Henry Segerman and Kyle VanDeventer
Henry Segerman is an associate professor in the department of mathematics at Oklahoma State University. His research interests are in three-dimensional geometry and topology, and in mathematical art and visualization. In visualization he works in 3D printing, spherical video, virtual, and augmented reality. He is the author of the book "Visualizing Mathematics with 3D Printing". Kyle VanDeventer is a graduating senior in aerospace engineering and mathematics at Oklahoma State University. He is interested in developing mechanisms and mechanical systems, specifically for use in aircraft architecture.
From a self-similar quadrilateral tiling, one can construct a grid of scissors by replacing each quadrilateral with a scissor linkage. This kinetic sculpture illustrates a theorem we proved: that the resulting linkage is deployable if the quadrilaterals are cyclic. The sculpture is actuated by a servo motor that sweeps one arm through approximately 135 degrees. This moves the entire mechanism through a family of cyclic quadrilateral tilings.