Pappos’s Theorem: Nine Proofs and Three Variations

  • Jürgen Richter-Gebert


We will begin our journey through projective geometry in a slightly uncommon way. We will have a very close look at one particular geometric theorem— namely The hexagon theorem of Pappos. Pappos of Alexandria lived around 290–350 CE and was one of the last great Greek geometers of antiquity. He was the author of several books (some of them are unfortunately lost) that covered large parts of the mathematics known at that time. Among other topics, his work addressed questions in mechanics, dealt with the volume/ circumference properties of circles, and even gave a solution to the angle trisection problem (with the additional help of a conic). The reader may take this first chapter as a kind of overture to the remainder of the book in which several topics that are important later on are introduced. Without any harm one can also skip this chapter on first reading and come back to it later.


Projective Plane Euclidean Geometry Projective Geometry Nondegeneracy Condition Conclusion Line 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Zentrum Mathematik (M10) LS GeometrieTU MünchenGarchingGermany

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