Wikipedia:Reference desk/Archives/Mathematics/2007 August 30

= August 30 =

Right triangle
How do you determine the length of the long side of a right triangle? —Preceding unsigned comment added by Lafaber mabel (talk • contribs) 16:59, August 30, 2007 (UTC)
 * You may find the Pythagorean theorem to be of use. &mdash; Lomn 17:02, 30 August 2007 (UTC)
 * Unless you live in a curved space, of course. &mdash;Tamfang 20:15, 2 September 2007 (UTC)

Gradient
Why is it that in the formula for the gradient $$m=\dfrac{y_2-y_1}{x_2-x_1}$$, where you have two points labelled $$(x_1, y_1)$$ for the first co-ordinate and $$(x_2 , y_2)$$ for the second, the letter "m" is used for gradient? Thanks, 81.151.242.78 17:31, 30 August 2007 (UTC)


 * You could use any letter. What's wrong with "m"? —Bromskloss 17:36, 30 August 2007 (UTC)


 * You could, yes, but 'm' is traditional for the gradient of a line. No idea why, though. This was asked at Talk:Slope last year, but no answers there yet. Algebraist 18:13, 30 August 2007 (UTC)
 * It's a good question (and a popular one) see http://mathforum.org/library/drmath/view/52477.html amongst possibles of "modulus of slope" or "monter" - (french) to climb this to me seems as near as one will get (from a maths teacher in quebec) see article:

"...His answer was approximately: 'In our system, the first letters of the alphabet, a, b, c... represent the constants, the last letters, x, y, z represent the unknown variables and the middle letters, m, n, p... represents the parameters.  When we started the explanations of slope, it was in studying the first degree equation:  y = mx + b.  x and y were the variables, b was fixed and considered as a constant, and what was appended to the coefficient of x as its value varied.  So it was a parameter and that is why we used m.'"

I tend to do the same and so tend to agree...213.249.232.26 18:39, 30 August 2007 (UTC)
 * Hmm, usually a,b,c,d are constant real parameters; f,g,h are functions, i,j,k,l,m,n are integer parameters or indeces; x,y,z and if needed w,s,t are variable arguments. (Igny 04:27, 31 August 2007 (UTC))
 * Mmmh, when? (examples?)213.249.232.202 07:24, 31 August 2007 (UTC)
 * example:
 * $$y_{ij}=\sum_{k,m,n}f_k(a_ix_{mn}+b_j)$$
 * (Igny 13:44, 31 August 2007 (UTC))
 * Oh yes. Good example - the question was about gradients anyway...87.102.88.202 14:50, 31 August 2007 (UTC)

While on the topic of traditional notation… While at university (I recently graduated, yay!) I was a teaching assistant at the maths department. As I was teaching my class, I used "q" for something that was usually represented by some other letter. Later, when I was processing assignments together with the other teaching assistants, some students could be spotted as mine because they used "q" as well. I had kind of left a watermark in my teaching and could see how it had spread. :-) —Bromskloss 19:14, 30 August 2007 (UTC)
 * I think your example is a pretty good illustration of how 'm' for slope has come about - your next step would be to write a maths text book (using q) then come back in 20 years time and then respond to questions such as "why is q always used for a variable"213.249.232.202 06:53, 31 August 2007 (UTC)
 * Note, however that the French word for slope is pente. deeptrivia (talk) 19:30, 30 August 2007 (UTC)