Ebisui's theorem and a (15<SUB>4</SUB>, 20<SUB>3</SUB>) configuration

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  • 蛭子井氏の定理と (15<SUB>4</SUB>, 20<SUB>3</SUB>) コンフィグレイション
  • エビスイシ ノ テイリ ト 15 4 20 3 コンフィグレイション

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Abstract

A simple geometric proof of Ebisui's theorem, if two triangles A1A2A3 and B1B2B3 are perspective and C3 = A1B2∩A2B1, C1=A2B3∩A3B2, C2=A3B1∩A1B3 then A1A2 A3 and C1C2C3 are also perspective, is given, which is using Desargues's theorem and its converse. With the theorem and an additional theorem, a (154, 203) configuration can be constructed, which is transitive both on points and lines.

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