If equilateral triangles are constructed outward on each side of any triangle, the centers of those three equilateral triangles themselves form an equilateral triangle. Popularly attributed to Napoleon Bonaparte, though the attribution is disputed by historians of mathematics.
Facts
StatementIf equilateral triangles are built outward (or all inward) on the three sides of any triangle, the centers of those equilateral triangles are themselves the vertices of an equilateral triangle. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Sources
1. Napoleon's Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, theorem statement sentenceQuote, lead paragraph, theorem statement sentence
In geometry, Napoleon's theorem states that if equilateral triangles are constructed on the sides of any triangle, either all outward or all inward, the lines connecting the centres of those equilateral triangles themselves form an equilateral triangle.
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