Napoleon Triangle, Equilateral Triangle

####Napoleon Triangle, Equilateral Triangle

Starting with an **arbitrary triangle**, we first build three equilateral triangles on all three sides (all outward or inward). Then, we connect the centers of the three equilateral triangles. Surprisingly, we always get an equilateral triangle, regardless of the staring triangle. That is the famous **Napoleon's Theorem**. A 3D model allows us to play with the 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, to begin with. Then, it becomes rather appealing after one sees the 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/EMAT6