A Dog in a Daisy Patch: Exploring the Recursive Playground

 

One of the most powerful and broadly applicable tools in mathematics is that of recursion, in which a solution to a problem can be stated in terms of solutions to simpler or smaller versions of the same problem. In this talk, we will give a friendly introduction to mathematical recursion through three otherwise unrelated puzzles. First, we will use the language of recurrence relations to solve the Tower of Hanoi of any height in the fewest moves. Second, we will use induction to find an optimal solution to the pirate game, a variant of the classic ultimatum game in game theory, for up to 200 pirates. Finally, we will investigate the surprising recursive solution to the Kakeya Needle Problem, a geometric curiosity posed 100 years ago that launched the field of geometric measure theory. While we will present partial mathematical proofs of each of the above problems, emphasis will be on an accessible exposition of the mathematical intuition, and hopefully an insight into the problem solving process in mathematics in general.