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Maryam Mirzakhani is also known for having obtained, with Alex Eskin and Amir Mohammadi, the magic wand theorem, so named because it made it possible to solve at a stroke many previously inaccessible problems. To explain it, let's first delve into translation surfaces. The illumination problem is one of its many applications.
The first hexagonal-faced flexagon studied had three stable positions. Methods were quickly found for constructing an associated hexaflexagon for a given number of stable positions — and even several different hexaflexagons…
Geometry abounds in problems that remain unsolved. Some date back to the Renaissance! In tribute to Richard Kenneth Guy (1916–2020), here are three, gleaned from his book Unsolved Problems in Geometry (with Hallard Croft and Kenneth John Falconer, Springer, 1991).
