Forms of the Plane · 3D
The Sphere
The circle turned through every direction
Spin a circle about its diameter and it sweeps out a sphere. From any direction, the sphere’s outline is the Monad: every view of it is the same circle.
- Surface
- 4πr²
- Volume
- 4⁄3 πr³
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane or lift it into four dimensions.
Facts
- Of all shapes with a given surface area, the sphere holds the most volume.
- Its shadow from every direction is a perfect circle: the only solid like this.
- Archimedes proved its volume is 2/3 of the cylinder around it, and asked for that on his tomb.
History and meaning
For Plato the sphere was the most perfect shape, and he made the cosmos a sphere. Soap bubbles, planets and raindrops all pull themselves into it.
Across the dimensions
- Equator of Hopf FibrationOne dimension up, the sphere becomes the 3-sphere, woven entirely from linked circles.
- Its slice The MonadThe circle is the sphere’s equator: turn and the sphere rises around it.
