Oloid Calculator

Name: Oloid - Geometry Calculator
Author: Jürgen Kummer

Calculations at an oloid. The oloid was discovered in 1929 by Paul Schatz. It is formed by two circles of the same size, which perpendicularly intersect in a way, so that the edge of one circle goes through the center point of the other. Around this figure, a convex hull is laid, which is the smallest enclosing shape without dent. The surface area matches that of a sphere of the same radius. The exact calculation of the volume is very complicated, therefore an approximation is used.
Enter one value and choose the number of decimal places. Then click Calculate.

Formulas:

a = \frac{4}{3} π r

l = 3 r

h = 2 r

A = 4 π r^{2}

V \approx 3.0524184684 \cdot r^{3}

pi:

π = 3.141592653589793...

The radius has a one-dimensional unit (e.g. meter), the surface area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit ^-1.

The oloid was discovered during the dissection of a cube and is related to the invertible cube discovered at the same time. Viewed perpendicular to its two edges, the oloid has the outline of a square.
A special feature of this shape is that it rolls across its entire surface, meaning that when rolling across a plane, every part of the oloid's surface touches the plane once per complete rotation. Very few such shapes are known.
One application for components in the shape of an oloid is the purification and aeration of water. In this case, the shape rotates in the liquid with a tumbling motion. The axes of rotation each pass perpendicularly through the center of a circle, thus rotating around two axes that are perpendicular to each other but spatially displaced. Other applications, such as ship propulsion, wind turbines, and other technical uses in which a rotating motion is an important component, are in the state of testing.

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