Thales and Pythagoras

  • Alexander Ostermann
  • Gerhard Wanner
Part of the Undergraduate Texts in Mathematics book series (UTM)


The most beautiful discoveries of this period concern relations between lengths (Thales’ intercept theorem), angles (the central angle theorem or Eucl. III.20) and areas (the Pythagorean theorem). A quick look at the index shows that these three theorems are by far the most basic and frequently used results of geometry. The only original documents which have survived from the pre-Euclidean period are some cuneiform Babylonian tablets (from approximately 1900 B.C.), the Egyptian Rhind papyrus and the Moscow papyrus from approximately the same period. The achievements of Thales, Pythagoras and his pupils the Pythagoreans are only documented in commentaries, often contradictory, written many centuries later.


Regular Polygon Central Angle Golden Ratio Pythagorean Theorem Regular Pentagon 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of InnsbruckInnsbruckAustria
  2. 2.Section de mathématiquesUniversité de GenèveGenève 24Switzerland

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