Cevane

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Three cevans AD , BE and CF through the three corners A , B and C.

A cevane or corner transversal is a straight line or segment in a triangle that connects a corner point with the opposite side (or its extension). Cevans are of central importance in triangular geometry and are named after Giovanni Ceva , who proved an important statement about them with Ceva's theorem, also named after him . The theorem provides a criterion for the existence of a common point of intersection of three cevans through the three corners of a triangle. Special cevans that always intersect at a common point are the three heights , the three bisectors and the three bisectors of a triangle. Other important sentences about Cevane are Stewart's Theorem and Routh's Theorem , which extends Ceva's theorem.

literature

  • Claudi Alsina, Roger B. Nelsen: Pearls of Mathematics: 20 geometric figures as starting points for mathematical exploratory trips . Springer, 2015, ISBN 9783662454619 , p. 59
  • Wolfgang Zeuge: Useful and beautiful geometry: a slightly different introduction to Euclidean geometry . Springer, 2018, ISBN 9783658228330 , p. 20

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