above to calculate the point at which  enters the plane.

Distance from point to plane is K. Alternatively, distance from point to plane is $$Ax_1 + By_1 + Cz_1 + D.$$

For example:

is defined as $$9x+12y+8z-108 = 0.$$

Point $$P$$ has coordinates $$(13,20,5).$$

 * At what point $$P_1$$ does the normal through $$P$$ enter ?

 * What is the distance from $$P$$ to $$P_1$$?

Convert the equation of  to direction cosines: $$\frac{9}{17}x+\frac{12}{17}y+\frac{8}{17}z-\frac{108}{17} = 0.$$

Using $$K = \frac{-(+ Ax_1 + By_1 + Cz_1 + D )}{AA1 + BB1 + CC1}.$$

$$K = \frac{-(+ \frac{9}{17}x_1 + \frac{12}{17}y_1 + \frac{8}{17}z_1 -\frac{108}{17} )}{A^2 + B^2 + C^2}$$ $$= -(+ \frac{9}{17}13 + \frac{12}{17}20 + \frac{8}{17}5 -\frac{108}{17} ) = -17.$$

Point $$P_1 = (13-17\frac{9}{17},\ 20-17\frac{12}{17},\ 5-17\frac{8}{17}) = (4,8,-3).$$

Distance from $$P$$ to $$P_1 = -17.$$

Plane and plane
If two planes are parallel:

 * they do not intersect.

 * their normals are parallel.

The distance between two parallel planes $$A_1x + B_1y + C_1z + D_1 = 0$$ and $$A_2x + B_2y + C_2z + D_2 = 0$$ is $$D_1 - D_2$$ provided that both planes are defined with direction cosines.

Intersection of 2 planes:

The intersection of plane and plane is a line. The word "intersection" implies that the two planes are not parallel.

If two planes intersect, the line normal to both normals is parallel to the line of intersection.

As the intersection of two planes, the line cannot be defined by a neat algebraic equation like that of the plane.

However the concept is useful because the intersection of line and plane or line and sphere can be solved with algebra.

The line defined as the intersection of two planes can be defined with the familiar point and direction numbers:

As point and direction numbers:

Line $$PQ$$ is defined as the intersection of two planes  and

Using any point (the origin $$O$$ is convenient,) calculate the coordinates of point $$R$$ within  and on the normal from point $$O$$ to.

Calculate the direction numbers of line $$PQ.$$

Calculate the direction numbers of line $$RS,$$ normal to both lines $$OR, PQ.$$

Point $$S$$ is the point at which line $$RS$$ enters.

Line PQ may be defined as point $$S$$ with direction numbers of line $$PQ.$$

Any point on line $$PQ$$ has distance $$0$$ from both planes  and

Algebraic method:

Let a line be defined by two planes:

$$\pi_1:\ x+y+z+1 = 0$$

$$\pi_2:\ x+2y+3z+4 = 0$$

From $$\pi_1,\pi_2$$ derive other equations:

$$\pi_3:\ y + 2z + 3 = 0\ \dots\ \pi_2 - \pi_1$$

$$\pi_4:\ x - z - 2 = 0\ \dots\ 2\pi_1-\pi_2$$

$$\pi_5:\ 2x + y - 1 = 0\ \dots\ 3\pi_1-\pi_2$$ $$$$

The line may be defined by any 2 of $$\pi_1,\ \pi_2,\ \pi_3,\ \pi_4,\ \pi_5.$$

To find a point on the line, let $$x = 0.$$

From $$\pi_4:\ z = -2$$

From $$\pi_5:\ y = 1$$

Therefore $$(0,1,-2)$$ is a point on the line and the line has direction numbers $$(A,B,C)=(-1,2,-1).$$

Any point on the line has coordinates $$(x+KA,\ y+KB,\ z+KC) = (0+K(-1),\ 1+K(2),\ -2+K(-1)).$$

For proof:

Substitute these values into $$\pi_1:$$ $$x+y+z+1 = (-K) + (1+2K) + (-2-K) + 1 = 0.$$

Substitute these values into $$\pi_2:$$ $$x+2y+3z+4 = (-K) + 2(1+2K) + 3(-2-K) + 4 = -K + 2 + 4K -6-3K + 4 = 0.$$

Line  defined as intersection of 2 planes:

Reviewing:
Now that information about the plane is available to the reader, some of the concepts above can be reviewed and simplified.

Point and line
Line $$PQ$$ and point $$M$$ are given.

