Area of a sphere I want to know if the following GIF is **accurate or not**. I saw that we **cannot** flatten a sphere without a _deformation_ (world map problem). And the GIF is actually "rolling" the sphere on a plane, projecting it so **does** this **implies** that the GIF is just here to help understand or is it false ? _I know that we could integrate to calculate the area but I wanted to know if this GIF was accurate !_ **Here is the GIF :** <

Answering in a more calculus-oriented way, because it's obvious that's what OP is asking for.

It is true that you can't flatten a sphere onto a flat plane with a _finite collection_ of pieces, but there's nothing stopping you from using an infinite number of pieces. The first part of the gif, before connecting all the little pieces, you're correct in that not being completely accurate. However, after cutting the sphere an infinite number of times, that geometric trick _can_ be done.

The real issue with the gif, however, is that it gives no intuition as to why the area is related to sine, instead of some other wave-like curve. If it helps you remember, well the by all means use that animation as you see fit. However, if you want a deeper explanation, these gifs won't help you.