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.