# Napoleon's and van Aubel's Theorems

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Starting with any triangle ABC, construct an equilateral triangle on each side, and then connect the centers of the triangles. The points form another equilateral triangle. This result is known as Napoleon's theorem.

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Contributed by: Robert Dickau (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

Snapshot 1: the triangle relationship holds even if the three points are collinear

Snapshot 3: the quadrilateral relationship holds even when the line segments do not intersect

M. Gardner, Chapters 5 and 14, *Mathematical Circus*, New York: Alfred A. Knopf, 1979.

## Permanent Citation