text:
Brittany Elmslie

Brittany Joyce Elmslie, (born 19 June 1994) is a former Australian competitive swimmer. She represented Australia at the 2012 and 2016 Summer Olympics in swimming, and won a gold medal in the 4 × 100 m freestyle relay at both Games.

Personal life
Elmslie was born in Nambour, Queensland. She was named a 2011–2012 YoungStar Sport Award winner for the Northside Chronicle. , she lives in Brisbane, having moved there from Noosa (where she attended Good Shepherd Lutheran College) in 2011 in order to improve her chances of making the Olympics. In 2011 she completed her final year of school at St Margaret's Anglican Girls' School.

Elmslie is 179 cm tall and weighs 73 kg.

Elmslie initially studied Business at Griffith University, majoring in Events and Sports Management. She subsequently changed her academic major to Media and Communications at Flinders University.

On June 2, 2020, Elmslie attributed her retirement from competitive swimming, to her own self-reflection after she did not qualify for the 2018 Commonwealth Games, and self-realisation at the finals of the 2019 Australian Swimming Championships in Adelaide, that she was keen on moving on from competitive swimming. Elmslie is currently mentoring young, aspiring athletes, promoting self-evaluation and sharing thought processes of elite athletes, through swimming programs, one-on-one coaching and technique efficiency coaching, conducted by her own business – Golden Perspective.

Swimming
Elmslie's best time in the 100-metre freestyle is 53.54 seconds and was set at the 2016 Hancock Prospecting Australian Swimming Championships. Her best time in the 50-metre freestyle is 24.74 seconds, set at the 2016 Swimming Australia Grand Prix. Her best time in the 200-metre freestyle is 1:56.79, set at the 2014 McDonald's Queensland Championships. Her best time in the 100-metre butterfly is 57.97 seconds set at the 2015 Australian Swimming Championships. She is a member of Brisbane Grammar School Swimming Club.

At the Guam hosted 2009 Junior Pan Pacific, Elmslie finished first in the 50-metre freestyle and fourth in the 100-metre freestyle. At the 2010 Telstra Australian Swimming Championships, she made the finals in the 50-metre freestyle. At the Hawaii hosted 2010 Junior Pan Pacific, she finished third in the 4×100-metre freestyle and fifth in the 50-metre freestyle.

In 2011, after moving to Brisbane to join other swimmers coached by Matt Brown, Elmslie increased her training regime and lost 6 kg. Her training partners included Emily Seebohm. At the 2012 Australian National Championships, she set a time of 1 minute 57.24 seconds in the 200-metre freestyle. She was selected to represent Australia at the 2012 Summer Olympics in the women's 4×200-metre freestyle swimming team event  in her first Olympics. Going into the games, her team was considered a medal favourite. She was set to compete in the Olympics as a teenager.

At the 2012 Summer Olympics, Elmslie represented the gold medal-winning Australia team (with Cate Campbell, Alicia Coutts and Melanie Schlanger in the final) of the 4 × 100 metre freestyle relay, where the team set a then-Olympic Record of 3:33.15. Elmslie also won two silvers, as part of the Australian teams in the competitive heats of both the 4 × 100 metre medley relay and the 4 × 200 metre freestyle relay.

At the 2013 Australian Swimming Championships she won silver in the 100-metre butterfly and bronze 50-metre freestyle events, qualifying for the 2013 World Aquatics Championships. At the World Championships, she teamed up with Bronte Campbell, Emma McKeon and Emily Seebohm in the heats of the 4×100-metre freestyle relay, finishing second in their heat and overall. In the final sisters Cate and Bronte Campbell, Emma McKeon and Alicia Coutts won the silver medal, finishing 0.12 of a second behind the United States team.

At the 2016 Summer Olympics, Elmslie represented the gold medal-winning Australia team (with sisters Cate Campbell and Bronte Campbell and Emma McKeon in the final, along with Madison Wilson in the heats) of the 4 × 100 metre freestyle relay. In the final of the event, the Australian team set a then 4 × 100 metres freestyle relay World Record time of 3:30.65. Elmslie also won silver as part of the Australian team in the competitive heats of the 4 × 100 metre medley relay.

Elmslie did not qualify for the 2018 Commonwealth Games. On April 23, 2019, Elmslie announced her retirement from competitive swimming, on her personal Instagram page, at the age of 24.

title: Brittany Elmslie


text:
taurokathapsia

Etymology
From Revived, variant of , from +. Apparently coined by, the excavator of Knossos, in ca. 1910.

Noun

 * 1)  Bull-leaping, as depicted in Bronze Age art, especially from Minoan Crete.

Translations

 * French: taurokathapsie, ,
 * German: Stiersprung
 * Greek:
 * Ancient Greek: ταυροκάθαψις
 * Italian: taurocatapsia
 * Spanish: taurocatapsia

source: wikimedia

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

title: taurokathapsia


text:
aphanitic

Adjective

 * 1)   Pertaining to aphanites, igneous rocks composed of microscopic mineral crystals (fine grains too small to be visible to the naked eye.

Translations

 * Polish: afanitowy
 * Portuguese: afanítico
 * Spanish:

title: aphanitic


text:
Talk:1975 Omaha tornado outbreak

Name of article
I've added a tornado table, since it was an outbreak, but I've omitted tornadoes across the Gulf States, being not sure if it was part of the same system. Anyone finding that the two zones are from the same system can add it to the table [--JForget 02:57, 8 March 2007 (UTC)

 * I moved the article named "Omaha Tornado of 1975" to "1975 Omaha tornado" IAW Naming conventions (events). --Rosiestep (talk) 23:06, 11 December 2008 (UTC)

Wow?
So... it's about a specific tornado but also the others?--Ssteiner209 (talk) 19:45, 10 April 2009 (UTC)

F4 or F5?
I believe this was an F4 not an F5. I could be wrong and if I am please put down the right data. Thank you.--Kevjgav (talk) 22:30, 26 January 2012 (UTC)

F1 tornado on East Coast during May 6 event; I tried to cite but could not
According to www.tornadohistoryproject.com, I had also noted that there was a confirmed tornado as far east as Talbot County, Maryland. I tried to add that as a reference, but for some unknown reason I could not do so. With that being said, I then deleted that quote and I am not going to bother with that edit-I am just going to leave this article "as-is."--Kevjgav (talk) 12:49, 24 August 2013 (UTC) The Talbot County tornado didn't directly hit land, which is probably why it isn't listed here. On July 28, 1967 there was an F1 in Neavitt, Maryland.--Kevjgav (talk) 17:57, 1 February 2015 (UTC)

title: Talk:1975 Omaha tornado outbreak


text:
Template:2018 NL Central standings/doc

Usage
This is a template that was created to easily update every article with the 2018 MLB National League Central standings. To use the update on any article, insert:

To highlight the Chicago Cubs, insert:

To use a different team, just replace the name of the team in the highlight parameter.

title: Template:2018 NL Central standings/doc


text:
Template:2019–20 NHL Eastern Conference standings/doc

Usage
This is a template that was created to easily update every article with the NHL Eastern Conference standings. This regular season was shorten due to the COVID-19 pandemic and the NHL adopted a special 24-team playoff tournament.

Here is the listing of all NHL division and conference standing templates for the 2019–20 NHL season.

 * Template:2019–20 NHL Eastern Conference standings
 * Template:2019–20 NHL Atlantic Division standings
 * Template:2019–20 NHL Metropolitan Division standings
 * Template:2019–20 NHL Eastern Conference Wild Card standings

 * Template:2019–20 NHL Western Conference standings
 * Template:2019–20 NHL Central Division standings
 * Template:2019–20 NHL Pacific Division standings
 * Template:2019–20 NHL Western Conference Wild Card standings


text:
User:Hassanherts19

Hassan Rauf Awan

Hassan Rauf Awan is the Founder and President of United South Asia. He was born on 10th April 1999 in Hazara Pakistan. Based In London United Kingdom He is Known For his Poetry and Debating Skills. Having Done his Earlier education from the most elite institutions of his country Army Burn Hall college and Cadet College Batrasi. Hassan is currently studying LLB (HONS) from University of Hertfordshire Where he is serving as Student Representative and Student Ambassador of student from more than 140 countries of the world. Hassan received various awards for debating on National and international Platforms. Also Being Involved in Student Politics, he has Spoken on various Topics in top leading Universities around the World. He was chief editor of his college magazine in 2016/17 and also served as President Urdu Society for a Year for Which He hosted Different Events Including All Pakistan Captain Usman Ali Shaheed Bilingual Competition 2016.He received Gold Medal For best debater at the age of seventeen in his college. In July 2019 Hassan Rauf Awan started the Organization of United South Asia which Was recognised By Hertfordshire Student Union Representing 8 Countries Of the South Asia Region.

“The Modern Era Demands us to be United for Better Future of our Masses”.

Hassan Rauf Awan

title: User:Hassanherts19


text:
Talk:Orcus (dwarf planet)/GA1

GA Review
The edit link for this section can be used to add comments to the review.''

Reviewer: Bryanrutherford0 (talk · contribs) 14:18, 20 September 2019 (UTC)

 * GA review (see here for what the criteria are, and here for what they are not)

