Geometry and Trigonometry

Titu Andreescu and Răzvan Gelca
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Titu Andreescu: University of Nebraska, American Mathematics Competitions
Răzvan Gelca: University of Michigan, Department of Mathematics

Chapter Chapter 1 in Mathematical Olympiad Challenges, 2000, pp 3-32 from Springer

Abstract: Abstract 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.

Keywords: Equilateral Triangle; Regular Polygon; Polygonal Surface; Radical Axis; Regular Pentagon (search for similar items in EconPapers)
Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-2138-8_1

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DOI: 10.1007/978-1-4612-2138-8_1

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