Without any technical jargon, this video classifies the Platonic Solids and suggests the idea of classifying the Archimedean Solids. Thanks to Vi Hart for inspiring me time and time again with wonderfully engaging content and form.
On Hackenbush and Winning Ways
Hackenbush serves as a point of first access to the wonderful world of Combinatorial Games and Surreal Numbers, as described by Berlekamp, Conway, and Guy in Winning Ways for Your Mathematical Plays. This video series introduces the notion of zero games and introduces some Hackenbush positions that seem to act like integers and simple fractions (1/2 and 1/4). Is it possible to make Hackenbush positions for all fractions?
Nim is profoundly simple and profoundly compelling. This video series focuses on developing basic strategy from the ground up, although my true fascination for this game lies in the almost Surreal structure of Nimbers.