That's what the article is about, you can divide a circle in an infinite number of polygons, but, somewhat unintuitively, you can't do that with spheres, only 5 divisions are possible ! If you try with hexagons, for example, you'll find that you can't join them without distorting them.
I only got as far as 'Approximations' before we started chatting. I can entirely understand it not working for polygons "tiling" the sphere up until they become infinitesimal, at which point they'd occupy all points on the sphere.
Um, I thought it didn't matter, that's like how long is the point that you make a curve out of when you're integrating to determine the length of a functions curve. But we could say square (or any shape that will tile a 2D plane), because at the limit as the side approaches zero, on the surface of a sphere, any region looks like a flat 2D plane?
I'm flying by the seat of my pants a bit here [in case you couldn't tell], it's a long time since I did any formal maths.
