The Arctic Circle Theorem
The Arctic Circle theorem is a statement about domino tilings of the aztec diamond. Roughly, it says that a large tiling chosen at random will have a random circular area in the center and a predictable "frozen" pattern outside of this circle. The following image is an artistic interpretation of this theorem as a pear pie created by Lizzie Buchanan, Beth Anne Castellano, Brian Mintz, and myself on March 25, 2023. The dough has been colored by beet juice, carrot juice, and blueberry tea. The surface of the pie represents the random circle and the tiles outside the pie represent the frozen regions.
Type 11 Pentagonal Tiling
In the 70s, an amateur mathematician named Marjorie Rice discovered four new pentagonal tilings of the plane after an expert claimed that all such tilings had been found. This pecan pie honoring her work was baked by Beth Anne Castellano, Brian Mintz, and myself on May 14, 2023. The darker pieces are colored with cocoa powder.
Aperiodic Monotile
In 2023, mathematicians David Smith, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss presented the first aperiodic monotile. This is a single shape which tiles the plane and always does so in a way that never repeats. This blueberry pie featuring their tiling was baked by Beth Anne Castellano, Brian Mintz, and myself on May 14, 2023. The pieces which were reflected (rather than just translated and rotated) are colored with a hibiscus tea.
Plancherel Measure
The Plancherel measure is a probability measure on integer partitions where a partition whose diagram has more standard fillings is more likely to appear. The measure is closely related to questions about random permutations like the expected length of a longest increasing subsequence. You can check out a more detailed description and a Sage notebook I used for sampling the random partition for this pie.
The pie, which was baked for pi day on March 14, 2024, is chocolate and peanut butter based on this recipe. Similar to the arctic circle theorem, there is interesting limiting behavior as the partitions grow very large, but I wasn't able to cut the chocolate squares small enough to capture this limit shape on the pie.
The pie, which was baked for pi day on March 14, 2024, is chocolate and peanut butter based on this recipe. Similar to the arctic circle theorem, there is interesting limiting behavior as the partitions grow very large, but I wasn't able to cut the chocolate squares small enough to capture this limit shape on the pie.