 * 1) It is reasonably well written.
 * a (prose, spelling, and grammar): b (MoS for lead, layout, word choice, fiction, and lists):
 * The article is written to a good prose standard and complies with the required sections of MoS, with one exception: the lead section is clear and relevant but a bit too long. MOS:LEADLENGTH indicates that the lead section of an article this size should be "one or two paragraphs." The final paragraph should be cut from the lead, since it appears to only contain information about Vanth and not Orcus; that content should be moved to the section on Vanth at the end of the body, where it will give that section a little more heft (I would put it between the two existing sentences of the final paragraph of the body).
 * I think the third paragraph of the lead should probably be cut as well (of course keeping all of the content in the body sections on Orcus's surface and cryovolcanism). I would probably keep the first sentence ("The surface of Orcus is...") but move it to the first paragraph after the sentence that establishes the body's diameter, which would improve the size balance between the two paragraphs. The rest of the detail here probably needs to wait for treatment in the body.
 * In the section "Size and magnitude", one sentence begins, "If the albedos of both bodies are the same...", but the next sentence says that a subsequent study has revealed that the albedos are not the same, requiring an upward revision of Vanth's estimated size; if that's true, then the "If they were the same..." sentence should be deleted as a distraction.
 * In "Spectra and surface", The first sentence of the third paragraph begins, "Orcus straddles the edge...", but to straddle something is to be on both sides of it at once. It's not yet known with certainty whether Orcus is big enough, but in reality it either is or is not, so "straddles" sends the wrong message. Maybe "Orcus sits at the threshold..."?
 * Regarding the use of Template:Minor planets navigator at the end: it doesn't seem like this footer navbox is really adding anything to the article without the adjacent minor planets included, but I see that we don't seem to have articles about either of them (and may never have, since neither may ever be especially notable). Probably this should be removed, unless it's serving some purpose I'm not seeing?
 * Another minor note: I would add a wikilink to psychopomp in the sentence in "Name" explaining Vanth's name, but it's not required.
 * 1) It is factually accurate and verifiable.
 * a (reference section): b (citations to reliable sources):  c (OR):  d (copyvio and plagiarism):
 * The article has citations and a reference section. The online citations included support the vast majority of the article's substantive content, and I'll AGF on some of the paywalled studies for plausible physical data. Earwig's copyvio tool shows a close match between some of this article's text about the IAU's naming conventions and some other wiki/fansites, but it looks to me like that's probably because those sites ripped off this article.
 * Comments: I see in the infobox that we have the margins of error for all the figures in the "Physical characteristics" section, but they seem to be omitted in the "Orbital characteristics" section. Is there a reason not to include the uncertainties with those figures as well? They seem to be included on the JPL page that's cited, in the form of standard deviations (rather than a 90% confidence interval or what have you). Also, the JPL page's orbital data seem to be based on Epoch 2019 April 27.0 (as do those on the Minor Planet Center page), but the infobox claims that its orbital characteristics figures are from Epoch 4 September 2017; where did the infobox numbers come from, and should they be replaced by the figures from the JPL site?
 * The section "Mass and density" speculates about the division of mass between Orcus and Vanth, but the preceding section ("Size and magnitude") seems to indicate that a 2017 study nailed down Vanth's diameter to within about ±2%. Does this datum render the talk about Vanth making up between 1/33 and 1/12 of the binary system's mass outdated? If the previous section is correct, then it sounds like the relative sizes are known to much greater precision than this now.
 * In "Orbit and rotation", I'm uncomfortable with the phrase "Orcus is currently 48.0 AU from the Sun"; this is a sort of claim that is certain to rapidly go out of date and need continual updating. Perhaps we could cut this out and then update the remainder of the sentence to something like "Orcus has its aphelion in 2019 and will then approach the Sun until reaching perihelion in [presumably about] 2143"? That at least would keep the article up to date for the next 124 years. The second paragraph in the same section includes the claim that a rotational period of "about 10.5 hours seems to be the most likely one." Why does that figure seem the most likely, if other studies have produced other figures? Indeed, the abstract of the cited article seems to me to suggest that its authors find the possibility of Vanth's being tidally locked to be at least plausible. This claim about likelihood doesn't seem warranted by the sources I can see (but the Ortiz et al. article is paywalled, so I can't read the full text).
 * I've updated the orbital parameters of Orcus from the JPL Small Body Database. About the uncertainties for the orbital characteristics, the figures in the infobox are rounded and the uncertainties listed on the JPL site are very small. There is no need to include the small uncertainties if nearly all of them don't exceed 0.001. Nrco0e (talk) 01:59, 23 September 2019 (UTC)
 * With that aside, I have resolved the rest of your assessments. Nrco0e (talk) 02:28, 23 September 2019 (UTC)
 * Oh, I see, the uncertainty is beyond the precision you're reporting. Fair enough! -Bryan Rutherford (talk) 14:43, 23 September 2019 (UTC)
 * 1) It is broad in its coverage.
 * a (major aspects): b (focused):
 * The article appears to cover the major aspects of the topic, including observational history, origin of name, characteristics of the body and of its orbit, and a brief summary of information about its moon. It also doesn't generally drift off topic, with a few exceptions: the chief is that it goes into too much detail about Vanth in the lead section (as discussed above). Another two come in the "Name" section, where the sentence describing the visual depiction of the deity Orcus in Etruscan tombs should be completely removed. In the same section, the discoverer's wife's given name isn't relevant and should be removed in the interest of privacy.
 * 1) It follows the neutral point of view policy.
 * Fair representation without bias:
 * The article maintains an appropriately neutral tone and doesn't e.g. lionize the body's discoverers.
 * 1) It is stable.
 * No edit wars, etc.:
 * 1) It is illustrated by images and other media, where possible and appropriate.
 * a (images are tagged and non-free content have fair use rationales): b (appropriate use with suitable captions):
 * The images are relevant and appropriate, and they all have good licenses and helpful captions. It would be nice to add alt-text to all the images, but it isn't required for GA.
 * 1) Overall:
 * Pass/Fail:
 * An interesting and informative article about a plutino! With a little polish, this should be able to reach the GA standard.
 * I have edited the article according to your recommendations. I will be waiting for your next assessments. Nrco0e (talk) 19:07, 21 September 2019 (UTC)
 * Wow, thank you for your quick and responsive editing! I'll look through the sources by the end of the day tomorrow and give any feedback there, but everything I've pointed out so far is now fixed. -Bryan Rutherford (talk) 20:38, 21 September 2019 (UTC)
 * By the way, if you haven't known already, most of the scientific papers cited in the article can be accessed from their arXiv preprints, which is linked near the end of the source citation. For your issue about the rotation period of Orcus, the full paper can be read at https://arxiv.org/abs/1010.6187. I hope this helps for your future reviews on science-related articles! Nrco0e (talk) 02:40, 23 September 2019 (UTC)
 * This all looks good! Thanks again for being so responsive; this article is hereby approved for GA! -Bryan Rutherford (talk) 14:43, 23 September 2019 (UTC)
 * This all looks good! Thanks again for being so responsive; this article is hereby approved for GA! -Bryan Rutherford (talk) 14:43, 23 September 2019 (UTC)

title: Talk:Orcus (dwarf planet)/GA1


text:
User:Mike Graham

Brief Bio
I am a Civil Engineering student at Texas A&M University. Guess that was brief. Mike Graham 19:13, 13 October 2006 (UTC)

title: User:Mike Graham


text:
Template:FVP

 This Wikiversity main namespace page is frequently visited.Please contribute to the improvement of this page by editing orleave your suggestions/comments on the discussion page (talk page). Use this template to request comments from people who browse Wikiversity and edits that will make the page more useful to learners. Use the template this way:

title: Template:FVP


text:
Wikipedia:Articles for deletion/Charles Doyle (writer)

The result was delete. Jo-Jo Eumerus (talk, contributions) 19:05, 26 September 2017 (UTC)

Charles Doyle (writer)

 * – ( View AfD View log  Stats )

A whole lot of life history and resume about a non-notable author. Legacypac (talk) 03:05, 19 September 2017 (UTC)
 * Note: This debate has been included in the list of United Kingdom-related deletion discussions. CAPTAIN RAJU (T) 04:27, 19 September 2017 (UTC)
 * Note: This debate has been included in the list of Authors-related deletion discussions. CAPTAIN RAJU (T) 04:27, 19 September 2017 (UTC)

 * Delete Non-notable author, marketeer, amateur golfer and driving charity trustee.--Pontificalibus (talk) 07:06, 19 September 2017 (UTC)
 * Note: This debate has been included in the list of Literature-related deletion discussions. ʍaɦʋɛօtʍ (talk) 11:21, 19 September 2017 (UTC)

 * Delete, just not sufficient WP:SIGCOV for this overstuffed PROMO. Note that source #5 article, described as a WSJ article, leads nowhere, so I searched the WSJ for "Charles Doyle" and got three hits, none about this Charles Doyle.  Source # 10, The Guardian is an op-ed he wrote.E.M.Gregory (talk) 21:01, 19 September 2017 (UTC)


text:
User:Charlotte Friender/sandbox

Filmmakers Without Borders
Filmmakers Without Borders (or FWB) is a non-profit organisation which promotes the use of media trainings and intercultural learning opportunities to connect ‘underserved youth’ from lower-income countries with fellow filmmakers. Its headquarters are in New York City, USA. Its primary spheres of activity are the Fellow Program and Connected Classrooms projects, which raise civic awareness through the art of filmmaking, education and community interactions. Through the placement of fellow filmmakers in overseas partners’ sites, FWB reaches out to students from remote areas of the globe with adequate technology, trainings on Media literacy, filmmaking skills and 21st century communication tools. By doing so, the organisation strives to inspire “the next generation of digital storytellers” to share their stories and achieve a long-term impact in their communities. FWB has no link with Reporters without Borders.

History
While backpacking around the globe and teaching English abroad, filmmaker and educator Corey Boling was inspired to create a Peace Corps-like organisation, dedicated to promote the art of filmmaking as a mean to empower youth from remote areas of the world.

Boling gathered a network of educators, artists and international development experts to act as FWB Board of directors, e.g. Eileen Newman from the Center for Bronx Nonprofits, Caits Meissner and Flonia Telegrafi from the Tribeca Film Institute, Dr. Monique Scott from the American Museum of Natural History. Corey Boling then assembled his staff and Advisory Board whose members are experienced with years of teaching media to students across the US and involved in organisations ranging from the Educational Video Center, Charlotte Street Films, Results for Development Institute (R4D), Institute to the NYC Department of Education, just to name a few.

The team started up its activities by securing partnerships with schools, non-profit and community organisations acting as placement sites in target locations across Asia, Latin America, Africa, and Oceania. They already have a track record of exchanges which helped undeserved youth around the globe to learn ways to tell their stories through filmmaking. In addition, they have started to cooperate with NYC-based schools and organisations such as the Bushwick Film Festival.

Mission
Filmmakers Without Borders aims at infusing youth from underserved communities with a sense of engagement and empowerment to globally change the world through visual storytelling. Its core mission goes beyond merely sending fellows from the US (and potentially Europe) in placement sites to teach specific skills to youth. It intends to enable young people to become change-makers by becoming aware of their role within their respective communities and societies while mastering the skills and craft of visual communication.

Main Activities
The Fellowship Program run in partnership with host placement sites, which is the core work of the organisation to date. Experienced professional filmmakers are offered the opportunity to spend one year abroad as volunteer media educators. Fellows work directly in overseas classrooms and teach local students ranging from middle and high-schools how to make short films and other multimedia projects. The process involves skills building activities (such as leaning creative writing, storytelling techniques, shooting and editing, etc.) and the production of three major short-film projects. While fellows oversees this learning process on site, FWB provides technical and logistical support throughout the year.

Connected Classroms. FWB team facilitates a closed collaboration between students from abroad and from the U.S. (up to January 2014, schools based in NYC) so that they can co-work on a film project and experience a long-distance cultural exchange, using modern communication software and online tools.

Outreach to local and global audiences. FWB supports both students and fellows from post production to distribution in order for their works to be exposed online and throughout the film festival circuit (both in-country and back in NYC).

Organisation
Currently, FWB, a registered 501(c)(3) organisation, consists of 10 staff members. It has a Board of Directors along with an Advisory Board including filmmakers, art educators and development experts. The organisation has been recently established by Corey Boling, FWB Executive Director, a filmmaker and educator who has worked considerably with such non-profit organizations as the Tribeca Film Institute, The Educational Video Center, and the Museum of the Moving Image .

Partners are schools and community organizations that FWB cooperates with to ensure the promotion of culturally specific and sustainable educational practices. So far, they secured partnership in Bangladesh, Bhutan, Cambodia, Honduras, India, Kenya, and Nepal, as well as Tanzania and Thailand.

FWB fundraises donations to fully cover the total cost for one-year fellowships (flights, housing, travel insurance, basic monthly stipend). In its start-up phase, Filmmakers Without Borders’s online campaign on the Kickstarter crowd-fundfing platform resulted successfully in gathering 117 backers donating $23,365.

title: User:Charlotte Friender/sandbox


text:
amfibija

Etymology
Ultimately from, borrowed via other European languages.

Noun

 * 1)  amphibian
 * 2) amphibious vehicle

Noun

 * 1) amphibian
 * 2) amphibious vehicle
 * 1) amphibious vehicle

title: amfibija


text:
Canticle of Canticles

Etymology
A calque of.

Proper noun

 * , a canonical book of the Hebrew Bible and Christian Old Testament.

title: Canticle of Canticles


text:
Help:Wikitext quick reference

Wikitext markup -- making your page look the way you want

 * You can see some more detailed examples at Help:Wiki markup examples.
 * If you want to try out things without danger of doing any harm, you can do so in the    :Sandbox.

