Broken symmetry is one of the most important concepts in physics from the second half of the twentieth century. Hence, surely all undergraduate physics majors should learn it. Here are the slides from a lecture I gave last week to PHYS2020 Thermodynamics and Condensed Matter. In the lecture and (in a tutorial) I get the students to try and solve the problem below.

I then illustrate the solution (and the associated equal angles) with bee hives and some videos of soap films.

This version is taken from the book Introduction to statistical physics by Herson Huang.

I first encountered the problem in my second year of graduate school when Jim Sauls (later to become my advisor) in the very first lecture of a graduate condensed matter course asked students to solve it "cold" [right there in the lecture and hand in a solution] without the suggested form of the solution given above.

I would be interested if someone knows the associated history of this problem.

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