Channel: Mathologer

Category: Education

Tags: rhombic dodecahedrontheoremrhombic triacontahedronprince rupert dropmcmullenwolfram alpha logoprince rupert cube3d printingrubik's cube illusion

Description: In this first part I'll introduce you to an amazing property of cubes that was only discovered around 1985. It is very surprising that it took so long for someone to notice this fundamental property of as basic a shape as a cube. It is also very surprising that even today hardly anybody has heard about it. Featuring lots of fancy cube shadows, Prince Rupert's paradoxical cube and a twisty puzzle that looks like a Skewb but isn't, among many other things. Here is the original paper that introduced the shadow theorem to the world: Volumes of Projections of unit Cubes, Peter McMullen, Bull London Math. Soc. (1984) 16: 278-280. In the second part of the video we'll explore higher-dimensional counterparts of the shadow theorem which then also put in context the two paradoxical warm-up exercises that I used as a hook for the first video: youtube.com/watch?v=xe-f4gokRBs Here is the link to the Smarter every day video that I mention: youtu.be/xe-f4gokRBs As usual thank you very much to Marty Ross and Danil Dimitriev for their help with this video and Michael Franklin for his help with recording this video.. Enjoy!