Forms of the Plane · 3D
Golden Shell
The golden spiral given a body
Give the golden spiral a body: a tube that widens by the golden ratio every quarter turn, coiled in one plane like a nautilus or an ammonite. The flat spiral is its exact middle slice.
- Growth / ¼ turn
- → φ
- Coiling
- planispiral
Turn it in your hands, strike it to hear the chord of its edges, slice it with a plane.
Facts
- Cut the shell through its middle and you get the flat golden spiral with its squares.
- The tube never changes shape as it grows, only size: growth by self-similarity.
- Nautilus and ammonite shells coil like this, though their growth rate is usually not exactly φ.
Across the dimensions
- Its slice Golden SpiralThe spiral gains a body that widens by φ every quarter turn: a shell whose middle slice is the flat spiral.
