text:
Geometry/Triangle

A triangle is a type of polygon having three sides and three angles. The triangle is a closed figure formed from three straightline segments joined at their ends. The Line Segments at the ends can be called the corners, angles, or vertices of the triangle. Since any given triangle lies completely within a plane, triangles are often treated as two-dimensional geometric figures. As such, a triangle has no volume and, because it is a two-dimensionally closed figure, the flat part of the plane inside the triangle has an area, typically referred to as the area of the triangle. A triangle must have at least some area, so all three corner points of a triangle cannot lie in the same line. The sum of the lengths of any two sides of a triangle is always greater than the length of the third side. The preceding statement is sometimes called the Triangle Inequality.

Categorized by angle
The sum of the interior angles in a triangle always equals 180o. This means that no more than one of the angles can be 90o or more. All three angles can all be less than 90oin the triangle; then it is called an acute triangle. One of the angles can be 90o and the other two less than 90o; then the triangle is called a right triangle. Finally, one of the angles can be more than 90o and the other two less; then the triangle is called an obtuse triangle.

Categorized by sides
If all three of the sides of a triangle are of different length, then the triangle is called a scalene triangle. If two of the sides of a triangle are of equal length, then it is called an isosceles triangle. In an isosceles triangle, the angle between the two equal sides can be more than, equal to, or less than 90o. The other two angles are both less than 90o. If all three sides of a triangle are of equal length, then it is called an equilateral triangle and all three of the interior angles must be 60o, making it equiangular. Because the interior angles are all equal, all equilateral triangles are also the three-sided variety of a regular polygon and they are all similar, but might not be congruent. However, polygons having four or more equal sides might not have equal interior angles, might not be regular polygons, and might not be similar or congruent. Of course, pairs of triangles which are not equilateral might be similar or congruent. Further discussion of ../Congruent Triangles/ and ../Similar Triangles/ may be found in those corresponding sections.

Opposite corners and sides in triangles
If one of the sides of a triangle is chosen, the interior angles of the corners at the side's endpoints can be called adjacent angles. The corner which is not one of these endpoints can be called the corner opposite to the side. The interior angle whose vertex is the opposite corner can be called the angle opposite to the side. Likewise, if a corner or its angle is chosen, then the two sides sharing an endpoint at that corner can be called adjacent sides. The side not having this corner as one of its two endpoints can be called the side opposite to the corner. The sides or their lengths of a triangle are typicaly labeled with lower case letters. The corners or their corresponding angles can be labeled with capital letters. The triangle as a whole can be labeled by a small triangle symbol and its corner points. In a triangle, the largest interior angle is opposite to longest side, and vice versa. Any triangle can be divided into two right triangles by taking the longest side as a base, and extending a line segment from the opposite corner to a point on the base such that it is perpendicular to the base. Such a line segment would be considered the height or altitude ( h ) for that particular base ( b ). The two right triangles resulting from this division would both share the height as one of its sides. The interior angles at the meeting of the height and base would be 90o for each new right triangle. For acute triangles, any of the three sides can act as the base and have a corresponding height. For more information on right triangles, see ../Right Triangles and Pythagorean Theorem/.

Area of Triangles
If base and height of a triangle are known, then the area of the triangle can be calculated by the formula: $$S = \frac{b \times h}{2}$$ ($$S$$ is the symbol for area) Ways of calculating the area inside of a triangle are further discussed under ../Area/.

Centres
The centroid is constructed by drawing all the medians of the triangle. All three medians intersect at the same point: this crossing point is the centroid. Centroids are always inside a triangle. They are also the centre of gravity of the triangle. The three angle bisectors of the triangle intersect at a single point, called the incentre. Incentres are always inside the triangle. The three sides are equidistant from the incentre. The incentre is also the centre of the inscribed circle (incircle) of a triangle, or the interior circle which touches all three sides of the triangle. The circumcentre is the intersection of all three perpendicular bisectors. Unlike the incentre, it is outside the triangle if the triangle is obtuse. Acute triangles always have circumcentres inside, while the circumcentre of a right triangle is the midpoint of the hypotenuse. The vertices of the triangle are equidistant from the circumcentre. The circumcentre is so called because it is the centre of the circumcircle, or the exterior circle which touches all three vertices of the triangle. The orthocentre is the crossing point of the three altitudes. It is always inside acute triangles, outside obtuse triangles, and on the right vertex of the right-angled triangle. Please note that the centres of an equilateral triangle are always the same point.

title: Geometry/Triangle


text:
Wikipedia talk:Education program archive/Duquesne University/UCOR 143 Global and Cultural Perspectives (Spring 2015)

Religion and drugs
I've removed an edit by MikeMill11 to Religion and drugs. See Talk:Religion and drugs for an explanation. If I can be of any help, please contact me. Seeing your edits simply being removed can be very frustrating; if necessary, I'm quite willing to offer some help. Joshua Jonathan - Let's talk!  07:09, 9 February 2015 (UTC)

Spirituality and compassion
For the whole class: Ton Lathouwers, More than anyone can do. Joshua Jonathan - Let's talk!  06:29, 11 February 2015 (UTC)

source: wikimedia

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


text:
Talk:David René de Rothschild

Dubious daughter
Various IPs, and several impersonations of User:Lollsan1900, claim the existence of a Rothschild daughter named "Baroness Olimpia Juliet de Rothschild" (b. 1988). However, there is no source for her existence. User:Brendon9111 refered to rothschildarchive.org, where there is one "Louise Lili Beatrice de Rothschild" (b. 1989). It seems unclear whether those persons are supposed to be identical. User:Parisness, claiming to "work in the france embassy here in Paris" (why is there a French embassy in Paris?), posted two documents on image dumps ( and ), which are of dubious origin and don't proof anything. After all, this "Baroness Olimpia" would not be the first heiress imposter. To sum it up, I have a lot of doubts about this. --bender235 (talk) 16:25, 2 March 2014 (UTC)

 * It's a french embassy, not Embassy of France. which countries french embassy I'm working for is not important? I have posted two documents about this person existens, a official invitation from the children embassy in macedonia and a copy of the picture id. The records states she was born 1988 in Florence, Italy with the name Olimpia Juliet Louise Lili Béatrice de Rothschild. Then back in 2007 she had her name legally changes to Baroness Olimpia de Rothschild (french official title), both her embassy papers and id states that name. Her mother is named Olimpia too, I guess it's a family name. User:Parisness

 * Is there any reliable source, such as media reports, etc. that support your claim for this person's existence? And I'm not talking about self-uploaded, image-manipulated personal ID. --bender235 (talk) 17:03, 2 March 2014 (UTC)

Baroness Olimpia de Rothschild and Louise Lili Béatrice de Rothschild are the same person, she goes under the name Baroness Olimpa de Rothschild. Name change after she got some french title. We went to same school, I have her on facebook, lol? Not like that is a source or anything but anyways :P She's born 1988 I don't know why the archive is wrong. She have a younger sister born 1989 tho. meaby that's why the mixup on the archive. --Brendon9111 (talk) — Preceding undated comment added 17:54, 2 March 2014 (UTC)

If you google the name with no title: Olimpia de Rothschild, you will get hits. --Brendon9111 (talk) — Preceding undated comment added 18:01, 2 March 2014 (UTC)

 * I'm sorry, but apart from this phony Facebook page there are no "Google hits" on "Olimpia de Rothschild". Only on Olimpia Anna Aldobrandini. I still have doubts this person exists, and/or is related to David de Rothschild. --bender235 (talk) 08:38, 3 March 2014 (UTC)

I know that she exists, dosen't matter tho. It's not like she have a own article on here. If all relatives connected to people with a article on here must be "googleble" the site would drastically decrease in spouse information. --Brendon9111 (talk) — Preceding undated comment added 18:07, 3 March 2014 (UTC)

Net worth
Anyone know? <IP_ADDRESS> (talk) 15:35, 15 March 2016 (UTC)

Fraud case
I have removed a link to a dubious source and reworded this part to be more neutral. As far as I can tell, this "news story" was based on an article published on a website run by or associated with the litigants. All sorts of anti-Rothschild rubbish was added to the "Activist Post" to pad out the article. This included deliberate confusion of two Rothschild run banks (Rothschild et Cie in France and Edmond Rothchild in Switzerland) and references to the "Affaire Macron" - an investigation into a minister formerly employed by Rothschild et Cie

External links modified
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title: Talk:David René de Rothschild


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Lojban/Vocatives

Since {ki'e} means approximately "Thank you," it might seem appropriate to respond by saying {fi'i}, seemingly corresponding to the English "You're welcome." However, {fi'i} means "welcome" in the sense of an invitation/acceptance only. In order to respond, {je'e} should be used.

{coi co'o} means "Greetings in passing." English speakers generally just say "Hi."

