Napoleon Triangle, Equilateral Triangle

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Napoleon's Equilateral Triangle, Equilateral Triangle Base Starting with any triangle at all, we build three equilateral triangles on each and every side (all outward or inward). Then, we connect the centers of those three equilateral triangles. Amazingly, we always get an equilateral triangle, no matter what the starting triangle is. That's the famous Napoleon's Theorem. A 3D model lets us experiment with these ideas and invites students to come up with their own questions. In this design, the base triangle measures 40mm by 50mm by 65mm, for reasons that don't really matter. One can start with any triangle of any size at all. The wall is 2mm thick; the bottom is 1.8mm deep. A bottomless version is also included. Aesthetically, it looks a bit strange to begin with, but then it becomes rather appealing after one sees the geometric connections. A proof is equally interesting, and there are many versions of that as well. References 1. https://en.wikipedia.org/wiki/Napoleon%27s_theorem 2. http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Kim/emat6690/essay1/Napoleon's%20Theorem/Napoleon%20theorem.htm