We consider several seemingly unrelated theorems, each with the word ellipse in the statement: Siebeck’s theorem, the elliptical range theorem, Poncelet’s theorem, and the Blaschke ellipse theorem.

Cayley graphs, constructed from the algebraic structure of groups, provide a natural framework for exploring complex combinatorial properties. In these graphs, vertices represent group elements and ...

A pair of mathematicians solved a legendary question about the proportion of vertices in a graph with an odd number of connections. “It’s a bit of a surprise, at least for me, that such a combination ...