20 citations · 87 across the 32 of their papers we have counts for
11 papers · 1 filter
A mathematical overview and some applications of gear design
Elisabetta A. Matsumoto, Henry Segerman
In this paper we give a brief overview of the geometry of involute gears, from a mathematical more than an engineering perspective. We also list some of the many variant geared mec…
Non-Euclidean Virtual Reality III: Nil
Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman +1
We describe a method of rendering real-time scenes in Nil geometry, and use this to give an expository account of some interesting geometric phenomena. You can play around with the…
Non-Euclidean Virtual Reality IV: Sol
Rémi Coulon, Elisabetta A. Matsumoto, Henry Segerman +1
This article presents virtual reality software designed to explore the Sol geometry. The simulation is available on 3-dimensional.space/sol.html
Non-euclidean virtual reality II: explorations of
Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto +1
We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulation of the product of two-dimensional hyperbolic space with one-dimension…
Non-euclidean virtual reality I: explorations of
Vi Hart, Andrea Hawksley, Elisabetta A. Matsumoto +1
We describe our initial explorations in simulating non-euclidean geometries in virtual reality. Our simulations of three-dimensional hyperbolic space are available at http://h3.hyp…
Conformally correct tilings
Saul Schleimer, Henry Segerman
We discuss the art and science of producing conformally correct euclidean and hyperbolic tilings of compact surfaces. As an example, we present a tiling of the Chmutov surface by h…
Visualizing Hyperbolic Honeycombs
Roice Nelson, Henry Segerman
We explore visual representations of tilings corresponding to Schläfli symbols. In three dimensions, we call these tilings "honeycombs". Schläfli symbols encode, in a very efficien…
Hypernom: Mapping VR Headset Orientation to S^3
Vi Hart, Andrea Hawksley, Henry Segerman +1
Hypernom is a virtual reality game. The cells of a regular 4D polytope are radially projected to S^3, the sphere in 4D space, then stereographically projected to 3D space where the…
The Quaternion Group as a Symmetry Group
Vi Hart, Henry Segerman
We briefly review the distinction between abstract groups and symmetry groups of objects, and discuss the question of which groups have appeared as the symmetry groups of physical…
Triple gear
Saul Schleimer, Henry Segerman
A relatively common sight in graphic designs is a planar arrangement of three gears in contact. However, since neighboring gears must rotate in opposite directions, none of the gea…
Sculptures in S^3
Saul Schleimer, Henry Segerman
We construct a number of sculptures, each based on a geometric design native to the three-dimensional sphere. Using stereographic projection we transfer the design from the three-s…