Geometry and Trigonometry

  • Titu Andreescu
  • Răzvan Gelca


Given two points A and B, if one rotates B around A through 60° to a point B’, then the triangle ABB’ is equilateral. A consequence of this result is the following property of the equilateral triangles, which was noticed by the Romanian mathematician D. Pompeiu in 1936. Pompeiu’s theorem is a simple fact, part of classical plane geometry. Surprisingly, it was discovered neither by Euler in the eighteenth century nor by Steinitz in the nineteenth.


Equilateral Triangle Regular Polygon Polygonal Surface Radical Axis Regular Pentagon 


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Copyright information

© Birkhäuser Boston 2000

Authors and Affiliations

  • Titu Andreescu
    • 1
  • Răzvan Gelca
    • 2
  1. 1.American Mathematics CompetitionsUniversity of NebraskaLincolnUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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