Pompeiu's theorem

Pompeiu's theorem is a result of plane geometry, discovered by the Romanian mathematician Dimitrie Pompeiu. The theorem is quite simple, but not classical. It states the following:

The proof is quick. Consider a rotation of 60° about the point C. Assume A maps to B, and P maps to P '. Then we have ${\displaystyle \scriptstyle PC\ =\ P'C}$, and ${\displaystyle \scriptstyle \angle PCP'\ =\ 60^{\circ }}$. Hence triangle PCP ' is equilateral and ${\displaystyle \scriptstyle PP'\ =\ PC}$. It is obvious that ${\displaystyle \scriptstyle PA\ =\ P'B}$. Thus, triangle PBP ' has sides equal to PA, PB, and PC and the proof by construction is complete.

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