Calculate the coordinates of point $$N$$ on line $$PQ$$ so that line $$MN$$ is normal to line $$PQ.$$

Calculate the direction numbers of line $$PQ:\ (A,B,C).$$

Using $$(A,B,C)$$ and point $$M$$ calculate the plane normal to line $$PQ$$ and containing point $$M,$$ plane $$MNR.$$

Point $$N$$ is the point at which line $$PQ$$ enters plane $$MNR.$$

Points of closest approach
Lines $$PQ,RS$$ are skew.

Calculate point $$R$$ so that distance from point $$R$$ to line $$PQ$$ is minimum.

Calculate direction numbers of line $$RT$$ normal to both $$PQ, RS.$$

Calculate direction numbers of line $$UV$$ normal to both $$PQ, RT.$$

Using direction numbers of line $$UV$$ and point $$P$$ or point $$Q,$$ calculate plane $$PQT.$$

Point $$R$$ is the point at which line $$SR$$ enters plane $$PQT.$$

Three planes
The intersection of 3 planes is a point. The word "intersection" implies that the three planes actually intersect.

Given three random planes, there are two situations that do not produce a point of intersection:

 * If two of the planes are parallel.

 * If the three planes form a "tent" or "awning."

In diagram to the right:

 * No two planes are parallel.

 * The line of intersection of any 2 planes is parallel to the third plane.

For example, line $$CD$$ is the line of intersection of two planes

Line $$CD$$ is parallel to  and there is no point of intersection.

Point of intersection:

In the diagram line $$CD$$ is line of intersection of two planes

Point $$E$$, the point of intersection of the 3 planes, is the point at which line $$CD$$ enters

Similarly:

 * Line $$EF$$ is common to  Point $$E$$ is the point at which line $$FE$$ enters

 * Line $$EG$$ is common to  Point $$E$$ is the point at which line $$GE$$ enters

=The sphere=

The sphere is the locus of a point that is always a fixed non-zero distance from a given fixed point.

Let the point be  and the distance be

Let  be any point on the surface of the sphere.

Then $$(x-d)^2 + (y-e)^2 + (z-f)^2 = r^2$$

$$x^2 - 2dx + d^2 + y^2 - 2ey + e^2 + z^2 - 2fz + f^2 = r^2$$

$$x^2 + y^2 + z^2 - 2dx - 2ey - 2fz + d^2 + e^2 + f^2 - r^2 = 0$$

$$x^2 + y^2 + z^2 + Ax + By + Cz + D = 0$$

where:

$$A = -2d,$$ $$B = -2e,$$ $$C = -2f,$$ $$D = d^2 + e^2 + f^2 - r^2.$$

Given a sphere defined as  the sphere may be defined as  where it is understood that the coefficients of $$(x^2,\ y^2,\ z^2)$$ are

reversing the conversion
Given a sphere defined as  calculate and

$$d = \frac{-A}{2},$$ $$e = \frac{-B}{2},$$ $$f = \frac{-C}{2},$$ $$r = \sqrt{ d^2 + e^2 + f^2 - D }.$$

and

Two definitions of the sphere:

 * , the algebraic definition of the sphere.

 * , the trigonometric definition of the sphere.

examples
Errors in definition:

The tuple  does not define a valid sphere because radius=0.

The tuple  does not define a valid sphere because the value $$( d^2 + e^2 + f^2 - D )$$ is negative. Consequently the value $$r = \sqrt{ d^2 + e^2 + f^2 - D }$$ is a complex number.

Sphere at origin:

If center of sphere is at origin, $$(d, e, f) = (0,0,0).$$

For example, a sphere at origin with radius $$7$$ may be defined as:

or

Point inside, on or outside sphere:

If distance from point to center $$< r,$$ point is inside sphere.

If distance from point to center $$== r,$$ point is on surface of sphere.

If distance from point to center $$> r,$$ point is outside sphere.

A sphere is defined as

3 points are given:

For each point, determine position of point relative to surface of sphere.

 * for point (3,4,3), distance from point to center is  Point is inside sphere.

 * for point (-3,19,0), distance from point to center  Point is on surface of sphere.

 * for point (9,-5,6), distance from point to center is  Point is outside sphere.

Sphere and line
Given a sphere and a line:

 * The line may pierce the sphere in 2 places,

 * The line may touch the sphere in 1 place, or

from the center of the sphere is always greater than the radius of the sphere.
 * The line may not touch or pierce the sphere. In other words, the distance to the line

The possible point/s of intersection may be calculated by trigonometry or by algebra.

