Hyperbolic coordinate system

  • #1
This system of coordinates:

zahyou_hyporg.gif


can be "translated" in terms of x and y, so:
[tex]x = \sqrt{\frac{\sqrt{u^2+v^2}+u}{2}}[/tex]
[tex]y = \sqrt{\frac{\sqrt{u^2+v^2}-u}{2}}[/tex]
Exist another form more simplified of write x and y in terms of u and v? I tried rewrite these expressions using the fórmulas of half angle but didn't worked...
 

Answers and Replies

  • #2
35,012
6,760
This system of coordinates:

zahyou_hyporg.gif


can be "translated" in terms of x and y, so:
[tex]x = \sqrt{\frac{\sqrt{u^2+v^2}+u}{2}}[/tex]
[tex]y = \sqrt{\frac{\sqrt{u^2+v^2}-u}{2}}[/tex]
Exist another form more simplified of write x and y in terms of u and v? I tried rewrite these expressions using the fórmulas of half angle but didn't worked...
What about squaring each equation?
After you do that, maybe an idea will come to you.
 

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