Classical problems of ancient mathematics

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The classic problems of ancient mathematics consist of three tasks from geometry that the experts occupied for a long time:

  • the squaring of the circle (to construct a square with the same area from a given circle in finitely many steps);
  • the trisection of the angle , also called trisection (to divide a given angle into three equal angles);
  • the doubling of the cube , also called the doubling of the cube or Delic's problem ( doubling the volume of a given cube).

Solutions were only allowed in finitely many steps with the so-called Euclidean tools , i.e. H. be brought about with compasses and a ruler without graduations. It was only in the 19th century that algebraic methods could prove for all three problems that they could not be solved in general with these simple tools.

Proofs of unsolvability

Carl Friedrich Gauß and Évariste Galois did important preparatory work. Pierre Laurent Wantzel found the final proof of the angle third and the doubling of the cube in 1837 , the proof of the impossibility of squaring the circle was provided by Ferdinand von Lindemann in 1882 by proving the transcendence of the circle number .

Web links

Wikibooks: The Three Ancient Problems  - Learning and Teaching Materials


  • Horst Hischer. The three classic problems of antiquity. Historical findings and didactic aspects. Hildesheim: Franzbecker, 2018 (2nd edition).