"ju'i" can be used as an attention-grabber such as the first word in each of the following utterances (if they started a conversation): "Attention, all shoppers", "So, I just got back from my date with Ryan", "Lo! Listen to the news which I bring". This is the function of the very first word of Beowulf. It can also return an audience's attention to the speaker/discussion, such as with some usages of "ahem", clearing the throat, or wrapping on a desk.

Exercises
In Exercises 1-7, give the most suitable Lojban word(s) to say in each situation.

01. The beginning of a conversation. 02. Begging. 03. During an oath. 04. Inviting a guest into your house. 05. Getting a group of people to listen to your announcement. 06. You desire the floor while someone else has it. 07. Leaving a party.

In Exercises 8-43, give the closest Lojban translation of the English sentences.

08. Attention! 09. Listen to me, Victoria. 10. I swear, Benjamin. 11. I don't understand, Christian. 12. I am Pete. 13. Goodbye, Jonathan. 14. Roger, Logan. 15. Wilco. 16. Hello, Rodrigo. 17. Hi, Bertand. 18. Wait! We're not done discussing this! 19. Hark! 20. Agreed. 21. Can I say something, Jose? 22. Just a minute, Jennifer. 23. I'm not done talking, Morgan. 24. Please, Sydney. 25. Over and out. 26. I appreciate that, Chloe. 27. Make yourself at home, Rachel. 28. May I speak, Jasmine? 29. Sorry for interrupting, Sophia, but... 30. I promise, Megan. 31. Thanks, Samuel. 32. Hold on, Nathan. 33. What did you say, Natalie? 34. I interrupt. 35. Greetings, Justin. 36. Uh-huh. 37. Thank you, Dylan. 38. At your service, Austin. 39. I'm listening, Kevin. 40. I understand, Julia. 41. "Houston, we have a problem." 42. Hello! Susan has just left Harold. 43. Hello, Susan! Harold has just left.

Answers to exercises
01. coi 02. pe'u 03. nu'e 04. fi'i 05. ju'i 06. ta'a 07. co'o

08. ju'i 09. ju'i. vektarias. 10. nu'e. bendjamen. 11. je'enai. krestien. 12. mi'e. pit. 13. co'o. janaten. 14. je'e. logen. 15. vi'o 16. coi. radrigos. 17. coi. bertrend. 18. fe'onai 19. ju'i 20. vi'o 21. be'e. xozeis. 22. re'inai. djenefer. 23. mu'onai. morgen. 24. pe'u. sednis. 25. fe'o 26. ki'e. clos. 27. fi'i. reitcel. 28. be'e. djezmen. 29. ta'a. sofias. 30. nu'e. meigen. 31. ki'e. semiul. 32. re'inai. neitan. 33. ke'o. netalis. 34. ta'a 35. coi. jesten. 36. je'e 37. ki'e. delen. 38. fi'i. .asten. 39. re'i. keven. 40. je'e. djulias. 41. doi xustyn. mi'a se nabmi 42. coi do'u la suzyn. la xeirold. puzi cliva 43. coi la suzyn. la xeirold. puzi cliva

title: Lojban/Vocatives


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Template:High School Mathematics Extensions/Matrices

Introduction
"Matrix" may be more popularly known as a giant computer simulation, but in mathematics it is a totally different thing. To be more precise, a matrix (plural matrices) is a rectangular array of numbers. For example, below is a typical way to write a matrix, with numbers arranged in rows and columns and with round brackets around the numbers:

\begin{pmatrix} 1 & 5&10&20 \\ 1&-3&-5&9\\ 3&-1&-1&-1\\ 3&2&4&-5 \end{pmatrix} $$ The above matrix has 4 rows and 4 columns, so we call it a 4 × 4 (4 by 4) matrix. Also, we can have matrices of many different shapes. The shape of a matrix is the name for the dimensions of the matrix (m by n, where m is the number of rows and n the number of columns). Here are some more examples of matrices:

This is an example of a 3 × 3 matrix:

\begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} $$

This is an example of a 5 × 4 matrix:

\begin{pmatrix} a&b&c&d\\ h&g&f&e\\ i&j&k&l\\ p&o&n&m\\ q&r&s&t\\ \end{pmatrix} $$

This is an example of a 1 × 6 matrix:

\begin{pmatrix} 1&2&3&4&5&6\\ \end{pmatrix} $$

The theory of matrices is intimately connected with that of (linear) simultaneous equations. The ancient Chinese had established a systematic way to solve simultaneous equations. The theory of simultaneous equations was furthered in the east by the Japanese mathematician, Seki and a little later by Leibniz, Newton's greatest rival. Later, Gauss (1777 - 1855), one of the three giants of modern mathematics, popularised the use of Gaussian elimination, which is a simple step by step algorithm for solving any number of linear simultaneous equations. By then the use of matrices to represent simultaneous equation neatly on paper (as discussed above) had become quite common1.

Consider the simultaneous equations:
 * $$x + y = 10$$
 * $$x - y = 4$$

it has the solution x = 7 and y = 3, and the usual way to solve it is to add the two equations together to eliminate the y. Matrix theory offers us another way to solve the above simultaneous equations via matrix multiplication (covered below). We will study the widely accepted way to multiply two matrices together. In theory with matrix multiplication we can solve any number of simultaneous equations, but we shall mainly restrict our attention to 2 × 2 matrices. But even with that restriction, we have opened up doors to topics simultaneous equations could never offer us. Two such examples are
 * 1) using matrices to solve linear recurrence relations which can be used to model population growth, and
 * 2) encrypting messages with matrices.

We shall commence our study by learning some of the more fundamental concepts of matrices. Once we have a firm grasp of the basics, we shall move on to study the real meat of this chapter, matrix multiplication.

Elements
An element of a matrix is a particular number inside the matrix, and it is uniquely located with a pair of numbers. E.g. let the following matrix be denoted by A, or symbolically:
 * $$A =

\begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} $$ the (2,2)th entry of A is 5; the (1,1)th entry of A is 1, the (3,3) entry of A is 9 and the (2,3)th entry of A is 8. The (i, j)th entry of A is usually denoted ai,j and the (i , j)th entry of a matrix B is usually denoted by bi,j and so on.

Summary

 * A matrix is an array of numbers
 * A m×n matrix has m rows and n columns
 * The shape of a matrix is determined by its number of rows and columns
 * The (i,j)th element of a matrix is located in ith row and jth column

Matrix addition & Multiplication by a scalar
Matrices can be added together. But only the matrices of the same shape can be added. This is very natural. E.g.

A = \begin{pmatrix} 1&x&2x\\ 1&3x&5x\\ 1&3&4\\ \end{pmatrix} $$

B = \begin{pmatrix} 2&9&8\\ 0&-1&8\\ 4&6&7\\ \end{pmatrix} $$ then

A + B = \begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} + \begin{pmatrix} 2&9&8\\ 0&-1&8\\ 4&6&7\\ \end{pmatrix} = \begin{pmatrix} 1+2&2+9&3+8\\ 4+0&5+(-1)&6+8\\ 7+4&8+6&9+7\\ \end{pmatrix} = \begin{pmatrix} 3&11&11\\ 4&4&14\\ 11&14&16\\ \end{pmatrix} $$

Similarly matrices can be multiplied by a number. We call the number a scalar to distinguish it from a matrix. The reader need not worry about the definition here, just remember that a scalar is simply a number.

5A = A + A + A + A + A = 5\begin{pmatrix} 1&2&3\\ 4&5&6\\ 7&8&9\\ \end{pmatrix} = \begin{pmatrix} 5&10&15\\ 20&25&30\\ 35&40&45\\ \end{pmatrix} $$ in this case the scalar value is 5. In general, when we do s × A, where s is a scalar and A a matrix, we multiply each entry of A by s.

Matrix Multiplication
The widely accepted way to multiply two matrices together is definitely non-intuitive. As mentioned above, multiplication can help with solving simultaneous equations. We will now give a brief outline of how this can be done. Firstly, any system of linear simultaneous equations can be written as a matrix of coefficients multiplied by a matrix of unknowns equaling a matrix of results. This description may sound a little complicated, but in symbolic form it is quite clear. The previous statement simply says that if A, x and b are matrices, then Ax = b, can be used to represent some system of simultaneous equations. The beautiful thing about matrix multiplications is that some matrices can have multiplicative inverses, that is we can multiply both sides of the equation by A-1 to get x = A-1b, which effectively solves the simultaneous equations.

