Napoleon Triangle, Equilateral Triangle

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Napoleon Triangle, Equilateral Triangle Starting with an arbitrary triangle, we first construct three equilateral triangles on all three sides - outward or inward. Then, we connect the centers of the three equilateral triangles. Surprisingly, we always get an equilateral triangle, regardless of the starting triangle. That is the famous Napoleon's Theorem. A 3D model allows us to play with ideas and invites students to pose questions. In this design, the base triangle measures 40mm, 50mm, and 65mm for no specific reasons. One can start with any triangle of any size. The wall is 2mm thick; the bottom is 1.8mm. A bottomless version is also included. Aesthetically, it seems a bit strange at first. Then, it becomes rather appealing after one sees geometric connections. A proof is equally interesting and there are many versions. References 1. https://en.wikipedia.org/wiki/Napoleon%27s_theorem 2. http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Kim/emat6690/essay1/Napoleon%27s%20Theorem/Napoleon%20theorem.htm