Given a sphere defined as  and a line defined as   calculate the point/s of intersection, if any.

By trigonometry:
Let center of sphere $$P = (3,5,-2).$$ and point $$M = (4,-5,10).$$

Calculate coordinates of point $$N$$ on the line so that line $$PN$$ is normal to the given line.

$$N = (5.5, 1, -3.5).$$

Calculate length $$PN = \sqrt{24.5} = 4.949747468305833.$$ This length is less than the radius of the sphere. The line intersects the sphere in 2 points. Let these points be $$S,T.$$

Length $$NS =$$ length $$NT = \sqrt{ (7)^2 - 24.5 } = \sqrt{24.5}.$$$$$$

Redefine the line so that direction numbers are direction cosines: $$\frac{1}{\sqrt{98}},\frac{4}{\sqrt{98}},\frac{-9}{\sqrt{98}}$$

Point $$S = ( 5.5 + \sqrt{24.5}\cdot\frac{1}{\sqrt{98}}, 1 + \sqrt{24.5}\cdot\frac{4}{\sqrt{98}}, -3.5 + \sqrt{24.5}\cdot\frac{-9}{\sqrt{98}} )$$

Point $$T = ( 5.5 - \sqrt{24.5}\cdot\frac{1}{\sqrt{98}}, 1 - \sqrt{24.5}\cdot\frac{4}{\sqrt{98}}, -3.5 - \sqrt{24.5}\cdot\frac{-9}{\sqrt{98}} )$$

Proof:

Distance from point  to center $$= \sqrt{ (6-3)^2 + (3-5)^2 + (-8-(-2))^2 } = 7 =$$ radius.

Distance from point  to center $$= \sqrt{ (5-3)^2 + (-1-5)^2 + (1-(-2))^2 } = 7 =$$ radius.

Direction numbers of line

Direction numbers of line

Lines  and original line are all parallel and all pass through point

Points  are on the original line.

By extending line with constant K
Let the line be defined as point and direction numbers:

Let the point at which the line enters the sphere be:

These values of $$(x,y,z)$$ satisfy the equation of the sphere:

$$x^2 + y^2 + z^2 + Ax + By + Cz + D = 0.$$

Therefore: $$(s+KE)^2 + (t+KF)^2 + (u+KG)^2 + A(s+KE) + B(t+KF) + C(u+KG) + D = 0$$

Expand and the result is:

$$(E^2 + F^2 + G^2)K^2 + (AE + BF + CG + 2Es + 2Ft + 2Gu)K + As + Bt + Cu + D + s^2 + t^2 + u^2 = 0.$$

This is a quadratic equation in $$K:$$

$$A_0K^2 + B_0K + C_0 = 0$$ where:

$$A_0 = E^2 + F^2 + G^2$$

$$B_0 = AE + BF + CG + 2Es + 2Ft + 2Gu$$ and

$$C_0 = As + Bt + Cu + D + s^2 + t^2 + u^2.$$

By algebra:
Let the sphere be defined as $$A_1, B_1, C_1, D_1$$

Let the line be defined as the intersection of 2 planes $$A_2, B_2, C_2, D_2$$ and $$A_3, B_3, C_3, D_3$$

The relevant equations are :

$$x^2 + y^2 + z^2 + A_1x + B_1y + C_1z + D_1 = 0\ \dots\ (1)$$

$$A_2x + B_2y + C_2z + D_2 = 0\ \dots\ (2)$$

$$A_3x + B_3y + C_3z + D_3 = 0\ \dots\ (3)$$

The point/s of intersection are the solution/s of these 3 equations for $$x, y, z.$$

The value/s of $$x$$ are the solution/s of the quadratic equation $$c_2x^2 + c_1x + c_0 = 0.$$

Exchange rows
Rows 2 and 3 may be exchanged, one for the other:

Exchange columns
If data supplied to  produces an error (as above), try exchanging two columns: Exchange appropriate columns in output to produce correct values:

Defined as 4 points
If 4 unique points on surface of sphere are known, the center and radius may be calculated.

