Finding the surface area of a sphere without (much) Calculus
Channel: Steven Gubkin
Date: 2020-12-30

We find the surface area of a sphere without using very much Calculus.

PDF of notes:
https://drive.google.com/file/d/1L9U0GuZB7iDAKUOAlJuMgx_6hQApqGJ9/view?usp=sharing

Outline:
What is area?
How area of polygons can be defined using scissors congruence.
How volume of polyhedra cannot be defined using scissors congruence.
How area of curved shapes is subtle, and needs some "proto-calculus" concepts to make sense of it.
The definition of pi.
How to find the area of a circle.
How to find the surface area of a cylinder.
How to find the surface area of a sphere by chopping both the sphere and the cylinder into pieces of approximately equal area, thereby showing that the sphere has the same surface area as the cylinder which just barely contains it.