for thanksgiving 2k4 we opted to construct a very large pie.
based on a prototype the previous year we were aware of a fundamental limitation of large pies, namely the crust to filling ratio. for traditional circular pies of radius R, the amount of filling scales as R2 while the crust only scales linearly so as the pie grows larger, the flaky crust is completely dominated by the creamy filling.
our solution was to construct a pie pan in the shape of a koch snowflake (whose perimter obeys completely different scaling laws), fill it with delicious pecan pie and bake in a custom backyard oven.
Step 1: layout design
the layout was determined by two constraints:
1. the finished product had to fit in the transport vehicle. this gave an maximum outside diameter of around 50 inches, conveniently close to the 24x48 inch sheet metal available at the local hardware store. this set the initial side length L of the largest triangle.
2. we only had access to crust of a finite constant thickness so the smallest triangle had to contain some reasonable amount of filling. (L/3)niter > minimum acceptable edge length suggested that we go no deeper
than 4 iterations.
A template covering (1/12) of the entire perimiter made reasonably quick work of laying out the pie pan edge.