The reader will surely come to understand matrix multiplication better as this chapter progresses. For now we should consider the simplest case of matrix multiplication, multiplying vectors. We will see a few examples and then we will explain process of multiplication

\begin{matrix}

A_{2\times 1} = \begin{pmatrix} 2\\ 9\\ \end{pmatrix} &, & B_{1\times 2} = \begin{pmatrix} 3 & 5 \end{pmatrix}

\end{matrix} $$

then

B_{1\times 2} \times A_{2\times 1} = \begin{pmatrix} 3 & 5 \end{pmatrix} \times \begin{pmatrix} 2\\ 9\\ \end{pmatrix} = \begin{pmatrix} (3 \times 2) + (5 \times 9) \end{pmatrix} = \begin{pmatrix} 51 \end{pmatrix}

$$

Similarly if:
 * $$ \begin{matrix}

A_{3\times 1} = \begin{pmatrix} 1\\ 2\\ 3\end{pmatrix} &, & B_{1\times 3} = \begin{pmatrix} 4 & 5 & 6\end{pmatrix}

\end{matrix} $$

then

B_{1\times 3} \times A_{3\times 1}= \begin{pmatrix} 4 & 5 &6 \end{pmatrix} \times \begin{pmatrix}1\\2\\3\\\end{pmatrix} = \begin{pmatrix}(4 \times 1) + (5 \times 2) + (6 \times 3)\end{pmatrix} = \begin{pmatrix} 32 \end{pmatrix} $$

A matrix with just one row is called a row vector, similarly a matrix with just one column is called a column vector. When we multiply a row vector A, with a column vector B, we multiply the element in the first column of A by the element in the first row of B and add to that the product of the second column of A and second row of B and so on. More generally we multiply a1,i by bi,1 (where i ranges from 1 to n, the number of rows/columns) and sum up all of the products. Symbolically:

 * $$ A_{1\times n} \times B_{n\times 1} = (\sum_{i=1}^na_{1,i}\times b_{i,1} )$$ (for information on the $$\sum$$ sign, see Summation_Sign)
 * where n is the number of rows/columns.

 * In words: the product of a column vector and a row vector is the sum of the product of item 1,i from the row vector and i,1 from the column vector where i is from 1 to the width/height of these vectors.

Note: The product of matrices is also a matrix. The product of a row vector and column vector is a 1 by 1 matrix, not a scalar.

Exercises
Multiply:
 * $$\begin{pmatrix}1&2\end{pmatrix}\begin{pmatrix}1\\2\end{pmatrix}$$

 * $$\begin{pmatrix}1\\2\end{pmatrix}\begin{pmatrix}1&2\end{pmatrix}$$

 * $$\begin{pmatrix}\frac{1}{8}&9\end{pmatrix}\begin{pmatrix}16\\2\end{pmatrix}$$

 * $$\begin{pmatrix}a&b\end{pmatrix}\begin{pmatrix}d\\e\end{pmatrix}$$

 * $$\begin{pmatrix}6 + 6b&3 - b\end{pmatrix}\begin{pmatrix}0\\0\end{pmatrix}$$

 * $$\begin{pmatrix}0&abc\end{pmatrix}

\begin{pmatrix}a\\0\end{pmatrix}$$

Multiplication of non-vector matrices
Suppose $$A_{m \times n}B_{n \times p} = C_{m \times p}$$ where A, B and C are matrices. We multiply the ith row of A with the jth column of B as if they are vector-matrices. The resulting number is the (i,j)th element of C. Symbolically:
 * $$c_{i,j} = \sum_{k=1}^{n}a_{i,k}\times b_{k,j}$$

 Example 1

Evaluate AB = C and BA= D, where
 * $$ A =

\begin{pmatrix} 3&2\\ 5&6\\ \end{pmatrix} $$ and
 * $$ B =

\begin{pmatrix} 2&6\\ 8&7\\ \end{pmatrix} $$

 Solution
 * $$c_{1,1} = \begin{pmatrix} 3&2 \end{pmatrix} \begin{pmatrix}2\\ 8\end{pmatrix} = (3\times 2 + 2\times 8) = 22$$
 * $$c_{1,2} = \begin{pmatrix} 3&2 \end{pmatrix} \begin{pmatrix}6\\ 7\end{pmatrix} = (3\times 6 + 2\times 7) = 32$$
 * $$c_{2,1} = \begin{pmatrix} 5&6 \end{pmatrix} \begin{pmatrix}2\\ 8\end{pmatrix} = (5\times 2 + 6\times 8) = 58$$
 * $$c_{2,2} = \begin{pmatrix} 5&6 \end{pmatrix} \begin{pmatrix}6\\ 7\end{pmatrix} = (5\times 6 + 6\times 7) = 72$$

i.e.
 * $$C =

\begin{pmatrix} 22&32\\58&72 \end{pmatrix} $$

 * $$d_{1,1} = \begin{pmatrix} 2&6 \end{pmatrix} \begin{pmatrix}3\\ 5\end{pmatrix} = (2\times 3 + 6\times 5) = 36$$
 * $$d_{1,2} = \begin{pmatrix} 2&6 \end{pmatrix} \begin{pmatrix}2\\ 6\end{pmatrix} = (2\times 2 + 6\times 6) = 40$$
 * $$d_{2,1} = \begin{pmatrix} 8&7 \end{pmatrix} \begin{pmatrix}3\\ 5\end{pmatrix} = (8\times 3 + 7\times 5) = 59$$
 * $$d_{2,2} = \begin{pmatrix} 8&7 \end{pmatrix} \begin{pmatrix}2\\ 6\end{pmatrix} = (8\times 2 + 7\times 6) = 58$$

i.e.
 * $$D =

\begin{pmatrix} 36&40\\59&58 \end{pmatrix} $$

Example 2  Evaluate AB and BA where
 * $$A =

\begin{pmatrix} 5&17\\ 2&7 \end{pmatrix} $$
 * $$B =

\begin{pmatrix} 7&-17\\ -2&5 \end{pmatrix} $$

 Solution

\begin{pmatrix} 5&17\\ 2&7 \end{pmatrix} \begin{pmatrix} 7&-17\\ -2&5 \end{pmatrix} = \begin{pmatrix} 1&0\\ 0&1 \end{pmatrix} $$

\begin{pmatrix} 7&-17\\ -2&5 \end{pmatrix} \begin{pmatrix} 5&17\\ 2&7 \end{pmatrix} = \begin{pmatrix} 1&0\\ 0&1 \end{pmatrix} $$

Example 3  Evaluate AB and BA where
 * $$A =

\begin{pmatrix} 2&6\\ 0&5 \end{pmatrix} $$
 * $$B =

\begin{pmatrix} 5&-6\\ 0&2 \end{pmatrix} $$

 Solution

\begin{pmatrix} 2&6\\ 0&5 \end{pmatrix} \begin{pmatrix} 5&-6\\ 0&2 \end{pmatrix} = \begin{pmatrix} 10&0\\ 0&10 \end{pmatrix} $$

\begin{pmatrix} 5&-6\\ 0&2 \end{pmatrix} \begin{pmatrix} 2&6\\ 0&5 \end{pmatrix} = \begin{pmatrix} 10&0\\ 0&10 \end{pmatrix} $$

Example 4  Evaluate the following multiplication:

\begin{pmatrix} a\\ b \end{pmatrix} \begin{pmatrix} c&d\\ \end{pmatrix} $$

 Solution

Note that:

\begin{pmatrix} a\\ b \end{pmatrix} $$ is a 2 by 1 matrix and

\begin{pmatrix} c&d\\ \end{pmatrix} $$ is a 1 by 2 matrix. So the multiplication makes sense and the product should be a 2 by 2 matrix.

\begin{pmatrix} a\\ b \end{pmatrix} \begin{pmatrix} c&d\\ \end{pmatrix} = \begin{pmatrix} ac&ad\\ bc&bd\\ \end{pmatrix} $$

Example 5  Evaluate the following multiplication:

\begin{pmatrix} 1\\ 2 \end{pmatrix} \begin{pmatrix} 3&4\\ \end{pmatrix} $$

 Solution

\begin{pmatrix} 1\\ 2 \end{pmatrix} \begin{pmatrix} 3&4\\ \end{pmatrix} = \begin{pmatrix} 1 \times 3& 1 \times 4\\ 2 \times 3& 2 \times 4 \\ \end{pmatrix} = \begin{pmatrix} 3& 4\\ 6& 8 \\ \end{pmatrix} $$

Example 6  Evaluate the following multiplication:

\begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} c&0\\ 0&d \end{pmatrix} $$

 Solution  $$ \begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} c&0\\ 0&d \end{pmatrix} = \begin{pmatrix} ac&0\\ 0&bd \end{pmatrix} $$

Example 7  Evaluate the following multiplication:

\begin{pmatrix} a&b\\ c&d \end{pmatrix} \begin{pmatrix} x\\ y \end{pmatrix} $$

 Solution  $$ \begin{pmatrix} a&b\\ c&d \end{pmatrix} \begin{pmatrix} x\\ y \end{pmatrix} = \begin{pmatrix} ax+by\\ cx+dy \end{pmatrix} $$

Note Multiplication of matrices is generally not commutative, i.e. generally AB ≠ BA.

