Elliptic trigonometry

JyN
Why aren't there trigonometric functions for elliptic geometry? There is trigonometry for circles and hyperbolas, but why not ellipses?

Answers and Replies

Science Advisor
Homework Helper
Hi JyN!
There is trigonometry for circles and hyperbolas, but why not ellipses?

ah, there is trigonometry only for the square hyperbola (ie with perpendicular asymptotes), just as there is only for the "square" ellipse (ie the circle).

JyN
Why can't trigonometry-like relationships exist for non-square hyperbolas and ellipses?

Science Advisor
Homework Helper
i expect they can be, but why would anyone bother with them, when the "square" functions can easily be adapted for the purpose?

waht
An angle in radians is defined as the length of the arc of a circle over its radius.

A slight problem occurs if you want to extend that to an ellipse because an ellipse is defined by two variables, major axis and minor axis. It would be interesting how to define an elliptic angle, length of arc of an ellipse over major axis or minor axis or their algebraic combination? But in either case, I don't know how this could be useful other than perhaps in an elliptical coordinate system.

Gold Member
Why aren't there trigonometric functions for elliptic geometry? There is trigonometry for circles and hyperbolas, but why not ellipses?

Is this what you had in mind? They're called Jacobi elliptic functions.

EDIT: Cross post!