Basic text formatting
For a list of HTML tags that are allowed, see HTML in wikitext. However, you should avoid HTML in favor of Wiki markup whenever possible.

Just show what I typed
A few different kinds of formatting will tell the Wiki to display things as you typed them.

Images, tables, video, and sounds
This is a very quick introduction (please do not forget to upload your files). For more information, see:
 * Images and sound files for help with media files
 * w:Help:Extended image syntax for how to arrange images on the page
 * Help:Table for how to create a table

Templates
Templates are segments of Wiki markup that are meant to be copied automatically ("transcluded") into a page. You add them by putting the template's name in.

Some templates take parameters, as well, which you separate with the pipe character.

title: Help:Wikitext quick reference


text:
Manuel Becerra

Manuel Becerra may refer to:

People

 * Manuel Becerra (settler) (1762–c. 1849), Tejano settler and politician
 * Manuel Becerra Bermúdez (1820–1896), Spanish politician
 * Manuel Becerra Fernández (1867–1940), Spanish politician who served as Minister of Justice during the Second Spanish Republic
 * Manuel Becerra Salazar (born 1983), Mexican poet

Places

 * Manuel Becerra (Madrid Metro), Madrid Metro Station

title: Manuel Becerra


text:
Bezgolosovo

Bezgolosovo (Безголосово) is a rural locality (a selo) and the administrative center of Bezgolosovsky Selsoviet, Aleysky District, Altai Krai, Russia. The population was 598 as of 2013. There are 13 streets.

Geography
Bezgolosovo is located on the Aley River, 15 km east of Aleysk (the district's administrative centre) by road. Bolshepanyushevo and Uspenovka are the nearest rural localities.

title: Bezgolosovo


text:
Calculus/Vectors

Introduction
In most mathematics courses up until this point, we deal with scalars. These are quantities which only need one number to express. For instance, the amount of gasoline used to drive to the grocery store is a scalar quantity because it only needs one number: 2 gallons.

In this unit, we deal with vectors. A vector is a directed line segment -- that is, a line segment that points one direction or the other. As such, it has an initial point and a terminal point. The vector starts at the initial point and ends at the terminal point, and the vector points towards the terminal point. A vector is drawn as a line segment with an arrow at the terminal point:

The same vector can be placed anywhere on the coordinate plane and still be the same vector -- the only two bits of information a vector represents are the magnitude and the direction. The magnitude is simply the length of the vector, and the direction is the angle at which it points. Since neither of these specify a starting or ending location, the same vector can be placed anywhere. To illustrate, all of the line segments below can be defined as the vector with magnitude $$4\sqrt2$$ and angle 45 degrees:

It is customary, however, to place the vector with the initial point at the origin as indicated by the black vector. This is called the standard position.

Component Form
In standard practice, we don't express vectors by listing the length and the direction. We instead use component form, which lists the height (rise) and width (run) of the vectors. It is written as follows:

$$\begin{pmatrix}\text{run}\\\text{rise}\end{pmatrix}$$

Other ways of denoting a vector in component form include:

$$\mathbf{(u_x,u_y)}$$ and $$\mathbf{\left\langle u_x,u_y\right\rangle}$$

From the diagram we can now see the benefits of the standard position: the two numbers for the terminal point's coordinates are the same numbers for the vector's rise and run. Note that we named this vector $$\mathbf{u}$$. Just as you can assign numbers to variables in algebra (usually $$x,y,z$$), you can assign vectors to variables in calculus. The letters $$u,v,w$$ are usually used, and either boldface or an arrow over the letter is used to identify it as a vector.

When expressing a vector in component form, it is no longer obvious what the magnitude and direction are. Therefore, we have to perform some calculations to find the magnitude and direction.

Magnitude
$$|\mathbf{u}|=\sqrt{u_x^2+u_y^2}$$

where $$u_x$$ is the width, or run, of the vector; $$u_y$$ is the height, or rise, of the vector. You should recognize this formula as the Pythagorean theorem. It is -- the magnitude is the distance between the initial point and the terminal point.

The magnitude of a vector can also be called the norm.

Direction
$$\tan(\theta)=\frac{u_y}{u_x}$$

where $$\theta$$ is the counter-clockwise angle made by the vector with the positive $$x$$-axis. This formula is simply the tangent formula for right triangles.

Vector Operations
For these definitions, assume: $$\mathbf{u}=\begin{pmatrix}u_x\\u_y\end{pmatrix},\mathbf{v}=\begin{pmatrix}v_x\\v_y\end{pmatrix}$$

Vector Addition
Vector Addition is often called tip-to-tail addition, because this makes it easier to remember.

The sum of the vectors you are adding is called the resultant vector, and is the vector drawn from the initial point (tip) of the first vector to the terminal point (tail) of the second vector. Although they look like the arrows, the pointy bit is the tail, not the tip. (Imagine you were walking the direction the vector was pointing... you would start at the flat end (tip) and walk toward the pointy end.)

It looks like this:

(Notice, the black lined vector is the sum of the two dotted line vectors!)

Numerically:

$$\binom46+\binom{1}{-3}=\binom53$$

Or more generally: $$\mathbf{u}+\mathbf{v}=\begin{pmatrix}u_x+v_x\\u_y+v_y\end{pmatrix} $$

Scalar Multiplication
Graphically, multiplying a vector by a scalar changes only the magnitude of the vector by that same scalar. That is, multiplying a vector by 2 will "stretch" the vector to twice its original magnitude, keeping the direction the same.

$$2\cdot\binom33=\binom66$$

Numerically, you calculate the resultant vector with this formula:

$$c\mathbf{u}=\begin{pmatrix}cu_x\\cu_y\end{pmatrix}$$, where $$c$$ is a constant scalar.

As previously stated, the magnitude is changed by the same constant:

$$|c\mathbf{u}|=|c||\mathbf{u}|$$

Since multiplying a vector by a constant results in a vector in the same direction, we can reason that two vectors are parallel if one is a constant multiple of the other -- that is, that $$\mathbf{u}||\mathbf{v}$$ if $$\mathbf{u}=c\mathbf{v}$$ for some constant $$c$$.

We can also divide by a non-zero scalar by instead multiplying by the reciprocal, as with dividing regular numbers:

$$\frac{\mathbf{u}}{c}=\frac{1}{c}\mathbf{u},c\ne0$$

Linear Functions

Given a function $$L$$ that accepts a vector as input and returns a vector or scalar as the output, function $$L$$ is considered to be "linear" if the following holds:

 * 1) For any vectors $$\mathbf{u}$$ and $$\mathbf{v}$$, it is the case that $$L(\mathbf{u}+\mathbf{v}) = L(\mathbf{u}) + L(\mathbf{v})$$.
 * 2) For any vector $$\mathbf{u}$$ and scalar $$c$$, it is the case that $$L(c\mathbf{u}) = cL(\mathbf{u})$$.

More generally, when given a function $$M$$ that has multiple vector valued parameters $$\mathbf{u}_1, \mathbf{u}_2, ..., \mathbf{u}_n$$, function $$M$$ is a "multi-linear" function if $$M$$ is linear with respect to each parameter while holding all other parameters constant:

For each $$i = 1, 2, ..., n$$ and vectors $$\mathbf{u}_1, \mathbf{u}_2, \dots, \mathbf{u}_n$$:
 * 1) For any vector $$\mathbf{v}$$ from the same vector space as $$\mathbf{u}_i$$, it is the case that $$M(\mathbf{u}_1,...,\mathbf{u}_i+\mathbf{v},...,\mathbf{u}_n) = M(\mathbf{u}_1,...,\mathbf{u}_i,...,\mathbf{u}_n) + M(\mathbf{u}_1,...,\mathbf{v},...,\mathbf{u}_n)$$
 * 2) For any scalar $$c$$, it is the case that $$M(\mathbf{u}_1,...,c\mathbf{u}_i,...,\mathbf{u}_n) = cM(\mathbf{u}_1,...,\mathbf{u}_i,...,\mathbf{u}_n)$$

If $$n = 2$$, then $$M$$ is "bilinear". Bilinear functions include the dot product and the cross product.

Dot Product
The dot product is a way of multiplying two vectors to produce a scalar value. Because it combines the components of two vectors to form a /scalar/, it is sometimes called a scalar product. If you were asked to take the 'dot product of two rectangular vectors' you would do the following: $$\mathbf{u}\cdot\mathbf{v}=u_xv_x+u_yv_y$$

It is very important to note that the dot product of two vectors does not result in another vector, it gives you a scalar, just a numerical value.

Another common pitfall may arise if your vectors are not in rectangular ('cartesian') format. Sometimes, vectors are instead expressed in polar coordinates, where the first component is the vector's magnitude (length) and the second is the angle from the $$x$$-axis at which the vector should be oriented. Dot products cannot be performed using the conventional method on these sorts of vectors; vectors in polar format must be converted to their equivalent rectangular form before you can work with them using the formula given above. A common way to convert to rectangular coordinates is to imagine that the vector was projected horizontally and vertically to form a right triangle. You could then use properties of sin and cos to find the length of the two legs the right triangle. The horizontal length would then be the x-component of the rectangular expression of the vector and the vertical length would be the y-component. Remember that if the vector is pointing down or to the left, the corresponding components would have to be negative to indicate that.

With some rearrangement and trigonometric manipulation, we can see that the number that results from the dot product of two vectors is a surprising and useful identity:

$$\mathbf{u}\cdot\mathbf{v}=|\mathbf{u}||\mathbf{v}|\cos(\theta)$$

where $$\theta$$ is the angle between the two vectors. This provides a convenient way of finding the angle between two vectors: $$\cos(\theta)=\frac{\mathbf{u}\cdot\mathbf{v}}{|\mathbf{u}||\mathbf{v}|}$$ Notice that the dot product is 'commutative', that is: $$\mathbf{u}\cdot\mathbf{v}=\mathbf{v}\cdot\mathbf{u}$$ Also, the dot product of two vectors will be the length of the vector squared: $$\mathbf{u}\cdot\mathbf{u}=u_xu_x+u_yu_y=(u_x)^2+(u_y)^2$$ and by the Pythagorean theorem, $$(u_x)^2+(u_y)^2=|\mathbf u|^2$$

The dot product can be visualized as the length of a projection of one vector on to the other. In other words, the dot product asks 'how much magnitude of this vector is going in the direction of that vector?'

Deriving the Dot Product
Start with the following definition for the dot product: $$\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos(\theta)$$ where $$\theta$$ is the angle between $$\mathbf{u}$$ and $$\mathbf{v}$$.

The formula $$\mathbf{u}\cdot\mathbf{v} = u_xv_x + u_yv_y$$ can be derived from the above definition through various approaches:

Approach #1

One of the more direct approaches is to use the law of cosines. Create a triangle $$\Delta AOB$$ with vertices $$A(u_x,u_y)$$, $$O(0,0)$$, and $$B(v_x,v_y)$$. The displacement $$\vec{OA} = \mathbf{u}$$, the displacement $$\vec{OB} = \mathbf{v}$$, and the displacement $$\vec{AB} = \mathbf{v}-\mathbf{u}$$. The angle $$\angle AOB = \theta$$.