Diagonal matrices
A diagonal matrix is a matrix with zero entries everywhere except possibly down the diagonal. Multiplying diagonal matrices is really convenient, as you need only to multiply the diagonal entries together.

Examples

The following are all diagonal matrices $$ \begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} c&0\\ 0&d \end{pmatrix} \begin{pmatrix} 1&0\\ 0&2 \end{pmatrix} \begin{pmatrix} 0&0\\ 0&0 \end{pmatrix} \begin{pmatrix} a&0&0\\ 0&c&0\\ 0&0&0 \end{pmatrix} $$

 Example 1  $$ \begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} e&0\\ 0&f \end{pmatrix} \begin{pmatrix} h&0\\ 0&i\\ \end{pmatrix} = \begin{pmatrix} aeh&0\\ 0&bfi\\ \end{pmatrix} $$

 Example 2  $$ \begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} a&0\\ 0&b \end{pmatrix} \begin{pmatrix} a&0\\ 0&b \end{pmatrix} = \begin{pmatrix} a^3&0\\ 0&b^3 \end{pmatrix} $$

The above examples show that if D is a diagonal matrix then Dk is very easy to compute, all we need to do is to take the diagonal entries to the kth power. This will be an extremely useful fact later on, when we learn how to compute the nth Fibonacci number using matrices.

Exercises
1. State the dimensions of C
 * a) C = An×pBp×m
 * b) $$C =

\begin{pmatrix} 10^{10}&20\\ 5000&0 \end{pmatrix} \begin{pmatrix} 1&2&3&4\\ 2&5&6&6 \end{pmatrix} $$

2. Evaluate. Please note that in matrix multiplication (AB)C = A(BC) i.e. the order in which you do the multiplications does not matter (proved later).
 * a)

\begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1\\ 1\\ \end{pmatrix}$$

 * b)

\begin{pmatrix} 3&1\\ 2&8\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&2\\ \end{pmatrix} \begin{pmatrix} 1&1\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 1\\ 1\\ \end{pmatrix}$$

3. Performing the following multiplications:

C = \begin{pmatrix} 1&2\\ 4&5 \end{pmatrix} \begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix}$$

D = \begin{pmatrix} 1&0\\ 0&1 \end{pmatrix} \begin{pmatrix} 1&2\\ 4&5\\ \end{pmatrix} $$ What do you notice?

The Identity & multiplication laws
The exercise above showed us that the matrix:

\begin{pmatrix} 1&0\\ 0&1 \end{pmatrix} $$ is a very special. It is called the 2 by 2 identity matrix. An identity matrix is a square matrix, whose diagonal entries are 1's and all other entries are zero. The identity matrix, I, has the following very special properties for all matrices A. We don't usually specify the shape of the identity because it's obvious from the context, and in this chapter we will only deal with the 2 by 2 identity matrix. In the real number system, the number 1 satisfies: r × 1 = r = 1 × r, so it's clear that the identity matrix is analogous to "1".
 * 1) $$A \times I = A$$
 * 2) $$I \times A = A$$

Associativity, distributivity and (non)-commutativity

Matrix multiplication is a great deal different to the multiplication we know from multiplying real numbers. So it is comforting to know that many of the laws the real numbers satisfy also carries over to the matrix world. But with one big exception, in general AB ≠ BA.

Let A, B, and C be matrices. Associativity means
 * (AB)C = A(BC)

i.e. the order in which you multiply the matrices is unimportant, because the final result you get is the same regardless of the order which you do the multiplications.

On the other hand, distributivity means
 * A(B + C) = AB + AC

and
 * (A + B)C = AC + BC

Note: The commutative property of the real numbers (i.e. ab = ba), does not carry over to the matrix world.

 Convince yourself

For all 2 by 2 matrices A, B and C. And I the identity matrix.

1. Convince yourself that in the 2 by 2 case:
 * A(B + C) = AB + AC

and
 * (A + B)C = AC + BC

2. Convince yourself that in the 2 by 2 case:
 * A(BC) = (AB)C

3. Convince yourself that:
 * $$AB\ne BA$$

in general. When does AB = BA? Name at least one case.

Note that all of the above are true for all matrices (of any dimension/shape).

Determinant and Inverses
We shall consider the simultaneous equations:
 * ax + by = α (1)
 * cx + dy = β (2)

where a, b, c, d, α and β are constants. We want to determine the necessary conditions for (1) and (2) to have a unique solution for x and y. We proceed:
 * Let (1') = (1) × c
 * Let (2') = (2) × a

i.e.
 * acx + bcy = cα (1')
 * acx + ady = aβ (2')

Now
 * let (3) = (2') - (1')
 * (ad - bc)y = aβ - cα (3)

Now y can be uniquely determined if and only if (ad - bc) ≠ 0. So the necessary condition for (1) and (2) to have a unique solution depends on all four of the coefficients of x and y. We call this number (ad - bc) the determinant, because it tells us whether there is a unique solution to two simultaneous equations of 2 variables. In summary
 * if (ad - bc) = 0 then there is no unique solution
 * if (ad - bc) ≠ 0 then there is a unique solution.

Note: Unique, we can not emphasise this word enough. If the determinant is zero, it doesn't necessarily mean that there is no solution to the simultaneous equations! Consider:
 * x + y = 2
 * 7x + 7y = 14

the above set of equations has determinant zero, but there is obviously a solution, namely x = y = 1. In fact there are infiinitely many solutions! On the other hand consider also:
 * x + y = 1
 * x + y = 2

this set of equations has determinant zero, and there is no solution at all. So if determinant is zero then there is either no solution or infinitely many solutions.

 Determinant of a matrix   We define the determinant of a 2 × 2 matrix
 * $$A = \begin{pmatrix}

a&b\\ c&d \end{pmatrix}$$ to be
 * $$\det (A) = ad - bc \!$$

Inverses
It is perhaps, at this stage, not very clear what the use is of the det(A). But it's intimately connected with the idea of an inverse. Consider in the real number system a number b, it has (multiplicative) inverse 1/b, i.e. b(1/b) = (1/b)b = 1. We know that 1/b does not exist when b = 0.

In the world of matrices, a matrix A may or may not have an inverse depending on the value of the determinant det(A)! How is this so? Let's suppose A (known) does have an inverse B (i.e. AB = I = BA). So we aim to find B. Let's suppose further that
 * $$A

= \begin{pmatrix} a&b\\ c&d \end{pmatrix}$$ and
 * $$B

= \begin{pmatrix} w&x\\ y&z \end{pmatrix}$$ we need to solve four simultaneous equations to get the values of w, x, y and z in terms of a, b, c, d and det(A).
 * aw + by = 1
 * cw + dy = 0
 * ax + bz = 0
 * cx + dz = 1

the reader can try to solve the above by him/herself. The required answer is
 * $$B = \frac{1}{\det(A)}\begin{pmatrix}

d&-b\\ -c&a \end{pmatrix} $$ In here we assumed that A has an inverse, but this doesn't make sense if det(A) = 0, as we can not divide by zero. So A-1 (the inverse of A) exists if and only if det(A) ≠ 0.

Summary

If AB = BA = I, then we say B is the inverse of A. We denote the inverse of A by A-1. The inverse of a 2 × 2 matrix
 * $$A =

\begin{pmatrix} a&b\\ c&d \end{pmatrix} $$ is
 * $$A^{-1} = \frac{1}{\det(A)}\begin{pmatrix}

d&-b\\ -c&a \end{pmatrix} $$ provided the determinant of A is not zero.

Solving simultaneous equations
Suppose we are to solve:
 * ax + by = α
 * cx + dy = β

We let
 * $$ A = \begin{pmatrix}a&b\\c&d\end{pmatrix}$$
 * $$ w = \begin{pmatrix}x\\y\end{pmatrix}$$
 * $$ \gamma = \begin{pmatrix}\alpha\\ \beta\end{pmatrix}$$

we can translate it into matrix form
 * $$ \begin{pmatrix}a&b\\c&d\end{pmatrix}\begin{pmatrix}x\\y\end{pmatrix} = \begin{pmatrix}\alpha\\ \beta\end{pmatrix}$$

i.e
 * $$ Aw = \gamma$$

If A's determinant is not zero, then we can pre-multiply both sides by A-1 (the inverse of A)

\begin{matrix} A^{-1}Aw &=& A^{-1}\gamma\\ Iw &=& A^{-1}\gamma\\ w &=& A^{-1}\gamma\\ \end{matrix} $$ i.e.
 * $$\begin{pmatrix}x\\y\end{pmatrix} = \frac{1}{ad-bc}\begin{pmatrix}d&-b\\-c&a\end{pmatrix}\begin{pmatrix}\alpha\\ \beta\end{pmatrix}$$

which implies that x and y are unique.

