19 Mar

Dürer's conjecture

Albrecht Dürer dedicated a nontrivial part of his career to laying out the geometric foundations of drawing and perspective. His five centuries old work is available online via Google books. The mathematical statement known as Dürer's conjecture was motivated by this work, but proposed much later, in 1975, by G.C. Shephard. The conjecture claims that any convex three-dimensional polytope has a nonoverlapping unfolding. This unfolding is obtained by cutting the boundary of the polytope along some of its edges resulting in a two-dimensional connected shape that can be flattened by unfolding along the remaining edges.

The model of a random polytope and one of its unfoldings below is an outcome of the AMSI vacation research scholarship project of RMIT student Fei Lu.

Fei's AMSI blog and report will be available soon on the AMSI page.

The WebGL code that displays the model was taken from here, and everything else was coded in python.