• the surface of a sphere is the same as it’s projection on a containing cylinder.
• it’s equal to 4 times it’s shadow.
• a rectangle on the sphere and it’s projection on the cylinder account for the same surface.
• the surface area for a sphere (4.pi.R²) is just the derivative of its volume (4/3.pi.R³).
• the perimeter of a circle (2.pi.R) is the derivative of its area (pi.R²). (this should be obvious a fundamental calculus)
  3Blue1Brown / [HN]

• Where do these circles come from? / shadertoy / More circles on a sphere of cubes