Bridging the gap between artistic and scientiﬁc activities, Paul Schatz (1898-1979) was an innovative sculptor, author, astronomer, mathematician and engineer who sought to bring harmony between nature and man. As a volunteer on the Western front during World War 1 he witnessed the human suffering and destruction of the environment, a vast chasm between the emotional and the cognitive-analytical abilities of humans. As a post-war student revolutionary in Munich he found in the humanities of Rudolf Steiner the tools of epistemological methodology and cognitive theory aligned with his unique artistic approach to problem solving.
The greatest discovery he made when he inverted the cube resulting in a three-dimensional body whose laws and properties he called the oloid. Understanding the complex movements of the oloid’s kinematic inversion led him to see this form as having numerous industrial applications. A ﬁrst and important success of his technical invention was owed to Willy A. Bachofen AG, the Basel machine factory that sold thousands of his Turbula mixers for industrial and pharmaceutical applications all over the world over the years. Schatz’s oloid shape when spinning has been used for numerous patents ranging from water pumps, water propulsion and water agitators that do not harm fish as the rhythm simulates the fin motion of aquatic species.
How Oloid geometry is revealed
The 3 equal parts of a cube, divided into a cube belt (blue-red) and two equal bar bodies (orange-red),
The shape formation of the oloid during the inversion of the cube belt.
Mathematical visualization of the resulting oloid.
A unique path
The exotic symmetry of the oloid has a consistent center of mass that when set in motion creates a mesmerizing meandering path. Although its shape is curved, it moves in a perfect straight line where every single point of its surface touches the ground.
"If the distance of two centers of disk is equal to the radius, then the convex hull produces another figure that rolls smoothly and is known as oloid."
- Paul Schatz 1975
Click here to download a .pdf of a full mathematical explanation