A Hyperbolic Coordinate Transformation in n-Sphere

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1. May 24, 2017

junt

$x= r Cosh\theta$

$y= r Sinh\theta$

In 2D, the radius of hyperbolic circle is given by:

$\sqrt{x^2-y^2}$, which is r.

What about in 3D, 4D and higher dimensions.

$\sqrt{x^2-y^2-z^2}$?

Does one call them hyperbolic n-Sphere? How is the radius defined in these dimensions. In addition these coordinates doesn't seem equivalent. For Cosh only span positive space, while Sinh span both positive and negative space. How can we resolve this? What another hyperbolic coordinate system is good that resolves this problem? I am mainly interested in changing my coordinates x,y,z, etc. to hyperbolic coordinate system.

2. May 29, 2017

PF_Help_Bot

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