These articles derive from work I did for my masters thesis on “affinely-regular” figures, which are things like regular polygons and Platonic solids after the application of an affine (or just linear) transformation. The primary result there was that one can decompose any figure (say, a polyhedron) into a “sum” of affinely-regular versions of that […]
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About the “Harmonious Figures” Category
About the “Hedronometry” Category
By the end of high school, most students should be familiar with the “three-dimensional” Pythagorean theorem (aka, “the distance formula”) that relates the length of the diagonal of a shoebox to the lengths of its edges. (Students should also know that this generalization extends to relate diagonals and edges in “any-dimensional” shoeboxes; always, the square […]
About the “Trigonometry” Category
Trigonometry is one of those topics that seems completely cut-and-dried, yet continues to offer-up new and fascinating results. As my company logo will attest, I’m particularly fond of (what I’ve dubbed) the Complete Triangle figure above. (See my post “(Almost) Everything you need to remember about trig…”.) Strictly speaking, this diagram isn’t new to mathematics, but […]
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