<commit_before>---
published: true
title: Sphere surface == four times its shadow (3Blue1Brown)
tags: math sphere
---
## Fun Facts

- 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. 

[![caption](https://img.youtube.com/vi/GNcFjFmqEc8/0.jpg)](https://www.youtube.com/watch?v=GNcFjFmqEc8)

- the surface area for a sphere is just the derivative of its volume.
- the perimeter of a circle is the derivative of its area.
(this should be obvious a fundamental calculus)

[\[HN\]](https://news.ycombinator.com/item?id=18584458)<commit_msg>[sphere]<commit_after>---
published: true
title: Sphere surface == four times its shadow (3Blue1Brown)
tags: math sphere
---
## Fun Facts

- 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. 

[![caption](https://img.youtube.com/vi/GNcFjFmqEc8/0.jpg)](https://www.youtube.com/watch?v=GNcFjFmqEc8)

- the surface area for a sphere (4.pi.R^2) is just the derivative of its volume (4/3.pi.R^3).
- the perimeter of a circle (2.pi.R) is the derivative of its area (pi.R^2).
(this should be obvious a fundamental calculus)

[\[HN\]](https://news.ycombinator.com/item?id=18584458)
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