Reckoning / Shape / Torus (anchor ring)
Solid · Rings
Torus (anchor ring)
A circle of radius r swept round an axis at distance R: a ring, a doughnut, an O-ring.
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Dimensions
Results
volume V
surface area S
Formulas
Pappus’s theorems: a shape swept round an axis gives a volume equal to its area times the distance its centre travels, here πr² × 2πR; the same for perimeter and surface.
Checked: the V, S formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
A solid with one hole through it, like a ring or a pipe. Its surface is a torus: Euler characteristic 0, genus 1. No stretching makes it a ball. More on the lens.