Category Archives: Uncategorized

Previously, we discussed which regular polytopes have vertex-sets that occur as proper subsets of the vertex-set of another regular polytope in the same dimension. In particular, when there is a Hadamard matrix of order 4k, then then the (4k−1)-dimensional simplex … Continue reading →

This is a digest of things that have happened this month, but which are individually too small to each warrant a separate cp4space post. Firstly, there have been a couple of exciting results in the field of combinatorics: The Erdős-Faber-Lovász … Continue reading →

There are two competing notions for describing a subset of the real numbers as being ‘small’: a null set is a subset of the reals with Lebesgue measure zero; a meagre set is a countable union of nowhere-dense sets. Both … Continue reading →

In January 2000, Erich Friedman considered the problem of finding a rigid unit-distance graph G containing a regular heptagon as a subgraph. That is to say, the graph is immersed in the plane such that: every edge of G must … Continue reading →

There’s a very elegant cryptographic construction discovered by Barreto and Naehrig in a 2005 paper. It is beautiful from a pure mathematical perspective, but also has an impressive application: it was* part of the ingenious mechanism by which Zcash supports … Continue reading →

Recall that the logarithm function (defined on the punctured complex plane) is multi-valued, with the different solutions to exp(x) = y differing by integer multiples of 2πi.   James Propp remarked that the values of the form i^i^i are a … Continue reading →