 Examples

Find the inverse of A, if it exists
 * a) $$ A = \begin{pmatrix}1&5\\2&3\end{pmatrix}$$
 * b) $$ A = \begin{pmatrix}10&2\\2&7\end{pmatrix}$$
 * c) $$ A = \begin{pmatrix}a&b\\3a&3b\end{pmatrix}$$
 * d) $$ A = \begin{pmatrix}3&5\\5&3\end{pmatrix}$$

 Solutions
 * a) $$A^{-1} = \frac{1}{-7}\begin{pmatrix}3&-5\\-2&1\end{pmatrix}$$
 * b) $$A^{-1} = \frac{1}{66}\begin{pmatrix}7&-2\\-2&10\end{pmatrix}$$
 * c) No solution, as det(A) = 3ab - 3ab = 0
 * d) $$A^{-1} = \frac{1}{-16}\begin{pmatrix}3&-5\\-5&3\end{pmatrix}$$

 Exercises

1. Find the determinant of
 * $$ A = \begin{pmatrix}\frac{2}{5}&\frac{2}{3}\\ \\ \frac{3}{2}& \frac{5}{2}\end{pmatrix}$$. Using the determinant of A, decide whether there's a unique solution to the following simultaneous equations

\begin{matrix} \frac{2}{5}x + \frac{2}{3}y = 0\\ \frac{3}{2}x + \frac{5}{2}y = 0 \end{matrix} $$

2. Suppose
 * C = AB

show that
 * det(C) = det(A)det(B)

for the 2 × 2 case. Note: it's true for all cases.

3. Show that if you swap the rows of A to get A' , then det(A) = -det(A' )

4. Using the result of 2

a) Prove that if:
 * $$A = P^{-1}BP$$

then det(A) = det(B)

b) Prove that if:
 * Ak = 0

for some positive integer k, then det(A) = 0.

5. a) Compute A5, i.e. multiply A by itself 5 times, where
 * $$A =

\begin{pmatrix} -1&6\\ -1&4\\ \end{pmatrix} $$

b) Find the inverse of P where

P = \begin{pmatrix} 1&-2\\ -1&3\\ \end{pmatrix} $$

c) Verify that
 * $$A =

P^{-1} \begin{pmatrix} 1&0\\ 0&2\\ \end{pmatrix} P $$

d) Compute A5 by using part (b) and (c).

e) Compute A100

Other Sections
Next Section > High_School_Mathematics_Extensions/Matrices/Linear_Recurrence_Relations_Revisited

Problem Set > High_School_Mathematics_Extensions/Matrices/Problem Set

Project > High_School_Mathematics_Extensions/Matrices/Project/Elementary_Matrices


text:
Cookbook:South American Cuisines

South American cuisines are partly based on the cuisines of Spain and Portugal, with heavy influence from the cuisine of various pre-European indigenous peoples. In Brazil, Western African influences are tremendously popular, especially near the coast.

 * Cuisine of Argentina
 * Cuisine of Brazil
 * Cuisine of Chile
 * Cuisine of Colombia
 * Cuisine of Guyana
 * Cuisine of Paraguay
 * Cuisine of Peru
 * Cuisine of Uruguay
 * Cuisine of Venezuela

title: Cookbook:South American Cuisines


text:
Wikiversity:Translator's Handbook

Institute for Multilingual Studies

Translator's Handbook

Interlingual Training Manual

This handbook is part of a learning path for Wikiversity participants who wish to become certified translators while helping to produce Wikiversity_translations.

Introduction
Essay: Why learn to translate?

Winning Essay goes here

The Interlingual Beta Club would like an enlightening and inspirational introduction to The Translator's Handbook. See certified translator for details.

Translating in groups
Some say translating is an art, some say it is a science. Here at the Translation Department, we think it's a matter of interpretation (pun intended).

For us it's a simple matter of getting the job done. Translating Wikiversity is a daunting task. No matter how or where you start, you're still at the tip of the iceberg. This version of the handbook is written in the English Language. German and Chinese versions are just right over there, but All Languages need to be taken into account. Impossible? You should never feel alone in this work. In the context of translating, participation is everything!

Reading:
 * Wikiversity translations/Recruiting translators

Learning Families
Wikiversity, using a method similar to, but more efficient than Multilingual coordination at Wikipedia must come up with its own approach to Foreign Language Learning (and teaching). Here we have a unique opportunity to collaborate between and among Wikiversity versions and Betas, and have a bit of fun doing it. The Interlingual Beta Club is made up of native speakers and writers from many languages and backgrounds. The imperative of collaboration between Schools, Divisions and Departments expedite the process in several ways:
 * 1) Media Studies can pair with Computer Science to design an audio interface for Computer assisted translation
 * 2) Audio Engineering can be used to record well-known public-domain literary works that have already been translated into numerous languages to present comparitive samples of the same texts across languages.
 * 3) Linguistic elements can be programmed into AI components to tweak the performance of machine translation systems.
 * 4) Brainstorm!!!

Schools: Media Studies | Linguistics | Computer Science | Language and Literature

Language Families
NEXT: Languages

Explore:
 * Languages and Language families
 * Category: Wikiversity translations
 * Wikibooks:Languages bookshelf

Linguistics
School:Linguistics - Portal:Linguistics

Lexicography
Many keywords on the various Wikipedias have links in the left sidebar to other language articles with the same name, but translated to the other language. Tables like this one can be made to tabulate these keywords:

Translation Lexicons and Dictionaries:
 * Rosetta Project
 * Eurodicautom European Terminology Database
 * Logos Dictionary
 * LookWAYup Dictionary
 * Majstro
 * Word Reference
 * Your Dictionaries English version of diccionarios.com
 * German dictionary and translation tool

This chapter of the Translator's Handbook may someday contain an expansive lexicon.

Machine Translation
Machine translation is a sub-field of Computational linguistics that investigates the use of computer software to translate text or speech from one natural language to another. At its basic level, MT performs simple substitution of atomic words in one natural language for words in another.

The Schools of Computer Science and Linguistics might someday meet at Computational linguistics to develop machine translation software for use at Wikiversity.
 * Altavista translation - "Babel fish"
 * Apertium - Free software machine translation toolkit.

Computer-assisted Translation
Computer-assisted translation, Computer-aided translation, or CAT is a form of translation wherein a human translator translates texts using computer software designed to support and facilitate the translation process.

See Computer-assisted translation

The Schools of Computer Science and Linguistics might someday meet at Computational linguistics to develop computer-assisted translation software for use at Wikiversity.

Appendix

 * Topic:Translation
 * Le Ton beau de Marot by Douglas Hofstadter. A book about translation.

See Template talk:InterlingualMainNavEn

title: Wikiversity:Translator's Handbook


text:
Ernst Ludwig Franke

Ernst Ludwig Franke (23 August 1886 – 28 December 1948) was an Austrian painter. His work was part of the painting event in the art competition at the 1936 Summer Olympics.

title: Ernst Ludwig Franke


text:
Lee Yi-chieh

Lee Yi-chieh (born 1992) is a Taiwanese actress.

Lee appeared in When Love Comes (2010 film) (2010) as Laichun. She won a best newcomer award at the 2011 Chinese Film Media Awards for her work in that film. Lee was Ximin, a college student, in When Green Turns to Gold (2018). Lee's character in Wild Sparrow (2019) was a young woman living in Zhongli District, struggling with romantic relationships and maintaining employment while raising her son. Lee shared the Best Actress Award at the Taipei Film Awards that year, with Liu Yin-shang. It was the first time that the award was given to two recipients.

title: Lee Yi-chieh


text:
Senator McClain

Senator McClain may refer to:

 * David H. McClain (born 1933), Florida State Senate
 * Edward McClain (Alabama politician) (born 1940), Alabama State Senate

title: Senator McClain


text:
Talk:Aurore Martin

This page says Aurore Martin was born in 1978. The French and spanish page say she was born in 1979. How can we clear this up? --Mariiwakura (talk) 19:47, 3 November 2012 (UTC)

title: Talk:Aurore Martin


text:
Norwegian

 * /Cover/
 * /Contributors/
 * Introduksjon ~ Introduction

Lessons

 * 1) Presenter deg Introducing Yourself [[Image:25%.svg]]
 * 2) Grunnleggende grammatikk Basic Grammar [[Image:25%.svg]]
 * 3) Kjekt å vite Nice to Know [[Image:25%.svg]]

