Artists
Henry Segerman
Associate Professor of Mathematics
Oklahoma State University
Stillwater, Oklahoma, USA
Statement
I am an associate professor in the department of mathematics at Oklahoma State University. My research interests are in three-dimensional geometry and topology, and in mathematical art and visualization. In visualization I work in 3D printing, spherical video, virtual, and augmented reality. I wrote the book "Visualizing Mathematics with 3D Printing".
Artworks
Expanding (3, 4, 5) Triangle
45.2 x 59.6 x 3.2 cm
PETG 3D printed plastic, M3 nuts and bolts
2025
The image shows two copies of this expanding triangular mechanism: (1) the green one is fully expanded, and (2) the white one is fully contracted. The mechanism is made of racks and gears that allow each side to extend. The sides are connected together through special gears at the corners of the triangle resulting in a mechanism with one degree of freedom.
The sides of the triangle have three, four, and five pairs of racks respectively, forming a pythagorean triple. Such a triangle can be made with essentially identical parts (in appropriate numbers) forming each side. Triangles with non-rationally related side lengths would require different designs, since the length of each edge must expand in proportion to its length.