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The Platonic Solids
Under the direction of: Julius Barbanel
Most mathematical historians agree that abstract mathematics began with the ancient Greeks. Students interested in a senior thesis in ancient Greek mathematics will have a number of specific areas from which to choose.
In Book XIII of Euclid's Elements, Euclid studied the so-called Platonic, or regular, solids. These are solids in space in which all faces are congruent regular polygons, and where the same number of faces meet at every vertex. Euclid showed that there are exactly five such solids: the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. He also described a construction for each.
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