Vocabulary
/Months and Weekdays/ | /Numbers/ | /Time/ | /Useful Expressions/

Appendices
Advanced Noun Inflection | Norwegian Pronunciation | Misunderstandings | Fast translation rules

title: Norwegian


text:
User:Issac eappen/sandbox

ISSAC EAPPEN

Issac Eappen, a novelist and Short story writer,is  belonging to the southern most part part of India,  that is Kerala. He mainly writes in the language, Malayalam which is the spoken language of more than 3.5 billion people in  Kerala,India.He has published more than 200 short stories  two novels and about 100 literary articles in  major literary publications in Malayalam, which have been collected in 18 books. He bagged many prestigious literary awards in Malayalam.Most of his works have been translated into English, Hindi, Tamil etc..''' His new Novel Jeevapusthakathil Perullavar  (The names in the Book of Life)published by the National Book Stall, Kottayam, Kerala

'''Issac Eappen's main works included 1. Souhruthathinte Velipadukal(The Revelations of Friendship) 2.Athellam maranakku(Let all that forget) 3.Nehruvinte Theevandi(Nehru's train) 4.Nagarathile Komalikal( The Clowns in the City) 5.Vasco da Gama Athava Moosa Abdulla( Vasco da Gama alias Moosa Abdulla) 6.Agniyil Oru nagaram( A city on Fire) 7.Snehathinte kadal Sparsam( The oceanic touch of love) 8.Utharathunikathayum Painkiliyium(The post modernism and pulp fiction) 9.Nagaram Rebeccayode Paranjathu( What the City told to Rebecca) 10.Paradesi Mokshayatra( The Pilgrims progress) 11.Oru Manjukalathinte Ormakkayi( In rememberance of a winter) 12.Kasumayan 13.Kolani Vazhcha( The colonial Rule) 14.Rashtrathinu Thee Pidikkumbol( When the nation caught fire) 15.Daivathinte Melvilasm(The Address of Almighty) 16.Pranayathinte Nanartyhangal(Synonyms of Love- Short stories) 17.Jeevaputhakathil Perullavar-Novel(Names in the Book of Life) 18.Ezhamathe Nila(The Seventh Floor) 19.Selected Stories(Kadha By NBS) 20.Aval chithra salabhangale pranayichirunnu(She was in love with butterflies) 21.kadal karayile kristhu.(Christ by the sea shore) 22.oru thirakadha and other stories. 23. liftum komaalium (The lift and the Clown) 24.SAMATHALAM KADANNU MALAKALILEKKU(From plainlands to mountain)

'Major awards Issac Eappen received...'' 1.Yuva sahitya Puraskaram. 2. T K Balan memorial navu puraskaram. 3. Thakazhi Award. 4.EVG Award. 5.Ponkunnam varkey Award. 6.Basheer Puraskaram 7.Kairali -Atlas Award. 8.State Institute of Language's Literary Puraskaram. 9.Abu Dhabi Sakthi Award. 10. PP Gopalan memorial Award. 11. Kottarakara Thamburan Awrad. 12.SK pottekatt Award''' 13.Riyadh Marthoma literary award for best book of the year 2014. 14.Yuvakala sahithi T V kochubava award for best collection of Short Stories.2014. 15. Payal Books Award

title: User:Issac eappen/sandbox


text:
Radley College Boat Club

Radley College Boat Club is a rowing club on the River Thames based in Lower Radley, Radley, Oxfordshire.

History
The club was founded in 1849. Abingdon>

National champions
Key
 * M men, +coxed, -coxless, x sculls, J junior, 16 under-16

title: Radley College Boat Club


text:
Talk:Perl/Fun with Named Colors

Questions? Comments? Other ideas? feel Free! CQ 16:47, 27 October 2006 (UTC)

Four suggestions to happier Perl code...
1) Do not use "-w" to enable warnings, it's antiquated and not recommended. Instead, import the warnings module with the line use warnings;

2) Declare all of your variables with my

3) Import the strict module with the line use strict;

4) Clean spacing and indenting leads to clean code. Unless you're golfing, spacing and indenting make things much easier to read. —The preceding unsigned comment was added by Innominate (talk • contribs) 21:42, 27 December 2006 (UTC).

title: Talk:Perl/Fun with Named Colors


text:
Urotrygon aspidura

Urotrygon aspidura, also known as the spiny-tail round ray or Panamic stingray, is a species of stingray native to the eastern-central and south-eastern Pacific, southern Baja, and the Gulf of California. It can grow up to 42 cm. They are severely threatened by shrimp fisheries.

title: Urotrygon aspidura


text:
Category:Tallahassee Tiger Sharks players

This category contains articles about people who played for the Tallahassee Tiger Sharks when they were in the East Coast Hockey League.


text:
Wikipedia:Articles for deletion/Ollie Sloan

The result was delete. Tone 08:43, 24 August 2020 (UTC)

Ollie Sloan

 * – ( View AfD View log  Stats )

Delete Musician that fails WP:MUSIC. I can't find any singles or albums that placed in the charts or any wider significant impact (e.g. YouTube views). Also much of the article content appears to be copy/pasted from the muscian's website, so there is probably a conflict of interest as well. Although his songs may have appeared in TV dramas and featured on national radio, that doesn't appear to be notable either by some significant subsequent impact. Seaweed (talk) 13:27, 16 August 2020 (UTC)
 * Note: This discussion has been included in the list of Bands and musicians-related deletion discussions. Shellwood (talk) 13:34, 16 August 2020 (UTC)
 * Note: This discussion has been included in the list of United Kingdom-related deletion discussions. Shellwood (talk) 13:34, 16 August 2020 (UTC)

 * Speedy delete and salt it per WP:SPAM, WP:MILL, and WP:NOT. There are unsourced statements that can't be verified that are bollocks; for example: "He is also well known on several social media sites such as YouTube, ... and Twitter." He has 15 videos on YouTube, less than a quarter of my partner's cooking show. He has 1,600 followers, less than half of what I have, on Twitter. He has zero followers on Facebook. The sourcing is terrible. In 2020 everybody knows we are not MySpace. This page is an insult to working musicians. Salt it with a vengeance. Bearian (talk) 23:51, 20 August 2020 (UTC)
 * Delete a non-notable musician.John Pack Lambert (talk) 19:55, 21 August 2020 (UTC)


text:
Paul Moore (soccer)

Paul Moore is a Canadian former soccer player who played most notably in the USL A-League, National Professional Soccer League, and with various Canadian soccer leagues.

Early career
Moore began his professional career in the Canadian National Soccer League with St. Catharines Wolves in 1995 and had a two-year tenure with the club. During his tenure with St. Catharines he achieved the CNSL Championship, and two league cups.

Toronto Lynx
On April, 1997 he signed with expansion franchise the Toronto Lynx in the USL A-League, his signing was announced in a press conference which revealed the team roster. Moore made his debut for the club on April 12, 1997 in the Lynx's first official match against Jacksonville Cyclones; the game would eventually result in a 3-1 defeat for the fledgling side. In total, he would appear in 2 matches for Toronto.

For the remainder of the year he returned to the CNSL with Toronto Supra, and featured in the CNSL Championship final against former club St. Catharines Wolves.

CPSL
In 1998, Moore signed with the Toronto Olympians of the newly formed Canadian Professional Soccer League. Midway through the season he was transferred to Glen Shields. In 2000, he signed with Toronto Croatia where he finished second in scoring for the club. He also assisted in securing the CPSL Championship after Croatia defeated the Toronto Olympians by a score of 2-1. The following season he returned to the Olympians.

Indoor career
He played at the indoor level with the Edmonton Drillers in the America-based National Professional Soccer League during the 1999-00 indoor season. He would appear in 4 matches and record a goal.

Ontario Cup
In 2009, he played with Markham Soccer Club in the Ontario Cup tournament.

