Napoleon's theorem
- Author:
- Chris Sangwin
- Topic:
- Geometry
Napoleon's theorem
Take any triangle. Construct equilateral triangles are constructed on the sides, either all outward or all inward. Then the centres of those equilateral triangles themselves form an equilateral triangle.
The triangle thus formed is called the inner or outer Napoleon triangle. The difference in area of these two triangles equals the area of the original triangle.