The lengths of the sides of the triangle are $$|OA| = |\mathbf{u}|$$, and $$|OB| = |\mathbf{v}|$$, and $$|AB| = |\mathbf{v}-\mathbf{u}|$$. Applying the law of cosines gives:

$$|AB|^2 = |OA|^2 + |OB|^2 - 2|OA||OB|\cos(\angle AOB)$$ $$\iff |\mathbf{v}-\mathbf{u}|^2 = |\mathbf{u}|^2 + |\mathbf{v}|^2 - 2|\mathbf{u}||\mathbf{v}|\cos(\theta)$$ $$\iff (v_x-u_x)^2 + (v_y-u_y)^2 = (u_x^2+u_y^2) + (v_x^2+v_y^2) - 2|\mathbf{u}||\mathbf{v}|\cos(\theta)$$ $$\iff - 2u_xv_x - 2u_yv_y = -2|\mathbf{u}||\mathbf{v}|\cos(\theta)$$ $$\iff |\mathbf{u}||\mathbf{v}|\cos(\theta) = u_xv_x + u_yv_y$$

Therefore $$\mathbf{u}\cdot\mathbf{v} = u_xv_x + u_yv_y$$.

Approach #2

A more intuitive derivation of $$\mathbf{u}\cdot\mathbf{v} = u_xv_x + u_yv_y$$ uses the fact that the dot product is a bilinear operator. To establish that the dot product is a bilinear operator, the following must be established:

 * 1) Holding $$\mathbf{u}$$ constant, the dot product $$\mathbf{u} \cdot \mathbf{v}$$ must be linear with respect to $$\mathbf{v}$$.
 * 2) Holding $$\mathbf{v}$$ constant, the dot product $$\mathbf{u} \cdot \mathbf{v}$$ must be linear with respect to $$\mathbf{u}$$.

Since it is readily apparent from the definition $$\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos(\theta)$$ that $$\mathbf{u}\cdot\mathbf{v} = \mathbf{v}\cdot\mathbf{u}$$, linearity with respect to $$\mathbf{v}$$ implies linearity with respect to $$\mathbf{u}$$. It is hence only necessary to establish that the dot product is linear with respect to $$\mathbf{v}$$ to establish bilinearity.

$$\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}||\mathbf{v}|\cos(\theta) = |\mathbf{u}|\text{proj}(\mathbf{v}|\mathbf{u})$$ where $$\text{proj}(\mathbf{v}|\mathbf{u}) = |\mathbf{v}|\cos(\theta)$$ is the "orthogonal projection" of vector $$\mathbf{v}$$ onto a line $$L(\mathbf{u})$$ whose direction is the direction of $$\mathbf{u}$$. $$\text{proj}(\mathbf{v}|\mathbf{u})$$ is the component of $$\mathbf{v}$$ that is parallel to $$L(\mathbf{u})$$. By drawing similar triangles, one observes that $$\text{proj}(\mathbf{v}|\mathbf{u})$$ is linear with respect to $$\mathbf{v}$$ while $$\mathbf{u}$$ is held constant. The dot product $$\mathbf{u}\cdot\mathbf{v} = |\mathbf{u}|\text{proj}(\mathbf{v}|\mathbf{u})$$ is linear with respect to $$\mathbf{v}$$, and therefore the dot product is a bilinear operator.

The bilinearity of the dot product now enables the derivation:

$$\mathbf{u}\cdot\mathbf{v} = \begin{pmatrix} u_x \\ u_y \end{pmatrix} \cdot \begin{pmatrix} v_x \\ v_y \end{pmatrix}$$ $$ = \left(u_x\begin{pmatrix} 1 \\ 0 \end{pmatrix} + u_y\begin{pmatrix} 0 \\ 1 \end{pmatrix}\right) \cdot \left(v_x\begin{pmatrix} 1 \\ 0 \end{pmatrix} + v_y\begin{pmatrix} 0 \\ 1 \end{pmatrix}\right)$$ $$ = \left(\left(u_x\begin{pmatrix} 1 \\ 0 \end{pmatrix} + u_y\begin{pmatrix} 0 \\ 1 \end{pmatrix}\right) \cdot \begin{pmatrix} 1 \\ 0 \end{pmatrix}\right)v_x + \left(\left(u_x\begin{pmatrix} 1 \\ 0 \end{pmatrix} + u_y\begin{pmatrix} 0 \\ 1 \end{pmatrix}\right) \cdot \begin{pmatrix} 0 \\ 1 \end{pmatrix}\right)v_y$$ $$ = \left(\begin{pmatrix} 1 \\ 0 \end{pmatrix} \cdot \begin{pmatrix} 1 \\ 0 \end{pmatrix}\right)u_xv_x + \left(\begin{pmatrix} 0 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 1 \\ 0 \end{pmatrix}\right)u_yv_x + \left(\begin{pmatrix} 1 \\ 0 \end{pmatrix} \cdot \begin{pmatrix} 0 \\ 1 \end{pmatrix}\right)u_xv_y + \left(\begin{pmatrix} 0 \\ 1 \end{pmatrix} \cdot \begin{pmatrix} 0 \\ 1 \end{pmatrix}\right)u_yv_y$$ $$ = 1u_xv_x + 0u_yv_x + 0u_xv_y + 1u_yv_y$$ $$ = u_xv_x + u_yv_y$$

Therefore $$\mathbf{u}\cdot\mathbf{v} = u_xv_x + u_yv_y$$.

Unit Vectors
A unit vector is a vector with a magnitude of 1. The unit vector of u is a vector in the same direction as $$\mathbf{u}$$, but with a magnitude of 1:

The process of finding the unit vector of $$\mathbf{u}$$ is called normalization. As mentioned in scalar multiplication, multiplying a vector by constant $$c$$ will result in the magnitude being multiplied by $$c$$. We know how to calculate the magnitude of $$\mathbf{u}$$. We know that dividing a vector by a constant will divide the magnitude by that constant. Therefore, if that constant is the magnitude, dividing the vector by the magnitude will result in a unit vector in the same direction as $$\mathbf{u}$$ :

$$\mathbf{w}=\frac{\mathbf{u}}{|\mathbf{u}|}$$, where $$\mathbf{w}$$ is the unit vector of $$\mathbf{u}$$

Standard Unit Vectors
A special case of Unit Vectors are the Standard Unit Vectors $$\mathbf{i},\mathbf{j}$$ : $$\mathbf{i}$$ points one unit directly right in the $$x$$ direction, and $$\mathbf{j}$$ points one unit directly up in the $$y$$ direction:

$$\mathbf{i}=\binom10$$

$$\mathbf{j}=\binom01$$

Using the scalar multiplication and vector addition rules, we can then express vectors in a different way: $$\binom{x}{y}=x\mathbf{i}+y\mathbf{j}$$

If we work that equation out, it makes sense. Multiplying $$x$$ by $$\mathbf{i}$$ will result in the vector $$\binom{x}{0}$$. Multiplying $$y$$ by $$\mathbf{j}$$ will result in the vector $$\binom0y$$. Adding these two together will give us our original vector, $$\binom{x}{y}$$. Expressing vectors using $$\mathbf{i},\mathbf{j}$$ is called standard form.

Projection and Decomposition of Vectors
Sometimes it is necessary to decompose a vector $$\mathbf{u}$$ into two components: one component parallel to a vector $$\mathbf{v} $$, which we will call $$\mathbf{u}_\parallel$$ ; and one component perpendicular to it, $$\mathbf{u}_\perp$$.

Since the length of $$\mathbf{u}_\parallel$$ is $$|\mathbf{u}|\cdot\cos(\theta)$$, it is straightforward to write down the formulas for $$\mathbf{u}_\perp$$ and $$\mathbf{u}_\parallel$$ :

$$\mathbf{u_\parallel}=|\mathbf{u}|*\frac{(\mathbf{u}\cdot\mathbf{v})}{(|\mathbf{u}||\mathbf{v}|)}*\frac{\mathbf{v}}{|\mathbf{v}|}=\frac{ \mathbf{u}\cdot\mathbf{v}}{|\mathbf{v}|^2}\mathbf{v}$$ and $$\mathbf{u}_\perp=\mathbf{u}-\mathbf{u}_\parallel$$

Length of a vector
The length of a vector is given by the dot product of a vector with itself, and $$\theta=0\ rad$$:

$$\mathbf{u}\cdot\mathbf{u}=|\mathbf{u}||\mathbf{u}|\cos(\theta)=|\mathbf{u}|^2$$

Perpendicular vectors
If the angle $$ \theta $$ between two vectors is 90 degrees or $$\tfrac{\pi}{2}$$ (if the two vectors are orthogonal to each other), that is the vectors are perpendicular, then the dot product is 0. This provides us with an easy way to find a perpendicular vector: if you have a vector $$ \mathbf{u}=\begin{pmatrix}u_x\\u_y\end{pmatrix}$$, a perpendicular vector can easily be found by either $$\mathbf{v}=\begin{pmatrix}-u_y\\u_x\end{pmatrix}=-\begin{pmatrix}u_y\\-u_x\end{pmatrix}$$

Polar coordinates
Polar coordinates are an alternative two-dimensional coordinate system, which is often useful when rotations are important. Instead of specifying the position along the $$x$$ and $$y$$ axes, we specify the distance from the origin, $$r$$, and the direction, an angle $$\theta$$.

Looking at this diagram, we can see that the values of $$x,y$$ are related to those of $$r$$ and $$\theta$$ by the equations $$\begin{matrix}x=r\cos(\theta)&r=\sqrt{x^2+y^2}\\y=r\sin(\theta)&\theta=\arctan\left(\frac{y}{x}\right)\end{matrix}$$

Because tan-1 is multivalued, care must be taken to select the right value.

Just as for Cartesian coordinates the unit vectors that point in the $$x$$ and $$y$$ directions are special, so in polar coordinates the unit vectors that point in the $$r$$ and $$\theta$$ directions are also special.

We will call these vectors $$\hat{\mathbf{r}}$$ and $$\hat{\boldsymbol{\theta}}$$, pronounced r-hat and theta-hat. Putting a circumflex over a vector this way is often used to mean the unit vector in that direction.

Again, on looking at the diagram we see,

$$\begin{matrix} \mathbf{i}=\hat{\mathbf{r}}\cos(\theta)-\hat{\boldsymbol{\theta}}\sin(\theta)&\hat{\mathbf{r}}=\frac{x}{r}\mathbf{i}+\frac{y}{r}\mathbf{j}\\ \mathbf{j}=\hat{\mathbf{r}}\sin(\theta)+\hat{\boldsymbol{\theta}}\cos(\theta)&\hat{\boldsymbol{\theta}}=-\frac{y}{r}\mathbf{i}+\frac{x}{r}\mathbf{j} \end{matrix}$$

Basic definition
Two-dimensional Cartesian coordinates as we've discussed so far can be easily extended to three-dimensions by adding one more value: $$z$$. If the standard $$(x,y)$$ coordinate axes are drawn on a sheet of paper, the $$z$$-axis would extend upwards off of the paper.

Similar to the two coordinate axes in two-dimensional coordinates, there are three coordinate planes in space. These are the $$xy$$-plane, the $$yz$$-plane, and the $$xz$$-plane. Each plane is the "sheet of paper" that contains both axes the name mentions. For instance, the $$yz$$-plane contains both the $$y$$ and $$z$$ axes and is perpendicular to the $$x$$-axis.

