### Abstract

The Erdős-Trost problem can be formulated in the following way: “If the triangle XY Z is inscribed in the triangle ABC—with X, Y, and Z on the sides BC, CA, and AB, respectively—then one of the areas of the triangles BXZ, CXY , AY Z is less than or equal to the area of the triangle XY Z.” There are many different solutions for this problem. In this note we take up a very elementary proof (due to Szekeres) and deduce that the class of ordered translation planes is the level in the hierarchy of affine planes where the Erdős-Trost statement still holds true. We also look at the conditions an absolute plane needs to satisfy for the validity of the Erdős-Trost statement.

Original language | English (US) |
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Pages (from-to) | 379-385 |

Number of pages | 7 |

Journal | Journal of Geometry |

Volume | 107 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1 2016 |

### Keywords

- area inequality
- Hilbert planes
- Ordered translation planes

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

*Journal of Geometry*,

*107*(2), 379-385. https://doi.org/10.1007/s00022-016-0312-8