Honors

 * St. Catharines Wolves
 * CNSL Championship: 1995
 * CNSL League Cup: 1995, 1996
 * Toronto Croatia
 * CPSL Championship: 2000

title: Paul Moore (soccer)


text:
Talk:Bill Thompson (technology writer)

Discussion
Please source the University Challenge claims, SqueakBox 16:43, 20 March 2006 (UTC)

I can't, I remember watching it though! It was in the Bamber Gascoigne days. Billy was a local hero then. (VOG)

What is a "degree in computing?" Silverweed 20:55, 17 June 2007 (UTC)
 * Edited to give a more accurate statement. Gordo (talk) 17:50, 21 November 2009 (UTC)

Refs for article development
The first 3 have been removed from Bill Thompson (technology writer) per WP:ELNO. The others are relevant URLs which could be worked in as article content when anyone has time. (I may do this myself.)
 * Working 4 an MP has  technical support provided by Bill Thompson
 * BBC article
 * Pair behind first Guardian website back together for BBC Archive

-- Trevj (talk) 14:33, 26 March 2012 (UTC)
 * http://news.bbc.co.uk/1/hi/7421099.stm
 * http://www.bbc.co.uk/blogs/radio/2011/08/10_years_of_the_internet_on_th.html
 * http://news.bbc.co.uk/1/hi/7421099.stm

'Wikipedia death hoax'
I removed a section of this article describing how he had been mistakenly described as dead in an earlier version of this article, and had written an article about it himself. I just don't think that's particularly significant or worth mentioning. Lots of people have been mistakenly claimed as dead in Wikipedia at one time or another (see Death hoax), but we don't normally note that in their articles. Robofish (talk) 11:51, 4 July 2012 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Bill Thompson (technology writer). Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20140904222034/http://www.brittensinfonia.com/about-us/meet-the-trustees/ to http://www.brittensinfonia.com/about-us/meet-the-trustees/

Cheers.— InternetArchiveBot  (Report bug) 13:13, 2 November 2016 (UTC)

title: Talk:Bill Thompson (technology writer)


text:
Talk:Ramapough Mountain Indians/Archive index

Report generated based on a request from Talk:Ramapough Mountain Indians. It matches the following masks: Talk:Ramapough Mountain Indians/Archive <#>, Talk:Ramapough Mountain Indians.


text:
Senator Greiner

Senator Greiner may refer to:

 * Jon Greiner (born 1951), Utah State Senate
 * Sandy Greiner (born 1945), Iowa State Senate
 * William P. Greiner (fl. 1910s–1930s), New York State Senate

title: Senator Greiner


text:
Talk:Antonio Escobar Huertas

Correct surname
Was he Huerta or Huertas? The former is more popular and the latter seems to be Catalan. Propositum (talk) 16:32, 13 January 2017 (UTC)

title: Talk:Antonio Escobar Huertas


text:
pompare

Verb

 * 1) to pump
 * 2) to pump up or pump out
 * 3) to exaggerate

Etymology
From.

Noun

 * 1) pumping

title: pompare


text:
Talk:Nina Samorodin

'''Hi Wikipedians, We would like someone to review this page. Thank you!'''

Your draft is looking good, citations should be properly cited starting next week. If you are having trouble finding images you could find pictures of Occoquan workhouse to add to this page. You are missing a lead, write 1-2 sentences giving an overview of her story highlighting major events Serenewilliams (talk) 16:21, 20 September 2019 (UTC)

title: Talk:Nina Samorodin


text:
User:KateyD/sandbox

Queensland Military Historical Society Incorporated

The Queensland Military Historical Society is incorporated in Queensland. Its mission is to promote understanding of Queensland's military history, through research and scholarship, the provision of a forum for discussion, and the development and exhibition of our collections. The Society envisions a community that will be curious about our military past, who will seek to analyse, record and share what has transpired, and be inspired by the understanding they gain. The aim of the Society is to promote and enhance community understanding of Queensland’s military history from 1824 to the present. To achieve this aim, the Society will develop a museum collection that portrays the military heritage of Queensland, and display, exhibit and interpret museum items, develop a library collection of published and unpublished information that document or support research into the military history of Queensland, conduct and participate in commemorative events and activities that enhance community understanding of Queensland’s military history, support, promote and publish research and scholarship into Queensland’s military history, and provide a forum for community participation, and engage members in commemorative and social activities that promote interest in Queensland’s military history, and provide opportunities for members to contribute in practical ways to the advancement of the society.

QMHS is located in the Fort Lytton Historical Precinct and operates a Museum in the Old Dining Hall building.

https://qmhs.com.au

Queensland Category:Society in Queensland

title: User:KateyD/sandbox


text:
Bolt (website)

Bolt was a social networking and video website active from 1996 to 2007 before reopening in April 2008. It was shut down for a period of one year due to copyright violations leading to bankruptcy. It was acquired by new owners on January 4, 2008 and operated successfully for several months before announcing plans to go offline in October 2008.

1996–2006
In 1996 Bolt.com was founded as a teen community by Dan Pelson and Jane Mount as part of Concrete Media. It was among the first social networking sites to appear on the Internet. It offered content that included daily horoscopes, chat rooms, message boards, tagbooks (a knowledge market feature), photo albums, internet radio, browser games, blogs, e-cards, an instant messenger service, a clubs feature (giving people with similar interests a common message board), and badges (a system of awards for user profiles). An email service was hosted, but it was discontinued due to email companies such as Yahoo and Google providing between 1 and nearly 3 gigabytes of email storage for free, rendering Bolt's email service obsolete. This was done without notifying its email subscribers. Bolt was also one of the first sites to give its members their own web page. In 2002, the badges became more sponsor-based, which led to Bolt becoming more commercial with an increase of ads into the users' activities. Company badges included Verizon Wireless, Gillette, and Sony.

Bolt was originally marketed towards teenagers to create content, meet people, and play games in a safe and age-appropriate environment. As members aged and stayed with the site, more members were college students and between ages 18–24. In 2005, Bolt.com launched its second iteration, Boltfolio. Touted by itself as the leader of the "cult of creativity", Boltfolio intended to provide a one-stop shop for creative users to upload their own photos, videos, and music, as well as write blogs or record directly from a webcam. The goal of Boltfolio was to provide a set of tools that would attract users of creative sites such as DeviantArt, YouTube, and Flickr.

2006–2009
In December 2005 Bolt Media finalized a deal to purchase InterMedia Inc., a small company focused on a video-sharing site, Yashi. Yashi and Boltfolio were integrated into one site, and in March 2006 Bolt Media opted to focus the company on this new property. Boltfolio became Bolt.com, moving the existing Bolt.com site to Bolt2.com. As 2006 wore on, creative Bolt members were featured less frequently on the site, taking a back seat to videos produced by Bolt staff, popular music videos, and viral videos that also were appearing on competing video sites.

On October 17, 2006, one week after announcing a revenue-sharing deal with YouTube, Universal Music filed suit against Bolt Media and another video site, Grouper. Universal contended that both sites allowed and encouraged their users to swap unlicensed music videos. Several weeks later, Bolt removed the music section from their site, without any explanation.

In February 2007, Bolt Media announced that it would be selling itself to GoFish, another online video company, for $30 million. According to Aaron Cohen, Bolt's CEO, Bolt would once again change its focus from uploaded content to content creation, saying that the former was no longer "interesting business". Cohen and Bolt president Jay Gould are also involved in a new project, called WikiYou, which has received seed funding from First Round Capital and Mayfield Fund.

On March 30, 2007, it was announced that Bolt2.com would shut down on April 6, 2007, ending more than 10 years of operations. This letter posted on the site to members of the community: "Well, the time had come. We have decided that it is time to officially say good-bye to Bolt2. In the past few years Bolt Media has explored new ideas, and grown in a different direction. As we continue to move in this direction it has become necessary that we need to make some difficult choices.

One of which is the closure of Bolt2. Although we value our loyal members, we are clearly moving in a new direction and need to focus our energies there. We recognize that many of you have been on the site for up to 10 years, and would like to thank you for your support and for allowing us to be a part of your lives. We hope you are able to take the time to reflect on the people who you may have met through Bolt2 and maintain these friendships after the site is down.

Much like pulling off a band-aid, the closure will be short and hopefully not too painful. The site will officially close on Friday, April 6th at noon (eastern standard time)."

Again, we would like to express our gratitude for your continued support of Bolt2. You have been a valuable part of our lives, and we hope to see you on Bolt in the future. On July 30, 2007, Digital Music News reported that the GoFish buyout of Bolt had been abandoned. This was later confirmed by GoFish in a press release.

Unable to withstand a lawsuit from copyright holders, Bolt.com filed for bankruptcy, and the site was shut down August 14, 2007.

On April 21, 2008, Bolt.com went live again. The domain was registered to Fundbolt, LLC, a limited liability company based in Irvington, New York.

On August 1, 2008, Bolt.com began integrating aspects of the old Bolt2.com site. Tagbooks, a popular way to ask questions and get answers from the broader community, were relaunched on the site.

On September 30, 2008, Bolt.com was announced to be shutting down once again. It was announced that this was due to the website's resurrection "not working out as they'd hoped". On October 6, 2008, the site was shut down. In December 2008, a notice was put up at the bottom of Bolt.com's old domain announcing the return of Bolt.com social network. The site was later re-opened, hosted by Ning. By July 2011, the site was once again shut down, until bolt3 launched.