Therefore, vectors can be extended to three dimensions by simply adding the $$z$$ value.

$$\mathbf{u}=\begin{pmatrix}x\\y\\z\end{pmatrix}$$

To facilitate standard form notation, we add another standard unit vector:

$$\mathbf{k}=\begin{pmatrix}0\\0\\1\end{pmatrix}$$

Again, both forms (component and standard) are equivalent.

$$\begin{pmatrix}1\\2\\3\end{pmatrix}=1\mathbf{i}+2\mathbf{j}+3\mathbf{k}$$

Magnitude: Magnitude in three dimensions is the same as in two dimensions, with the addition of a $$z$$ term in the radicand.

$$|\mathbf{u}|=\sqrt{u_x^2+u_y^2+u_z^2}$$

Three dimensions
The polar coordinate system is extended into three dimensions with two different coordinate systems, the cylindrical and spherical coordinate systems, both of which include two-dimensional or planar polar coordinates as a subset. In essence, the cylindrical coordinate system extends polar coordinates by adding an additional distance coordinate, while the spherical system instead adds an additional angular coordinate.

Cylindrical coordinates
The cylindrical coordinate system is a coordinate system that essentially extends the two-dimensional polar coordinate system by adding a third coordinate measuring the height of a point above the plane, similar to the way in which the Cartesian coordinate system is extended into three dimensions. The third coordinate is usually denoted $$h$$ (or simply $$z$$, i.e., same notation as Cartesian coordinate system), making the three cylindrical coordinates $$(r,\theta,h)$$ (or $$(r,\theta,z)$$).

The three cylindrical coordinates can be converted to Cartesian coordinates by
 * $$\begin{align}x&=r\cos(\theta)\\y&=r\sin(\theta)\\z&=h\end{align}$$

Spherical coordinates

Polar coordinates can also be extended into three dimensions using the coordinates $$(\rho,\phi,\theta)$$ (or $$(\rho,\varphi,\theta)$$), where $$\rho$$ is the distance from the origin, $$\phi$$ (or $$\varphi$$) is the angle from the $$z$$-axis (called the colatitude or zenith and measured from 0 to 180°) and $$\theta$$ is the angle from the $$x$$-axis (as in the polar coordinates). This coordinate system, called the spherical coordinate system, is similar to the latitude and longitude system used for Earth, with the origin in the centre of Earth, the latitude $$\delta$$ being the complement of $$\phi$$, determined by $$\delta=90^\circ-\phi$$ , and the longitude $$l$$ being measured by $$l=\theta-180^\circ$$.

The three spherical coordinates are converted to Cartesian coordinates by
 * $$\begin{align}x&=\rho\sin(\phi)\cos(\theta)\\y&=\rho\sin(\phi)\sin(\theta)\\z&=\rho\cos(\phi)\end{align} $$

 * $$\rho=\sqrt{x^2+y^2+z^2}$$

 * $$\theta=\arctan\left(\frac{y}{x}\right)$$

 * $$\phi=\arccos\left(\frac{z}{\rho}\right)$$

Cross Product
The cross product of two vectors is a determinant:

 * $$\mathbf{u}\times\mathbf{v}=

\begin{vmatrix} \mathbf{i}&\mathbf{j}&\mathbf{k}\\ u_x&u_y&u_z\\ v_x&v_y&v_z \end{vmatrix}$$

and is also a pseudovector.

The cross product of two vectors is orthogonal to both vectors. The magnitude of the cross product is the product of the magnitude of the vectors and the sin of the angle between them.
 * $$|\mathbf{u}\times\mathbf{v}|=|\mathbf{u}||\mathbf{v}|\sin(\theta)$$

This magnitude is the area of the parallelogram defined by the two vectors.

The cross product is linear and anticommutative. For any numbers $$a,b$$ ,
 * $$\mathbf{u}\times\left(a\mathbf{v}+b\mathbf{w}\right)=a\mathbf{u}\times\mathbf{v}+b\mathbf{u}\times\mathbf{w}\qquad\mathbf{u}\times\mathbf{v}=-\mathbf{v}\times\mathbf{u}$$

If both vectors point in the same direction, their cross product is 0.

Deriving the Cross Product

Start with the following definition for the cross product: $$\mathbf{u}\times\mathbf{v} = (|\mathbf{u}||\mathbf{v}|\sin\theta)\hat{\mathbf{n}}$$. Vector $$\hat{\mathbf{n}}$$ is a unit length vector that is perpendicular to both $$\mathbf{u}$$ and $$\mathbf{v}$$ and oriented according to the "right hand rule". Angle $$\theta$$ is the counterclockwise angle from $$\mathbf{u}$$ to $$\mathbf{v}$$ within the plane that is orthogonal to $$\hat{\mathbf{n}}$$.

The formula $$\mathbf{u}\times\mathbf{v} = (u_yv_z-u_zv_y)\mathbf{i} + (u_zv_x-u_xv_z)\mathbf{j} + (u_xv_y-u_yv_x)\mathbf{k}$$ can be derived by exploiting the bilinearity of the cross product. To establish the cross product as a bilinear operator, the following must be established:

 * 1) Holding $$\mathbf{u}$$ constant, the cross product $$\mathbf{u}\times\mathbf{v}$$ must be linear with respect to $$\mathbf{v}$$.
 * 2) Holding $$\mathbf{v}$$ constant, the cross product $$\mathbf{u}\times\mathbf{v}$$ must be linear with respect to $$\mathbf{u}$$.

From the definition $$\mathbf{u}\times\mathbf{v} = (|\mathbf{u}||\mathbf{v}|\sin\theta)\hat{\mathbf{n}}$$, the anticommutative property of the cross product can be inferred: $$\mathbf{u}\times\mathbf{v} = -\mathbf{v}\times\mathbf{u}$$ (vector $$\hat{\mathbf{n}}$$ reverses direction when $$\mathbf{u}$$ and $$\mathbf{v}$$ are swapped). This means that linearity with respect to $$\mathbf{v}$$ implies linearity with respect to $$\mathbf{u}$$. It is hence only necessary to establish that the cross product is linear with respect to $$\mathbf{v}$$ to establish bilinearity.

$$\mathbf{u}\times\mathbf{v} = (|\mathbf{u}||\mathbf{v}|\sin\theta)\hat{\mathbf{n}} = |\mathbf{u}|\textbf{rotate}(\textbf{perp}(\mathbf{v}|\mathbf{u})|\mathbf{u})$$ where:
 * $$\textbf{perp}(\mathbf{v}|\mathbf{u})$$ is the component of $$\mathbf{v}$$ that is perpendicular to a line $$L(\mathbf{u})$$ whose direction is the direction of $$\mathbf{u}$$. $$\textbf{perp}(\mathbf{v}|\mathbf{u}) = (|\mathbf{v}|\sin\theta)\hat{\mathbf{m}}$$ where vector $$\hat{\mathbf{m}}$$ is a unit length vector that is parallel to $$\textbf{perp}(\mathbf{v}|\mathbf{u})$$.
 * $$\textbf{rotate}(\mathbf{w}|\mathbf{u})$$ is a 90 degree counterclockwise rotation of $$\mathbf{w}$$ around $$L(\mathbf{u})$$. Note that $$\textbf{rotate}(\hat{\mathbf{m}}|\mathbf{u}) = \hat{\mathbf{n}}$$.

It can easily be observed that $$\textbf{perp}(\mathbf{v}|\mathbf{u})$$ is linear with respect to $$\mathbf{v}$$ with $$\mathbf{u}$$ held constant, and that $$\textbf{rotate}(\mathbf{w}|\mathbf{u})$$ is linear with respect to $$\mathbf{w}$$ with $$\mathbf{u}$$ held constant. The cross product $$\mathbf{u}\times\mathbf{v} = (|\mathbf{u}||\mathbf{v}|\sin\theta)\hat{\mathbf{n}} = |\mathbf{u}|\textbf{rotate}(\textbf{perp}(\mathbf{v}|\mathbf{u})|\mathbf{u})$$ is linear with respect to $$\mathbf{v}$$, and therefore the cross product is a bilinear operator.

The bilinearity of the cross product now enables the derivation:

$$\mathbf{u}\times\mathbf{v} = (u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k})\times(v_x\mathbf{i}+v_y\mathbf{j}+v_z\mathbf{k})$$ $$ = v_x((u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k})\times\mathbf{i}) + v_y((u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k})\times\mathbf{j}) + v_z((u_x\mathbf{i}+u_y\mathbf{j}+u_z\mathbf{k})\times\mathbf{k})$$ $$ = u_xv_x(\mathbf{i}\times\mathbf{i}) + u_yv_x(\mathbf{j}\times\mathbf{i}) + u_zv_x(\mathbf{k}\times\mathbf{i}) + u_xv_y(\mathbf{i}\times\mathbf{j}) + u_yv_y(\mathbf{j}\times\mathbf{j}) + u_zv_y(\mathbf{k}\times\mathbf{j}) + u_xv_z(\mathbf{i}\times\mathbf{k}) + u_yv_z(\mathbf{j}\times\mathbf{k}) + u_zv_z(\mathbf{k}\times\mathbf{k})$$ $$ = u_xv_y\mathbf{0} + u_yv_x(-\mathbf{k}) + u_zv_x\mathbf{j} + u_xv_y\mathbf{k} + u_yv_y\mathbf{0} + u_zv_y(-\mathbf{i}) + u_xv_z(-\mathbf{j}) + u_yv_z\mathbf{i} + u_zv_z\mathbf{0}$$ $$ = (u_yv_z-u_zv_y)\mathbf{i} + (u_zv_x-u_xv_z)\mathbf{j} + (u_xv_y-u_yv_x)\mathbf{k}$$

Therefore $$\mathbf{u}\times\mathbf{v} = (u_yv_z-u_zv_y)\mathbf{i} + (u_zv_x-u_xv_z)\mathbf{j} + (u_xv_y-u_yv_x)\mathbf{k}$$.

Triple Products
If we have three vectors we can combine them in two ways, a triple scalar product, $$\mathbf{u}\cdot(\mathbf{v}\times\mathbf{w})$$ and a triple vector product $$\mathbf{u}\times(\mathbf{v}\times\mathbf{w})$$

The triple scalar product is a determinant
 * $$\mathbf{u}\cdot(\mathbf{v}\times\mathbf{w})=\begin{vmatrix}u_x&u_y&u_z\\v_x&v_y&v_z\\w_x&w_y&w_z\end{vmatrix}$$

If the three vectors are listed clockwise, looking from the origin, the sign of this product is positive. If they are listed anticlockwise the sign is negative.

The order of the cross and dot products doesn't matter.
 * $$\mathbf{u}\cdot(\mathbf{v}\times\mathbf{w})=(\mathbf{u}\times\mathbf{v})\cdot\mathbf{w}$$

Either way, the absolute value of this product is the volume of the parallelepiped defined by the three vectors $$\mathbf{u},\mathbf{v},\mathbf{w}$$

The triple vector product can be simplified $$\mathbf{u}\times(\mathbf{v}\times\mathbf{w})=(\mathbf{u}\cdot\mathbf{w})\mathbf{v}-(\mathbf{u}\cdot\mathbf{v})\mathbf{w}$$ This form is easier to do calculations with.

The triple vector product is not associative. $$\mathbf{u}\times(\mathbf{v}\times\mathbf{w})\ne(\mathbf{u}\times\mathbf{v})\times\mathbf{w}$$

There are special cases where the two sides are equal, but in general the brackets matter. They must not be omitted.

Three-Dimensional Lines and Planes
We will use $$\mathbf r$$ to denote the position of a point.

The multiples of a vector, $$\mathbf a$$ all lie on a line through the origin. Adding a constant vector $$\mathbf b$$ will shift the line, but leave it straight, so the equation of a line is,
 * $$\mathbf{r}=s\mathbf{a}+\mathbf{b}$$

This is a parametric equation. The position is specified in terms of the parameter $$s$$.

