Los Angeles Math Circle

5/11 -- Beginners Circle: Taxicab geometry and problem solving (Oleg Gleizer)

We will learn the last tool we need to figure out why Sam Loyd's configuration of the 15 puzzle is not solvable. Called the taxicab (a.k.a. L1) geometry, it is important in various areas of math and physics and quite entertaining in its own right. In particular, we will see that a taxicab geometry circle is ... a square! Once finished, we will solve some cool olympiad-style problems.