Show how to distribute nine points around the surface of a sphere in such a way that each point is equidistant from its four nearest neighbors.
(In reply to
re: Solution  Using spherical trig by Charlie)
As your solution is different from mine, I thought I'd add a variable to see how yours looks.
The way I mapped 3D coordinates (turning circles into ellipses with 1/4 the height, then applying a vertical shift) does cause some distortion (since it doesn't move the north and south poles).
I was worried that my solution (x=3/5, h=3/5 on Desmos) looks a bit too low, but again its hard to know.
Your latitude corresponds to h=sqrt(5)/3
and I added a width variable w=2/3
It does look better. https://www.desmos.com/calculator/a2s7jvcska
And now you can make h any value you wish.
I didn't look closely at your formula. I've never learned spherical trig either. I remember a perplexus problem years ago that required it.

Posted by Jer
on 20210604 12:29:12 