Any linear combination of two vectors, $$\mathbf{a},\mathbf{b}$$ lies on a single plane through the origin, provided the two vectors are not colinear. We can shift this plane by a constant vector again and write
 * $$\mathbf{r}=s\mathbf{a}+t\mathbf{b}+\mathbf{c}$$

If we choose $$\mathbf{a},\mathbf{b}$$ to be orthonormal vectors in the plane (i.e. unit vectors at right angles) then $$s,t$$ are Cartesian coordinates for points in the plane.

These parametric equations can be extended to higher dimensions.

Instead of giving parametric equations for the line and plane, we could use constraints. E.g., for any point in the $$xy$$ plane $$z=0$$

For a plane through the origin, the single vector normal to the plane, $$\mathbf n$$, is at right angle with every vector in the plane, by definition, so
 * $$\mathbf{r}\cdot\mathbf{n}=0$$

is a plane through the origin, normal to $$\mathbf n$$.

For planes not through the origin we get
 * $$(\mathbf{r}-\mathbf{a})\cdot\mathbf{n}=0\qquad\mathbf{r}\cdot\mathbf{n}=\mathbf{a}\cdot\mathbf{n}$$

A line lies on the intersection of two planes, so it must obey the constraint for both planes, i.e.
 * $$\mathbf{r}\cdot\mathbf{n}=a\qquad\mathbf{r}\cdot\mathbf{m}=b$$

These constraint equations con also be extended to higher dimensions.

Introduction to Vector-Valued Functions
Vector-Valued Functions are functions that instead of giving a resultant scalar value, give a resultant vector value. These aid in the creation of direction and vector fields, and are therefore used in physics to aid with visualizations of electric, magnetic, and many other types of fields. They are of the following form:

$$\mathbf{F(t)}=\begin{pmatrix}\mathbf{a_1(t)}\\\vdots\\\mathbf{a_n(t)}\end{pmatrix}$$

Limits, Derivatives, and Integrals
Put simply, the limit of a vector-valued function is the limit of its parts.

Suppose $$\lim_{t\to c}\mathbf{F}(t)=\mathbf{L}=\begin{pmatrix}\mathbf{a_1}\\\vdots\\\mathbf{a_n}\end{pmatrix}$$
 * Proof

Therefore for any $$\varepsilon>0$$ there is a $$\phi>0$$ such that

$$0<|t-c|<\phi\implies|\mathbf{F}(t)-\mathbf{L}|<\varepsilon$$

But by the triangle inequality $$|a_1|\le|\mathbf{F}|\le|a_1|+\cdots+|a_n|$$

$$|a_1(t)-a_1|\le|\mathbf{F}(t)-\mathbf{L}|$$

So

$$0<|t-c|<\phi\implies|a_1(t)-a_1|<\varepsilon$$

Therefore $$\lim_{t\to c}a_1(t)=a_1$$

A similar argument can be used through parts $$a_n(t)$$.

Now let $$\lim_{t\to c}\mathbf{F}(t)=\mathbf{L}=\begin{pmatrix}\mathbf{a_1}\\\vdots\\\mathbf{a_n}\end{pmatrix}$$ again, and that for any $$\varepsilon>0$$ there is a corresponding $$\phi>0$$ such $$0<|t-c|<\phi$$ implies

$$|a_n(t)-a_n|<\frac{\varepsilon}{n}$$

Then

$$0<|t-c|<\phi\implies|\mathbf{F}(t)-\mathbf{L}|\le\frac{\varepsilon_1}{n}+\cdots+\frac{\varepsilon_n}{n}=\varepsilon$$

therefore:

$$\lim_{t\to c}\mathbf{F}(t)=\mathbf{L}=\begin{pmatrix}\mathbf{a_1}\\\vdots\\\mathbf{a_n}\end{pmatrix}=\begin{pmatrix}\lim\limits_{t\to c}\mathbf{a_1(t)}\\\vdots\\\lim\limits_{t\to c}\mathbf{a_n(t)}\end{pmatrix}$$

From this we can then create an accurate definition of a derivative of a vector-valued function:

$$\begin{align} \mathbf{F}'(t)&=\lim_{h\to0}\frac{\mathbf{F}(t+h)-\mathbf{F}(t)}{h}=\begin{pmatrix}\mathbf{a_1(t)}\\\vdots\\\mathbf{a_n(t)}\end{pmatrix}\\ &=\lim_{h\to0}\frac{\begin{pmatrix}\mathbf{a_1(t+h)}\\\vdots\\\mathbf{a_n(t+h)}\end{pmatrix}-\begin{pmatrix}\mathbf{a_1(t)}\\\vdots\\\mathbf{a_n(t)}\end{pmatrix}}{h}\\ &=\begin{pmatrix}\lim\limits_{h\to0}\dfrac{a_1(t+h)-a_1(t)}{h}\\\vdots\\\lim\limits_{h\to0}\dfrac{a_n(t+h)-a_n(t)}{h}\end{pmatrix} \end{align}$$

The final step was accomplished by taking what we just did with limits.

By the Fundamental Theorem of Calculus integrals can be applied to the vector's components.

In other words: the limit of a vector function is the limit of its parts, the derivative of a vector function is the derivative of its parts, and the integration of a vector function is the integration of it parts.

Velocity, Acceleration, Curvature, and a brief mention of the Binormal
Assume we have a vector-valued function which starts at the origin and as its independent variables changes the points that the vectors point at trace a path.

We will call this vector $$\mathbf{r}(t)$$, which is commonly known as the position vector.

If $$\mathbf{r}$$ then represents a position and t represents time, then in model with Physics we know the following:

 * $$\mathbf{r}(t+h)-\mathbf{r}(t)$$ is displacement.
 * $$\mathbf{r}'(t)=\mathbf{v}(t)$$ where $$\mathbf{v}(t)$$ is the velocity vector.
 * $$|\mathbf{v}(t)|$$ is the speed.
 * $$\mathbf{r}''(t)=\mathbf{v}'(t)=\mathbf{a}(t)$$ where $$\mathbf{a}(t)$$ is the acceleration vector.

The only other vector that comes in use at times is known as the curvature vector.

The vector $$\mathbf{T}(t)$$ used to find it is known as the unit tangent vector, which is defined as $$\frac{\mathbf{v}(t)}{|\mathbf{v}(t)|}$$ or shorthand $$\mathbf{\hat v}$$.

The vector normal $$\mathbf{N}$$ to this then is $$\frac{\mathbf{T}'(t)}{|\mathbf{v}(t)|}$$.

We can verify this by taking the dot product

$$\mathbf{T}\cdot\mathbf{N}=0$$

Also note that $$|\mathbf{v}(t)|=\frac{ds}{dt}$$

and

$$\mathbf{T}(t)=\frac{v}{|v|}=\frac{\frac{dr}{dt}}{\frac{ds}{dt}}=\frac{dr}{ds}$$

and

$$\mathbf{N}=\frac{\mathbf{T}'(t)}{|\mathbf{v}(t)|}=\frac{\frac{dT}{dt}}{\frac{ds}{dt}}=\frac{dT}{ds}$$

Then we can actually verify:

$$\frac{d}{ds}(\mathbf{T}\cdot\mathbf{T})=\frac{d}{ds}(1)$$

$$\frac{dT}{ds}\cdot\mathbf{T}+\mathbf{T}\cdot\frac{dT}{ds}=0$$

$$2\mathbf{T}\cdot\frac{dT}{ds}=0$$

$$\mathbf{T}\cdot\frac{dT}{ds}=0$$

$$\mathbf{T}\cdot\mathbf{N}=0$$

Therefore $$\mathbf{N}$$ is perpendicular to $$\mathbf{T}$$

What this gives rise to is the Unit Normal Vector $$\frac{\frac{dT}{ds}}{\left|\frac{dT}{ds}\right|}$$ of which the top-most vector is the Normal vector, but the bottom half $$(|\frac{dT}{ds}|)^{-1}$$ is known as the curvature. Since the Normal vector points toward the inside of a curve, the sharper a turn, the Normal vector has a large magnitude, therefore the curvature has a small value, and is used as an index in civil engineering to reflect the sharpness of a curve (clover-leaf highways, for instance).

The only other thing not mentioned is the Binormal that occurs in 3-d curves $$\mathbf{T}\times\mathbf{N}=\mathbf{B}$$, which is useful in creating planes parallel to the curve.

title: Calculus/Vectors


text:
Moto Z4

The Moto Z4 (stylized as Moto z⁴ by Motorola) is an Android phablet developed by Motorola Mobility, as the successor to the Moto Z3 and Moto Z3 Play. It was released in May 2019, and made available in June.

Hardware
The SD675 SOC is much closer to the SD636 from the Moto Z3 Play than the SD835 from the Moto Z3. Benchmarks from Cnet shows it beating the Moto Z3 Play, roughly tieing the Pixel 3A and losing to the Moto Z3 and OnePlus 6T.

The front and rear cameras were upgraded compared to the previous models. The rear camera goes from two 12MP to a single 48MP. The front camera goes from 12MP to 25MP.

The battery is upsized from the 3000mAh found on the Moto Z3 to 3600mAh.

The 3.5mm headphone jack returns after being absent on the Moto Z3.

Reception
Cnet scored it a 7 out of 10 while stating "As a budget phone, the Moto Z4 doesn't beat the similarly priced Pixel 3a XL or OnePlus 6T."

title: Moto Z4


text:
Scientific computing

Computational science, also known as scientific computing or scientific computation (SC), is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems. It is an area of science which spans many disciplines, but at its core it involves the development of models and simulations to understand natural systems.

 * Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve science (e.g., biological, physical, and social), engineering, and humanities problems
 * Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components needed to solve computationally demanding problems
 * The computing infrastructure that supports both the science and engineering problem solving and the developmental computer and information science

Best Practices
The purpose of this resource is to describe best practices in the field of scientific computing. Computing has become an essential scientific tool in research, yet techniques in this discipline are often not taught.

Summary of Best Practices (reproduced from Wilson et al 2014)

 * 1) Write programs for people, not computers.
 * 2) A program should not require its readers to hold more than a handful of facts in memory at once.
 * 3) Make names consistent, distinctive, and meaningful.
 * 4) Make code style and formatting consistent.
 * 5) Let the computer do the work.
 * 6) Make the computer repeat tasks.
 * 7) Save recent commands in a file for re-use.
 * 8) Use a build tool to automate workflows.
 * 9) Make incremental changes.
 * 10) Work in small steps with frequent feedback and course correction.
 * 11) Use a version control system.
 * 12) Put everything that has been created manually in version control.
 * 13) Don't repeat yourself (or others).
 * 14) Every piece of data must have a single authoritative representation in the system.
 * 15) Modularize code rather than copying and pasting.
 * 16) Re-use code instead of rewriting it.
 * 17) Plan for mistakes.
 * 18) Add assertions to programs to check their operation.
 * 19) Use an off-the-shelf unit testing library.
 * 20) Turn bugs into test cases.
 * 21) Use a symbolic debugger.
 * 22) Optimize software only after it works correctly.
 * 23) Use a profiler to identify bottlenecks.
 * 24) Write code in the highest-level language possible.
 * 25) Document design and purpose, not mechanics.
 * 26) Document interfaces and reasons, not implementations.
 * 27) Refactor code in preference to explaining how it works.
 * 28) Embed the documentation for a piece of software in that software.
 * 29) Collaborate.
 * 30) Use pre-merge code reviews.
 * 31) Use pair programming when bringing someone new up to speed and when tackling particularly tricky problems.
 * 32) Use an issue tracking tool.

title: Scientific computing


text:
Wikipedia:Articles for deletion/Adam Goldenberg

The result was   delete. The Bushranger One ping only 03:04, 25 July 2012 (UTC)

Adam Goldenberg

 * – ( View AfD View log  •  Stats )

Completing a nomination on behalf of an IP who may have left an earlier comment on the talk page: "Really does not seem even remotely notable enough for Wikipedia. — Preceding unsigned comment added by <IP_ADDRESS> (talk) 08:35, 26 May 2012 (UTC)" Malcolmxl5 (talk) 00:19, 11 July 2012 (UTC)
 * Note: This debate has been included in the list of Canada-related deletion discussions.  • Gene93k (talk) 11:55, 11 July 2012 (UTC)
 * Note: This debate has been included in the list of Authors-related deletion discussions.  • Gene93k (talk) 11:55, 11 July 2012 (UTC)
 * Note: This debate has been included in the list of Politicians-related deletion discussions.  • Gene93k (talk) 11:55, 11 July 2012 (UTC)

 * Delete. Claim to notability is as a speechwriter and political advisor. For this, he fails WP:POLITICIAN as he does not receive significant coverage in reliable sources that are independent of the subject. Lots of trivial references in unrelated subjects are akin to WP:BOMBARDMENT. Location (talk) 17:17, 11 July 2012 (UTC)
 * Relisted to generate a more thorough discussion so a clearer consensus may be reached.

