Solve Change of Variable: Triangular to Square/Rectangle

[Suitengu]

[SOLVED] Change of Variable

In case of the triangular area with vertices: (-1 1) (0 0) and (1 1), how would you do a change of variable to make that look like a square or rectangular region in terms of u an v?

x = (1/2)(u+v) y = (1/2)(u-v)

so

u = x+y v = x-y

 

[HallsofIvy]

No (continuous) change of variable will make a 3 sided region into a 4 sided region!

 

[Suitengu]

oh. well what i did was to do the change of variable and then do the intervals as if i had a whole quadrilateral region and then i halved the answer. It seems to be right but i am not sure however.

 

[HallsofIvy]

Choosing u= x+y, v= x- y as coordinates will make two sides of the triangle, y= -x and y= x correspond to u= 0 and v= 0 respectively. The third side of the triangle, y= 1, becomes u+ v= 2.

I have no idea what you mean by "intervals" or what answer you "halved". Apparently this was part of a larger problem you haven't mentioned.