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December 27th, 2016, 02:00 AM   #1
Senior Member

Joined: Jul 2015
From: Florida

Posts: 116
Thanks: 2

Math Focus: non-euclidean geometry
Does anyone know this function?

This is a family of functions $\alpha=f(\lambda)$ where a third variable $\upsilon$ sets the curve:

$\alpha={\cot}^{-1}\left(\cos\,\upsilon\quad\tan\quad\sin^{-1}{\left( \frac{\sin\quad\frac{\lambda}{ 2}}{\sin\quad\upsilon}\right)\right)$

It is a smooth function that approaches a sine curve when $\upsilon\to0$, and that approaches a hyperbola when $\upsilon\to\frac{\pi}{2}$.
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 December 27th, 2016, 02:28 AM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,541 Thanks: 516 Math Focus: Yet to find out. Looks like a filter of sorts
 December 27th, 2016, 02:33 AM #3 Senior Member     Joined: Jul 2015 From: Florida Posts: 116 Thanks: 2 Math Focus: non-euclidean geometry It's a geometric function. It finds the tangent of a small circle on a sphere using trigonometry.
 December 27th, 2016, 02:42 AM #4 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,541 Thanks: 516 Math Focus: Yet to find out. Looks like you know what the function is
 December 27th, 2016, 02:50 AM #5 Senior Member     Joined: Jul 2015 From: Florida Posts: 116 Thanks: 2 Math Focus: non-euclidean geometry I'm asking if anyone else knows. Some of the online experts claim that this is just some set of trivial rotations. I'm wondering if anybody here knows for sure what this is. Has anyone seen it before?

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