 * Please add new comments below this notice. Thanks, — Crisco 1492 (talk) 02:48, 18 July 2012 (UTC)

 * Delete as failing WP:POLITICIAN. Stuartyeates (talk) 01:24, 21 July 2012 (UTC)


text:
Our Pathetic Age

Our Pathetic Age is the sixth studio album by American music producer DJ Shadow, released through Mass Appeal Records on November 15, 2019. It features the singles "Rocket Fuel" (featuring De La Soul) and "Rosie". It also features collaborations with Run the Jewels, Ghostface Killah, Nas, and Raekwon, among others.

Background
DJ Shadow said that "despite the title, it's a hopeful, vibrant album", elaborating that "People are addicted to, and addled by, distraction; they're angry and confused, and disaffected by their own governmental institutions. There's songs that are inspired by this energy and seek to harness it, to make sense of it. In some cases, there's attempts to salve the wound; in others, the songs merely observe but don't offer solutions."

Composition
The album contains two sections: the first (tracks 1–11) contains instrumental tracks, while the second (tracks 12–26) features songs with guest vocalists.

Critical reception
On Metacritic, which assigns a weighted average score out of 100 to reviews from mainstream critics, the album received an average score of 69, based on 13 reviews, indicating "generally favorable reviews".

Thomas Hobbs of Pitchfork wrote, "Shadow deserves credit for spotlighting so many enigmatic underground characters, something he has done throughout his career, but the overabundance of ideas and conflicting styles quickly becomes jarring."

title: Our Pathetic Age


text:
West Riding Limited

The West Riding Limited is a named passenger train operating in the United Kingdom.

History
The West Riding Limited was introduced by the London and North Eastern Railway in 1937 to operate between London King's Cross and Leeds and Bradford. The company built a new set of carriages, identical to the Coronation sets of 1935 which comprised four twin articulated coaches with two kitchen cars in each train set. There were seats for 48 first class and 168 third class passengers. It travelled from King's Cross to Bradford at an average speed of 63.3 mph. The service started on 27 September 1937 when the first train was hauled by LNER Class A4 Dominion of New Zealand which had only entered service three months earlier.

The train was stored for the duration of the Second World War and service resumed in 1949.

The name has been retained by London North Eastern Railway and as of 2024 is operated as the 06:30 departure from Bradford Forster Square, arriving at London King's Cross at 08:59.

title: West Riding Limited


text:
sosialisoida

Etymology
(see 🇨🇬). Adapted with the verbal suffix.

Verb

 * 1)  to socialise/socialize
 * 2)  to steal,  arbitrarily take into possession
 * 3)  to socialise/socialize

title: sosialisoida


text:
Wikiversity:Outreach

Please list here institutions that you think would be interested in collaborating with Wikiversity. Please try to be specific about what kinds of collaboration you think might be possible. For example, you might know of specific kinds of activities they do that Wikiversity could help with and vice versa.

Workspaces
Some groups have created workspaces within Wikiversity to facilitate learning, and also so that they could link to Wikiversity learning projects, thereby using resources in a more direct way. Some examples include, SchoolForge and UNIT-E. If your group would like a workspace at Wikiversity, please feel free to create a page in the main namespace using your organization's name as the page title. For the sake of keeping Wikiversity somewhat organized, it would be appreciated if you would add Category:Workspaces at the bottom and other appropriate categories at the bottom and include links on your page to relevant Schools, Divisions and Departments.

Meta Collab at Wikia
Meta Collab at Wikia now has a Wikiversity article, discussion area and Wikiversity update section. A local Wikiversity article, Wikia, in the main namespace includes an opt-in listing for Wikiversity projects that would like to be represented at their appropriate spots within the Wikia metacommunity. Please provide constructive feedback on the talk page here or at Talk:Wikia. Thanks in advance.

Ideas

 * Global Text Project - "The goal is to create a free library of 1,000 electronic textbooks for students in the developing world." The Global Text Project is managed by the Center for Information Systems Leadership, Terry College of Business, The University of Georgia. See also: Wikiversity and Wikibooks services.

 * Psychology Wikia- the psychology wikia group was interested in collaboration.

 * Wikimedia Youth Camp - suggested by Erik Moeller.

 * California Open Source Textbook Project

 * WikiEducator - WikiEducator is an evolving community intended for the collaborative planning of education projects linked with the development of free content.

 * Curriki

 * Qedoc - Qedoc specialises in creating highly interactive learning activities and does so on a primarily charitable basis for the open educational resources community. Our software is not yet appropriate for creating interactive learning activities for MediaWiki-driven sites like Wikiversity. However Qedoc is interested in developing such a technology. A discussion page for the proposal has been started here (page could be transferred to Wikiversity if this is adopted as a project). Wikiversity people are requested to express views and help steer planning.

 * Vietnam OpenCourseWare This is the result of the cooperation between Vietnam Education Foundation (VEF), Vietnamese Ministry of Education and Training (MOET), and VASC Software and Media Company (VASC) since 2005. Our aspiration is to make OCW/OER features rich, accessible, and reusable at no cost for Vietnamese faculty members, students and self-learners.

 * Center for Village Science - contains innovative simple and low cost/no cost science experiments and other teaching aids, which could be helpful to the teachers to improve the science teaching especially for the teachers in the villages (India).

 * Le web pédagogique - French OER blogging site; perhaps for consideration by the French Wikiversity.

Projects

 * /Wikipedia outreach/. Wikipedia generally prohibits discussion of topics on article talk pages, and that is often violated, with users being threatened, on occasion, with blocks. Wikiversity invites discussion as part of "learning by doing" that is core to our mission. This outreach project will organize the placement of sister wiki templates on Wikipedia articles, the development of a local discussion guideline that could be interwiki linked in a the generic w:Template:Not a forum talk page template, presenting Wikiversity as a place to discuss topics of interest, and then guidance as to how to do that nondisruptively. The project will then organize outreach activities, to ensure maximum visibility while minimizing duplication and disruption.

Institutions

 * Phoenix Union Cyber High School - internet-based curriculum, computer studios not classrooms, self-paced learning, opened 2006. See also: Wikihigh.
 * NASA education programs - U.S. government based, so all public domain.
 * Florida virtual school - 20,000 students learning online
 * Cranbrook Educational Community
 * SchoolForge - a "foundry" ...for information, tools and materials needed to "forge" or make a school and all its parts... Local: SchoolForge
 * Science Online - science education wiki
 * FreeCulture.org - an international student movement for free culture wiki site, Local: FreeCulture.org
 * The "Shtooka Project" is a cooperative project with the goal of creating audio material and software tools needed to learn foreign languages. Local: Shtooka Project
 * OmegaWiki (previous names: Ultimate Wiktionary, WiktionaryZ) is a new multilingual version of Wiktionary. It runs on an extension of MediaWiki.
 * OER Commons - an index of educational resources (website) - wants to work with Wikiversity on idexing, tagging, ...
 * MIT OpenCourseWare
 * Virtual Seminar University - a free online university sponsored by Sam's Club

Case studies

 * Call for Participation of Linguists - at Wikipedia.

External resources

 * outreach.wikimedia.org

title: Wikiversity:Outreach


text:
aestivoautumnal

Etymology
From +  +.

Adjective

 * 1)  Relating to or happening in summer and autumn.

Translations

 * Portuguese: estivo-outonal

title: aestivoautumnal


text:
John Austin Meyer

John Austin Meyer (St. Marys September 18, 1919 - Pittsburgh January 28, 1997) was an aerial photographer in the US Army Air Forces during World War II and a professor of Nuclear and Radiation Chemistry.

Life
Meyer was born in St. Marys on September 18, 1919. In Saint Mary's Catholic High School he participated in camera club continuing into the towns camera club, and at the age of 21 he worked as a photographer and pursued studies in chemistry.

Meyer enlisted in the United States Army Air Corps on March 18, 1941. After basic training in Langley Field, Virginia he was assigned to Dow Field, Bangor, Maine. After initially being put off by the army because he couldn't bring his photographic equipment, he befriending Corporal Busch who got promoted to Sergeant, and helped Meyer into the photography department. Meyer had a four-month training program in aerial photography at the Air Force Photo School in Denver, then assigned to the US base at Gander, Newfoundland in August 1942 as chief photographic officer.

Among other aerial photographers in Gander, his work helped create the first aerial mapping and photographic studies of cloud formations taken by the Air Corps in the area. He also assisted in anti submarine spotting patrol and other classified flight missions.

After being discharged in 1955, Meyer enrolled at Pennsylvania State University and received a bachelor's degree and masters in chemistry and worked as an analytical research chemist at Gulf Research and Development Company. He then was awarded a research fellowship at the State University of New York's College of Forestry eventually becoming a faculty member. He trained in nuclear and radiation chemistry at Brookhaven National Laboratory, and became a professor of Nuclear and Radiation Chemistry at the university.

Meyer developed a method of impregnating wood with a liquid polymer still in use today for wood floorings, handles, and musical instruments.

Studying for his PhD, he met and married Marion Waterman during her masters who eventually retired as Assistant Dean Emeritus of the School of Management at Syracuse University. John and Marion would go on to develop scholarships and awards for students at various colleges. John died in Pittsburgh on January 28, 1997.

title: John Austin Meyer


text:
User:Appletross

Wikipedia user appletross is a student at Columbia College in Chicago. She spent her formative years in Palm Beach Florida. She studies Cultural Studies and Photography. Her influences include Laszlo Maholy-Nagy, Roland Barthes and An Albatross. She enjoys boats, puppies and magnolias

title: User:Appletross


text:
Talk:Earthee

November 2019
I created this article. , who accepted my draft in September 2019, has been indefinitely blocked for Paid-contribution disclosure. In November 2019, the article was moved back from article space to draft space and was tagged Undisclosed paid. However, I'm not connected to Ceethekreator or the subject of the article. I don't have any conflict of interest. The duo who made the 2015 album is American and has been inactive since 2016. I'm a Japanese Wikipedian from Tokyo. All I want to say is that I'm not paid for my contributions in Wikipedia. I don't know what I can do to prove it. <IP_ADDRESS> (talk) 13:09, 24 November 2019 (UTC)

title: Talk:Earthee


text:
User:James Chilowera

James Chilowera was born on 17th March, 1994 at Maluku village T/A Kachere in Dedza district. He is a sixth born son in the family of seven children. James started primary school at Kaphatenga in Salima, then at Katewe and later at Kamphemba in Dedza district. He attended Chawa Community day secondary School and later at Katewe Community where he obtained Malawi School Certificate of Education in the year 2017 and was the best student. In September 2018 James Chilowera was selected to Lilongwe teachers training college. Currently he is there doing teaching certificate.

title: User:James Chilowera


text:
User:JKizzieHumanities/Mickey Zacchilli

Mickey Zacchilli is an comic artist and illustrator living in Providence, Rhode Island. Zacchilli's comic, Academy 123, was on the shortlist for the 2019 Cartoonist Studio Prize, and her comic Lovers Only was nominated for an Ignatz Award in 2018.