Bolt and American Idol
In 2003 Bolt was the official message board for Fox's American Idol during the second season in 2003. This created a swarm of new members signing up to talk only about American Idol. This did not sit well with the veterans, as the quality of discussion on the site greatly dwindled. FOX later created and maintained their own message boards for the third season, but cross promotion still continued with AI sponsored quizzes, avatars, and badges. By the fourth season, the cross promotion was gone, but the message boards were still created and maintained. There were no message boards created for the fifth season of American Idol.

title: Bolt (website)


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Template:Did you know nominations/Dominique Allen

Dominique Allen, Clive Allen (basketball)

 * ... that Dominique Allen, daughter of Birmingham Bullets "legend" Clive Allen, has been called up to the senior British basketball team for the first time at the 2012 Summer Olympics?
 * Reviewed: Charlemagne class battleship, Jonathan Hammond (sport shooter)
 * Comment: For the Olympic period.

Created/expanded by Miyagawa (talk). Self nom at 20:51, 10 July 2012 (UTC)

 * Symbol confirmed.svg Good to go. Chienlit (talk) 21:49, 10 July 2012 (UTC)


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Portal talk:Education

If you want to experiment with a radical new version of Portal:Education you can work at Portal:Educationnew.

If you update featured content on this portal, make sure that you update Portal:Education/Featured.

Note: this discussion page started at Wikibooks in the context of creating a Wikiversity school of education. A new page for the School of Education was started at this website before the old page from Wikibooks was imported to Portal:Education. Portal:Education has now been adapted as the general education portal of Wikiversity. School of Education is currently the main content development project for the School of Education. Newer discussion about Wikiversity education in general is after the older material about the School of Education.

Older discussion from Wikibooks
The text in this section came from Wikibooks.

suggestion
I suggest more and more poeple to join this part, for Education is the way who we transfer our knowledge and who we influence the future.

I use the "Educating", "Teaching", "Answering" to envolve the differnt School of Education, mainly Authoritic Education and Democratic Education; but as believing the democratic way, I cannot write objectively.

This topic of 'Education' is so vast, that it might be too imposing for people to start. I would love to start a sub-topic, say 'Distance Education'. If that was possible. - anyway, just a suggestion.

I moved the topics of elearning, instructional design, blended learning, and (new) learning management systems to the Instructional Technology page, thinking these were properly sub-topics.

For the next few weeks (April, 2005) my students have an assigment to contribute to this section. We welcome your comments and additions.

 * Tspannaus

Introduction
I think some serious planning is needed to get the School of Education up and running. There are many methods for this and I'd like to suggest one particular approach. You can thank Rudyard Kipling's Just So Stories and in particular the poem that comes after "The Elephant's Child"

I keep six honest serving-men

(They taught me all I knew);

Their names are What and Why and When

And How and Where and Who.

Creating a strategy for the School of Education
First we need to ask why a School of Education is needed. Then taking into account the answer to the why question we need to look at what outcomes the School of Education should provide. We need to answer this question in the context of what technology will be used, who will be involved in the project, where they come from and the time frame for the project. Then we can work out how to achieve these outcomes. At this early stage it's important to clarify why the School of Education is needed. Without a clear motivation for the project people are unlikely to commit time and energy into building this project. If there is no clear reason for the project it's likely to get bogged down in the myriads of possible outcomes for the project.

A method of deciding why we need the School of Education
There is a two part method to clarify the reason for the project. The first step is to generate a long list of as many reasons as possible. This should be done without any constraints as to what is feasible or even sensible. The second step is to priorities this list and select the reasons that participants feel are most important. The reason for the long list is to explore a wide range of possibilities for the project. Things out of the leftfield sometimes produce a wining combination.

Fantasy School of Education
To generate a long list of reasons to setup the School of Education we could ask as many people as possible to describe their fantasy School of Education. This could be a description of the School 10 years from now or the kind of School they would want to study or teach at. We can then conduct a pole or some other voting system on this list to identify the most important reasons. Mystictim 01:43, 4 August 2006 (UTC) 01:43, 4 August 2006 (UTC)

My Fantasy School of Education
Please add your version of a fantasy School of Education below:

Our approach to learning hasn't changed much since Plato's Academy. The School of Education will lead the coming revolution in learning. With the massive changes in technology we need a new approach to learning and the School of Education will be where this change takes place. The School will be a cutting edge center of excellence for the study of learning through out the world. It will lead the way in developing and implementing learning strategies and tactics focusing on virtual delivery but with application to traditional methods. It will lead they way in promoting a truly international curriculum for world citizens of today and the future. Education needs to move from a proprietor and authoritarian approach to a shared and egalitarian one. The School of Education will work with all the other schools to identify and promote the best methods for learning and the appropriate use of technology. Any institute running teacher training course at all levels will come to this site for the best teacher training learning materials. The School of Education will be the place for research into education and learning. Mystictim

Newer discussion after the move from Wikibooks
my fantasy school of education goes back to Plato's teacher, the utterly curious and completely courageous Socrates. Socrates talked with everyone, learned from everyone, and shared with everyone. he's perhaps our first wikiversitian. he taught for free, thought no subject above or below him, and was unmoved by government authorities. my fantasy school of education goes back to the origins of the scholar as a student who takes others with him on an unending quest for learning. Using wiki technology this would translate into collaborative learning as collaborative writing in terms of a number of forms: the essay, the dialogue, creative narrative, and so on. --Smithgrrl 02:37, 30 August 2006 (UTC)

One of the things that struck me about the description in the actual Portal page, was how there are more students then teachers and that students/non-experts should not be afraid to start adding content right away. It seems to me that the point of view of those new to any subject is invaluable to improving the learning process. I am new to HTML and taking classes in Web Design. I have contributed to this area because I think that what I have freshly experienced gives me an insight into how learning a completely unfamiliar subject might be done. I think this point could be stressed more in general around Wikiversity to help gain more support for this project and to increase the confidence of potential contributors. Talonhawk 04:16, 20 September 2006 (UTC)

New page format
I have started Portal:Educationnew where we can make a new version of Portal:Education. My main goal is to include featured content and links to other Wikiversity content about education. --JWSchmidt 18:30, 19 January 2007 (UTC)
 * The contents of the older version of the portal were copied to Portal:Education/Wikiversity model. --JWSchmidt 02:29, 20 January 2007 (UTC)

Wikihigh
Some of the people here would probably be able to contribute to the Wikihigh project, which is an attempt to emulate a complete high school education here at Wikiversity. Any help there would be much appreciated. The Jade Knight 20:29, 30 March 2007 (UTC)

Discussion Revival
Here, in the introduction to this portal, is an example where the rejection of "online courses" suggests that any definitions of WV possessing lessons are being replaced with definitions of WV possessing "learning materials" and "learning activities". They are no coexisting. Paradoxically some of these "learning activities" consist of the development of online courses by a class of students. At the moment this note is one of my breadcrumbs. I will develop this into a complete argument later. Mbrad 18:10, 13 February 2010 (UTC)

title: Portal talk:Education


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Til the World Ends (Three Dog Night song)

"Til the World Ends" is a song written by Dave Loggins and performed by Three Dog Night, who in 1972 had had a Top 20 hit with Loggins' "Pieces of April": produced by Bob Monaco and Jimmy Ienner and arranged by Jimmie Haskell, "Til the World Ends" was featured on the 1975 Three Dog Night album, Coming Down Your Way.

The final Top 40 hit for Three Dog Night, "Til the World Ends" reached #32 on the Hot 100 in Billboard also ranking on the magazine's Adult Contemporary chart with a #11 peak. Outside of the US, "Til the World Ends" went to #26 on the Canadian pop chart in 1975, and reached #9 on the Canadian adult contemporary chart.


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Talk:Gender schema theory

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 24 August 2020 and 2 December 2020. Further details are available on the course page. Student editor(s): Cjames2020. Peer reviewers: Oogunnaike, Hannahjameson, LanceGreen15, Dcdelafuente7.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 21:40, 17 January 2022 (UTC)

Untitled
This article seems a good overview of the topic, but had some obvious omissions that are needed to bring balance. I.e. How had this theory been received? What are the criticisms of this theory? (An obvious one is that the theory - at least as described by the article - is a purely socio-psychological one that doesn't grapple with the biological foundations of sexual identity and their interactions with the psyche). -- — Preceding unsigned comment added by <IP_ADDRESS> (talk • contribs)

title: Talk:Gender schema theory


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User:Maltusnet

Hello, my name is Alfonso (Maltusnet or Maltus in wikis) and I work in the Department of Economics of the Universidad de Alicante (Spain), where I'm doing my PhD. I teach also classes on micro and macroeconomics. In order to contact with me, please go to my user page in the spanish wikiversity.

de:Benutzer:Maltusnet es:Usuario:Maltusnet

title: User:Maltusnet


text:
User:Cat1ady

Hi! I'm a UMass Lowell employee providing factual updates to Wikipedia. I'm interested in poetry, art, and design, and I love cats (but not the word feline). Drop by any time to leave me a message on my talk page!

title: User:Cat1ady