G H Hardy A course in pure mathematics

[storm4438]

1. Homework Statement [/b]
3. if X m and n are positive rational numbers, X(m^2 ~ n^2) , 2Xmn , and X(m^2+n^2) are positive rational numbers. Hence show how to determine any number of right-angle triangles the lengths of all whose sides are rational

Homework Equations

The Attempt at a Solution

What does the tilde mean in this context, he doesn't explain use it anywhere else or explain what it is. Also what does "determine any number of right-angle triangles..." mean? Is it asking you to find a general expresion for the lengths of the sides of a triangle whose sides are rational?
-Thanks

 

[SammyS]

...
What does the tilde mean in this context, he doesn't explain use it anywhere else or explain what it is.

I believe that the tilde represents a modified form of subtraction. In this case it means to subtract the smaller number from the larger. In other words, it's the absolute value of the difference.

Also what does "determine any number of right-angle triangles..." mean? Is it asking you to find a general expression for the lengths of the sides of a triangle whose sides are rational?
-Thanks

A right-angle triangle, is a triangle having one right angle. It is usually referred to as simply a 'right triangle'.