Our meeting on 21 April 2012

This as a really fun meeting!The math details are at the bottom. First here's an account of the attendance, menu, etc.

Two new attendees were Susan Gregson (math/education at UC) and Tara Smith (math department at UC and currently as NSF). We all gained some weight as Linda brought bagels and Steve Phelps brought coffee. The overall mood was one of shuffling around in the morning, having some breakfast, and thinking about interesting questions and puzzles before actually getting to work.

Despite the fact that we intended to talk about algebra at this session we ended up focusing on a problem that was expressed geometrically. While we did manage some algebraic approaches to the puzzle the cleanest resolution used facts about factoring rotations as products of line reflections (algebra, I assert!).

In the end, we asked a lot of interesting questions easily posed in the context of our problem and made some progress on them.

Lenore and Steve Pe used complex numbers/coordinates to simplify some of the algebra and reach a conclusion that we'll revisit at some point.

The puzzle

The question we talked about was this. It is about a map to secret treasure in a region dominated by two big trees --- a pine tree P and an oak tree O. The instructions to find where the treasure is buried are are to start somewhere --- a point S --- and walk directly towards P. Turn left 90 degrees and walk the same distance again. Put a stake in the ground at this location S1. Return to S and walk to O. Turn right 90 degrees and walk the same distance again. Put a stake in the ground at this location S2. The treasure is located at the midpoint of the segment from S1 to S2.

Here's a a GeoGebra file that sets out the problem.


The puzzle is to explain why the location of the treasure is independent of the starting point S.

(more later... or someone else add something here)