From above, equation of sphere is: $$x^2 + y^2 + z^2 + Ax + By + Cz + D = 0$$

When $$x, y, z$$ are known and $$A, B, C, D$$ are unknown the above equation becomes: $$xA + yB + Cz + (1)D + x^2 + y^2 + z^2 = 0\ \dots\ (1)$$

With four points provided, equation $$(1)$$ may be used to construct a system of 4 simultaneous equations that, when solved, provide the values $$(A, B, C, D).$$

For example:

The above matrix of 4 rows by 5 columns is input to function See Solving_M_by_(M+1)

Center as intersection of 3 planes
Let center of sphere be $$(d, e, f).$$

Let 4 points on surface of sphere be $$(a,b,c),\ (g,h,j),\ (k,l,m),\ (n,p,q).$$

$$(d-a)^2 + (e-b)^2 + (f-c)^2 = r^2$$

$$(d-g)^2 + (e-h)^2 + (f-j)^2 = r^2$$

$$(d-k)^2 + (e-l)^2 + (f-m)^2 = r^2$$

$$(d-n)^2 + (e-p)^2 + (f-q)^2 = r^2$$

$$(d-a)^2 + (e-b)^2 + (f-c)^2 = (d-g)^2 + (e-h)^2 + (f-j)^2$$ or

$$(d-a)^2 + (e-b)^2 + (f-c)^2 - ( (d-g)^2 + (e-h)^2 + (f-j)^2 ) = 0\ \dots\ (1)$$

$$(d-a)^2 + (e-b)^2 + (f-c)^2 - ( (d-k)^2 + (e-l)^2 + (f-m)^2 ) = 0\ \dots\ (2)$$

$$(d-a)^2 + (e-b)^2 + (f-c)^2 - ( (d-n)^2 + (e-p)^2 + (f-q)^2 ) = 0\ \dots\ (3)$$

When expanded, equation $$(1)$$ above has the form $$Ad + Be + Cf + D = 0.$$ This is the equation of the plane normal to line $$((a,b,c),\ (g,h,j),$$ 'line'$$)$$ and containing the point midway between points $$(a,b,c),\ (g,h,j).$$ For function  see  "Solving_3_by_4"

=Third line=

Given:

 * has direction numbers

 * has direction numbers

 * is cosine of angle between  and

 * is cosine of angle between  and

Calculate direction numbers of line3.

In the diagram:

has direction cosines $$[a_1, b_1, c_1].$$

has direction cosines $$[a_2, b_2, c_2].$$

$$\theta_1$$ is angle between  and

$$\theta_2$$ is angle between  and

$$= \cos(\theta_1).$$

$$= \cos(\theta_2).$$

Length

Length

Point  has coordinates

Point  has coordinates

is normal to  and contains point

is normal to  and contains point

Point  is on line of intersection of   and and point  is distance   from point

Point  may have no value. $$(\theta_1 + \theta_2 < \angle MON)$$

Point  may have 1 value. $$(\theta_1 + \theta_2 = \angle MON)$$

Point  may have 2 values. $$(\theta_1 + \theta_2 > \angle MON)$$

For function  see  "Solving_3_by_4"

An example:

Rotate line through given angle
Given:

 * defined as

 * wholly within  and with direction numbers

 * angle $$\theta$$

Calculate:

 * direction numbers of  wholly within   and making angle $$\theta$$ with

This is a special case of function  above in which   makes the angle of $$90^\circ$$ with the normal to the plane, and angle $$\theta$$ with A simple example:

Spokes of a wheel
Given:

 * defined as

 * wholly within  and with direction numbers

Rotate  5 times through $$72^\circ,$$ wholly within

5 times $$72^\circ = 360^\circ.$$ After 5 rotations the direction cosines $$[a_1, b_1, c_1]$$ match their initial values.

By algebra
Ensure that all values $$[a_1,b_1,c_1],\ [a_2,b_2,c_2]$$ are direction cosines.

The relevant equations are:

$$a_1 \cdot a_3 + b_1 \cdot b_3 + c_1 \cdot c_3$$  $$\dots\ (1)$$

$$a_2 \cdot a_3 + b_2 \cdot b_3 + c_2 \cdot c_3$$  $$\dots\ (2)$$

$$a_3^2 + b_3^2 + c_3^2 = 1\ \dots\ (3)$$

Because $$a_3$$ may have exactly $$0$$ or $$1$$ or $$2$$ values, $$a_3$$ is the solution of the quadratic equation $$C_2\cdot a_3^2 + C_1\cdot a_3 + C_0 = 0$$ where $$C_2, C_1, C_0$$ are as defined in the python code below.

Then values $$b_3, c_3$$ may be calculated as shown below.

