Pompeiu's theorem [SEP] named after
Pompeiu's theorem
Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu. The theorem is simple, but not classical. It states the following:
The proof is quick. Consider a rotation of 60° about the point "B". Assume "A" maps to "C", and "P" maps to "P" '. Then formula_1, and formula_2. Hence triangle "PBP" ' is equilateral and formula_3. Then formula_4. Thus,
published the theorem in 1936, however August Ferdinand Möbius had published a more general theorem about four points in the Euclidean plane already in 1852. In this paper Möbius also derived the statement of Pompeiu's theorem explicitly as a special case of his more general theorem. For this reason the theorem is also known as the "Möbius-Pompeiu theorem".
External links.
- MathWorld's page on Pompeiu's Theorem
- Pompeiu's theorem at cut-the-knot.org