I’ve been working on some equations to quantify distortion due to projecting planar objects onto spherical surfaces.
For instance, suppose you wanted to calculate the surface area of a polygon projected onto a sphere, or the surface area of Idaho. How would you do this? Is the area of the polygon in flatland proportional to the area of the polygon on a sphere? Nope, it’s not that simple. It even involves a little calculus.
Equations and examples (hopefully) coming soon.