The function above simplifies to:

Normal to 2 lines
This is the special case in which  and the calculation of $$a_3$$ becomes:

$$C_2\cdot a_3^2 = -C_0$$

$$a_3^2 = \frac{A_3^2}{A_3^2 + B_3^2 + C_3^2}$$

$$a_3 = \frac{A_3}{\sqrt{A_3^2 + B_3^2 + C_3^2}}$$

whence: $$b_3 = \frac{a_3\cdot B_3}{A_3} = \frac{B_3}{\sqrt{A_3^2 + B_3^2 + C_3^2}}$$

and $$c_3 = \frac{-(a_3\cdot a_1 + b_3\cdot b_1)}{c_1}$$

Normal to X,Y axes
In this case the result below was derived from "# output line 3" in the Python code above. 3 -0.0, 0.0, 1.0], [-0.0, 0.0, -1.0

=Links to Related Topics=

Coordinate_systems

Functions_(mathematics)/Graphs/Coordinations

Functions_(mathematics)/Graphs

Investigating_3D_geometric_algebra

Line_(Geometry)

Functions_(mathematics)/Graphs/Cartesian_Coordinate

title: Introduction to Cartesian Geometry


text:
Muhammad Ahmed Bashir

Muhammad Ahmed Bashir (born 1 December 1949) is a Pakistani hurdler. He competed in the men's 110 metres hurdles at the 1972 Summer Olympics.

title: Muhammad Ahmed Bashir


text:
5th Royal Tank Regiment

5th Royal Tank Regiment (5 RTR) was an armoured regiment of the British Army in existence for 52 years, from 1917 until 1969. It was part of the Royal Tank Regiment, itself part of the Royal Armoured Corps. It originally saw action as E Battalion, Tank Corps in 1917.

At the Battle of Cambrai in late 1917, during the First World War, the squadron of tanks led by Arthur George Griffiths made a huge impact on the battle. The commanding general asked for the squadron of tanks to be doubled in size, and so Griffiths's squadron evolved into the 5th Tank Regiment.

The regiment saw wide-ranging service in the Second World War, and fought in nearly all of the major allied campaigns from the 1940 retreat from France through the Western Desert Campaign, Normandy and on into Germany. It became part of the 22nd Armoured Brigade, of the 7th Armoured Division.

In December 1946, the regiment was the first to use Centurion tanks in regular service.

In 1960, under the command of Hugo Ironside, it amalgamated with 8th Royal Tank Regiment without change of title. It was disbanded in 1969.

The 5th Royal Tank Regiment Reunion Association holds annual reunions.

In 2007, an image of a 1944 tank commander in the 5th Royal Tank Regiment uniform was used on one of a series of Royal mail stamps featuring British Army uniforms.

Commanding officers
The commanding officers included:
 * 1959–1960: Lt.-Col. Allan Taylor
 * 1960–1961: Lt.-Col. Hugo Ironside
 * 1961–1963: Lt.-Col. Edward Anstey
 * 1963–1966: Lt.-Col. Peter E. Dey
 * 1966–1968: Lt.-Col. Roy L.C. Dixon
 * 1968–1969: Lt.-Col. Richard Lawson

title: 5th Royal Tank Regiment


text:
Talk:Douglas French

Did he really stand down?!
As I remember, French was defeated in 1997; he did not "stand down". Is that the correct language? Or should it refer to French's defeat by Tess kingham?

title: Talk:Douglas French


text:
Donlon

Donlon may refer to:

People

 * Alphonsus J. Donlon (1867–1923), American Jesuit priest
 * Billy Donlon (born 1977), American college basketball coach
 * Chris Donlon (born 1977), Australian rules football field umpire
 * Denise Donlon (born 1956), Canadian executive, television producer, television host
 * Dolores Donlon (1920–2012), American model and actress
 * Marguerite Donlon (born 1966), Irish dancer, choreographer and ballet director
 * Mary H. Donlon (1893–1977), American lawyer and politician
 * Peter Donlon (1906–1979), American rower
 * Roger Donlon (1934–2024), retired United States Army officer

Places

 * Mary Donlon Hall, a residence hall located on Cornell North Campus

title: Donlon


text:
Nebraskan

Adjective

 * Of, or pertaining to, Nebraska or its culture

Noun

 * 1) A native or resident of the state of Nebraska in the United States of America.

Translations

 * French:, Nébraskaine, , Nébraskienne

title: Nebraskan