[+]
Maekawa and Kawasaki's Theorems Revisited and Extended:
Maekawa's Theorem, Kawasaki's Theorem, history (Justin, Huffman, Husimi),
Robertson's 1977 paper, manifolds without boundary, strata, volumes,
degree of map, higher dimensions, Justin's Theorem, GaussBonnet Theorem,
tessellations on a sphere


The theorems named after Maekawa and Kawasaki are the fundamental theorems of flat origami. They are bread & butter results for modern origami design. What is seldom seen is a result of Jacques Justin that generalizes both of these theorems and shows that they are fundamentally related to each other. We will prove Justin's Theorem in a way that shows how all these flat origami results are just a consequence of the GaussBonnet Theorem. We will also see how Kawasaki's Theorem was actually (kind of) proved previously by a British mathematician named Robertson, except that Robertson's version holds in arbitrary dimension. 
[No handwritten notes for this lecture.] 

Slides, page 1/68 •
[previous page] •
[next page] •
[PDF]
Slides, page 1/68 • [previous page] • [next page] • [PDF] 
The video above should play if your web browser supports either modern Flash or HTML5 video with H.264 or WebM codec. The handwritten notes and slides should advance automatically. If you have any trouble with playback, email Erik.