Session 3 Divisibility by 11 Problem

Here is my scratch paper from this summer as I worked on this problem while lounging on the grass pool-side.  It blew in the wind when I got in the pool and made a topologically interesting object!

I think I've got the answer, but I don't have a convincing proof yet that my result is the smallest possible.  Can you find a way to support your answer?

Math and Games Images

Konigsberg Bridge Problem  > Graph Theory > Topology

Atomic Structure  > Knot Theory > Science Applications

Kelvin's model of atoms as knotted ether is not pictured above but was being considered in the 1860s, so it would fall between Dalton's model and the plum pudding model.

Math as Game

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game. 
A Mathematician's Apology by G. H. Hardy (London 1941).