Style
Zacchilli's style was described as "filled with an amazing, wild, feral crackle" in The Providence Phoenix by culture writer Greg Cook. Hand-lettered text and speech bubbles drawn directly from character's mouths are features of Zacchilli's style.

Works
2018, Space Academy 123 ISBN<PHONE_NUMBER>634

2015-2018, Lovers Only, LCCN<PHONE_NUMBER>

2014, RAV ISBN<PHONE_NUMBER>600

title: User:JKizzieHumanities/Mickey Zacchilli


text:
Talk:List of programmable logic controller manufacturers

The List Describe Programmable Logic Controller
I am an experienced engineer with Programmable Logic Controller and the list here described Programmable Logic Controller. They are NOT Power line communication. Zawthet (talk) 16:08, 18 July 2015 (UTC)
 * So why not add companies that you think are in the Power line communication space? Ottawahitech (talk) 22:19, 4 September 2015 (UTC)

This list is a mess
The title says "PLC", which is ambiguous. Shortly after it was created, "PLC" was disambiguated to stand for "power line communication", but then in February 2017 that was abruptly changed to "programmable logic controller", so as a result this list is a mix of manufacturers of both kinds of equipment. Arteitle (talk) 16:32, 3 July 2018 (UTC)


text:
dates of births

Usage notes

 * For an explanation of the subtle distinction between the plural forms “dates of birth” and “dates of births”, see the usage note at the entry for “date of birth”.

title: dates of births


text:
Actuarial science

Actuarial science applies mathematical and statistical methods to finance and insurance, particularly to risk assessment. Actuaries are professionals who are qualified in this field through actuarial examinations or university-based education (but the credentialing usually requires passing a series of examinations), and work experience.

Actuarial mathematics deal with the mathematics of uncertainty and risk. Some of the key areas where actuarial mathematics are principally applied are mortality studies, financial risk, risk and ruin theory, credibility theory, demography, reliability study and graduation of statistical data.

Actuarial science includes a number of interrelating disciplines, including probability and statistics, finance, and economics. Historically, actuarial science used deterministic models in the construction of tables and premiums. Modern approaches incorporate the stochastic simulation of random variables, such as interest rates.

Studying Actuarial Science
Studying Actuarial Science can be a task that is both challenging and rewarding. It requires a very good basis in mathematics as it requires heavy use of statistics. In the U.K., few universities offer an actuarial related degree. Among those, the Queen's University of Belfast, Heriot-Watt, City and Kent universities are some of them that can offer full exemptions from the CT series of examinations of the Institute or Faculty of Actuaries.

Actuaries are involved in the following areas :
 * Life insurance
 * Short term or general insurance
 * Pensions
 * Institutional investments, etc.

Study materials for actuarial examinations
Society of Actuaries (SOA):

 * Exam P
 * Wikibooks: Probability

 * Exam FM
 * Wikibooks: Financial Math FM

title: Actuarial science


text:
brain freeze

Noun

 * 1)  A pain in the head from eating or drinking something cold; a cold-stimulus headache.
 * 2)  Failure to remember something, with the sense that recall is imminent.
 * 3) * 2011, James N. Laditka et al., "Older adults' concerns about cognitive health: commonalities and differences among six United States ethnic groups", Ageing and Society, vol. 31 (7), p. 1214:
 * I call it a brain freeze at this age, but whenever you have some kind of a problem remembering something, you think, oh, you know, you automatically think about Alzheimer’s.
 * I call it a brain freeze at this age, but whenever you have some kind of a problem remembering something, you think, oh, you know, you automatically think about Alzheimer’s.

Translations

 * German: ,

title: brain freeze


text:
Sid Lewis

Sidney Scot Lewis  (born May 30, 1964) is a former American football defensive back. He had played for the New York Jets of the National Football League (NFL) in 1987. He was drafted by the Jets in the tenth round of the 1987 NFL Draft. He played college football at Penn State University.

title: Sid Lewis


text:
G. R. Motha

George Rosario Motha (22 November 1892 – 1950) was a Ceylonese politician, lawyer and Tamil activist.

Motha was elected to the first Parliament of Ceylon in 1947 representing the Ceylon Indian Congress as the member for the Maskeliya electorate. He was strongly opposed to Ceylon Citizenship Act No 18 of 1948, whereby Indian Tamils were legally denied Ceylon citizenship, speaking and voting against the Act. Motha stating in parliament that not only would many Indian Tamils be unable to prove their paternal genealogy but also the Sinhalese community would be automatically recognised effectively discriminating against the Indian Tamil population.

Motha died in 1950 and his seat representing the Maskeliya electorate was filled by Abdul Aziz, following a by-election in March 1950.

title: G. R. Motha


text:
The Ontological Argument

Part of Philosophy>Philosophy of Religion

Overview
The ontological argument proposes that God's existence can be proved a priori, that is, by intuition and reason alone. It was first put forward by Anselm of Canterbury in the Proslogium.

The argument works by examining the concept of God, and arguing that it implies the actual existence of God; that is, if we can conceive of God, then God exists — it is thus self-contradictory to state that God does not exist. This is obviously a controversial position, and the ontological argument has a long history of detractors and defenders.

The argument's different versions arise mainly from using different concepts of God as the starting point. For example, Anselm starts with the notion of God as a being than which no greater can be conceived, while Descartes starts with the notion of God as being maximally perfect (as having all perfections).

Suggested Reading

 * St Anselm, "The Ontological Argument" From Proslogium.

 * William L. Rowe, "The Ontological Argument."
 * Gaunilo of Marmoutiers, "On Behalf of the Fool."
 * Gaunilo of Marmoutiers, "On Behalf of the Fool."

Enyclopedia Articles

 * The Ontological Argument from [The Internet Encyclopedia of Philosophy] article by Kenneth Einar Himma
 * Ontological Arguments from the [Stanford Encyclopedia of Philosophy]
 * Ontological Argument from Wikipedia]

Lecture Notes

 * Existence of God: Ontological Argument by Sally Haslanger. Part of 24.00 Problems of Philosophy, Fall 2005

title: The Ontological Argument


text:
Properties of matter

States of Matter
Solid, Liquid, Gas, Plasma

Gases
On a macroscopic level, gases are notable because of their ability to expand to the size and shape of a container. In addition, gases belong to the only state of matter that is governed by universal laws.

There are a few standard variables that are characteristic of all gases:

 * $$\ p $$ is the pressure (N/m2)
 * $$\ V $$ is the volume (L)
 * $$\ n $$ is the number of moles of gas
 * $$\ R $$ is the gas constant 8.314472 Joules/mol*K
 * $$\ T $$ is the temperature in kelvin (K)
 * $$\ a' $$ is the measure of attraction between the particles
 * $$\ b' $$ is the space enclosed in one particle
 * $$\ k $$ is Boltzmann's Constant, equal to 1.380650524×1023 joule/kelvin

Ideal Gas Law

 * $$\ pV = nRT $$

There are 4 gas laws that, when combined, yield the Ideal Gas Law (often pronounced "Pivnert"). The Ideal Gas Law assumes that particles have no attractions to each other (they do in actuality) and that particles of a mass are infinitely small (they aren't). However, the ideal gas law is accurate for all gases at high temperatures and low pressures. The only times when it becomes highly inaccurate are near the boiling and sublimation points of gases.

Charles' Law

 * $$\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \mathrm{or} \qquad \frac {V_2}{V_1} = \frac{T_2}{T_1} \qquad \mathrm{or} \qquad V_1T_2 = V_2T_1$$

This is used to determine the effects of a change in temperature on the volume of a gas at constant pressure and vice versa.

Boyle's Law

 * $$\qquad\qquad {p_1} {V_1} = {p_2} {V_2} $$

This law is used to determine the effects of a change in pressure on the volume of an ideal gas if temperature is constant and vice versa.

Gay - Lussac's Law

 * $$\frac{p_1}{T_1}= \frac {p_2}{T_2}$$

This law is used to calculate the effects of temperature on pressure, and vice versa. Note that there is no known way to increase pressure while keeping volume and number of moles constant besides simply raising the temperature. Additionally, note that if pressure were to suddenly drop, the temperature would also drop. This is the mechanism by which refrigerators operate.

Avogadro's Law
Any two gases with the same volume at the same temperature and pressure contain the same number of particles. At 273.15 K and 101.3 kPa, this works out to approximately 22.4 litres.

Van der Waals equation

 * $$\left(p + \frac{a'}{V^2}\right)\left(V-b'\right) = kT$$

The van der Waals equation takes into account the fact that particles of a gas do actually take up space (i.e., at 0 kelvins they would still have a volume) and that particles of a gas are attracted to each other by dipole-dipole forces, London dispersion forces and van der Waals forces.

Organic Compounds
Organic compounds always contain carbon-hydrogen bonds, i.e., at least one carbon is bonded to at least one hydrogen. Naming conventions are determined by IUPAC, the International Union of Pure and Applied Chemistry. For more information, see Nomenclature.

Inorganic Compounds
Inorganic compounds are those which contain no hydrogen-carbon covalent bonds. Two major types exist: Ionic and Network Covalent. Ionic compounds are based on positive ions (cations), normally metal ions, attracted to negative ions (anions) by electromagnetic forces. The vast majority of ionic compounds are solids, although research into liquid ionic compounds looks promising. Ionic compounds are sometimes soluble in water, but not always. Network covalent compounds are those which have molecules that are infinitely repeatable in all directions. Atoms are bonded by shared electrons and are not charged. Examples include diamonds, graphite, and quartz (silicon dioxide).

For more info, see Inorganic Chemistry

物質の性質

title: Properties of matter


text:
impotens

Etymology
From.

Adjective

 * 1) Powerless, weak, feeble, impotent, helpless, puny.
 * 2) Unable to control, having no power over; incapable of.
 * 3) Unbridled, unrestrained, headstrong, wild, violent, excessive.

Etymology
From.

Noun

 * 1) impotence

Etymology
From.

Noun

 * 1) impotence

Noun

 * 1) impotence (erectile dysfunction, etc.)
 * 2) impotence (powerlessness, incapacity)
 * 1) impotence (powerlessness, incapacity)

title: impotens


text:
User:BetteDavis4ever

Hi. I'm from Belgrade, so you can find me in Serbian Wikipedia. I write about movies, especially about the stars of the Golden Age of Hollywood. I like Bette Davis and Sandra Bullock very much. Just enough. :)

{| class="wikitable"

sr:Korisnik:Boleyn

title: User:BetteDavis4ever


text:
unsheath

Verb

 * 1) To deprive of a sheath; to draw from the sheath or scabbard, as a knife or sword.

title: unsheath