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

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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. — Lomn 17:02, 30 August 2007 (UTC)

Unless you live in a curved space, of course. —Tamfang 20:15, 2 September 2007 (UTC)

Gradient

Why is it that in the formula for the gradient $m=\frac{y_2-y_1}{x_2-x_1}$, 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:

$y_{ij}=\sum _{k,m,n}{f}_k(a_i{x}_{mn}+b_j)$

(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)