Solid · Rings
Barrel
A solid with circular ends and bulging sides. Here the staves are parabolic arcs.
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Dimensions
Results
volume V
Formulas
Exact when the profile is a parabola. Gaugers also used πh(2D² + d²)/12, which is exact when the staves are arcs of an ellipse instead.
Checked: the V formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a ball: its surface can be stretched onto a sphere without tearing, so its Euler characteristic is 2. More on the lens.