Відео

A short "work in progress" exploring the 10-cell, a regular tessellation of the 3-dimensional sphere. It begins by showing how six of the 10 fundamental regions can be generated by a screw motion around one line (which appears as a fixed circle with a 3-color stripe). This motion is repeated with a boundary framework, and then using full size for the fundamental regions. Then we fly along the p...

In 2006 Professor John Sullivan of the Technical University Berlin won a contest to determine the new logo of the International Mathematical Union. His submission features the Borromean rings, a set of 3 interlocked rings with many cultural and mathematical connections. He created, together with colleague Charles Gunn, this short movie to introduce the Borromean rings and the particular form ch...

I've assembled some simple examples of rigid body motion using 2D projective geometric algebra, including euclidean, hyperbolic and elliptic examples of the 2D free top. This is based on my Ph. D. thesis (TU-Berlin, 2011).

A brief, graphical introduction to the Poinsot motion of the Euler top, featuring 3D line geometry to represent velocity and momenta states.

How can you make good flat maps of the round earth?' Our story begins with Mercator's world map of 1569, the first angle-preserving (or 'conformal') world map. His idea fell on fruitful soil, from which a new branch of mathematics has developed. The movie shows some of the highlights of this development, yielding a series of elegant visual forms which arise as 'conformal maps' on a variety of s...

A short introduction to the Sudanese Moebius Band. Discovered circa 40 years ago by Sue Goodman and Dan Asimov, it is unique in that its boundary curve is a geometric circle.

Introduction to an unusual mechanical linkage discovered 90 years ago by the Swiss engineer Paul Schatz. It concludes with a look at the oloid, a surface derived from the motion of the linkage, that has found practical applications in various fields.

Transition from normal 3-point perspective to conformal curvilinear perspective, using the example of a tessellation of 3-space by hexagonal prisms.