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Napoleon Triangle, Equilateral Triangle

3D model description

####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/EMAT6680.F99/Kim/emat6690/essay1/Napoleon%27s%20Theorem/Napoleon%20theorem.htm

  • 3D file format: STL

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Creator

STEAM educator, learning from and working with K-12 STEAM teachers to explore new ideas of teaching and engagement. I firmly believe ART is at the core of STEM learning or all human learning! I owe my ideas and designs to the hundreds of K-12 children and teachers and university professors I have had the pleasure of working with, in multiple disciplines-- math, science,engineering language arts, social studies, early childhood education and more! All mistakes, of course, are mine! There is no warranty or liability whatsoever implied or explicit behind the designs or ideas. They are all posted for their potential educational values.

When working with children, please strictly observe all safety and health procedures! Please refer to the NSTA safety guides: http://www.nsta.org/safety/.

LGBU Contact: LGBU@SIU.EDU

License

CC BY



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