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, and. Hence triangle PBP ' is equilateral and. Then. Thus, triangle PCP ' has sides equal to PA, PB, and PC and the proof by construction is complete (see drawing). Further investigations reveal that if P is not in the interior of the triangle, but rather on the circumcircle, then PA, PB, PC form a degenerate triangle, with the largest being equal to the sum of the others; this observation is also known as Van Schooten's theorem. Generally, by the point P and the lengths to the vertices of the equilateral triangle - PA, PB, and PC two equilateral triangles ( the larger and the smaller) with sides a_1 and a_2 are defined: The symbol △ denotes the area of the triangle whose sides have lengths PA, PB, PC. Pompeiu published the theorem in 1936; however August Ferdinand Möbius had already published a more general theorem about four points in the Euclidean plane 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.