Pie Art — Alexander N. Wilson

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.

Young's Lattice

Pies often have a lattice on top, so I decided to decorate this apple pie with a small subset of Young's lattice. This partially ordered set is an important object in the representation theory of the symmetric group. The boxes of the Young diagrams on this pie are created with beet-dyed dough.

Nontrivial \(\pi_1\) Pie

For a topological space \(X\) (if that term is unfamiliar to you, think of a shape like a sphere or a donut) and a point \(x\in X\), its fundamental group \(\pi_1(X;x)\) consists of all loops in the space starting and ending at \(x\) where two loops are considered equivalent if one can be deformed to another via a relationship called homotopy. The fundamental group is called trivial if every loop can be contracted to a single point.

I baked this pear pie for pi day 2025, but the idea originated from two Oberlin students (Sams Niemann and Thiel). If \(X\) is taken to be the filling of the pie, then \(X\) is topologically equivalent to a solid torus (i.e. a donut). Hence, its fundamental group is \(\pi_1(X;x)\cong\mathbb{Z}\). Try to think of a loop through the filling that can't be squeezed down to a point without leaving the filling!

A pear pie with a pear sitting in the center, surrounded by the pie.

A slice of the pear pie in the previous photo, showing that the crust is topologically a circle