So a few days ago, I learned that the distance between 2 vertices on a regular pentagon with side length 1 is the golden ratio (~1.618). So I wondered, is there anything else that this can be applied to?

From there, I created this Desmos graph. It allows you to find the ratio between the side length of a regular n-gon and a line connecting points across the shape, “missing” a specific number of vertices.

I find it interesting that sine is associated with this. Obviously, it makes sense why, but I wonder if this graph could allow you to find sine and cosine by “using a straightedge and compass.” I don’t know yet, but I’m still messing around with it. Check it out for yourself!