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# Tag Archives: Fano plane

## Pappus and Diophantus

This post is inspired by a nice article by Adrian Rice and Ezra Brown in the latest BSHM Bulletin, titled “Commutativity and collinearity: a historical case study of the interconnection of mathematical ideas, Part II”. Pappus’ Theorem states that, if … Continue reading

Posted in exposition, history
Tagged Fano plane, Kirkman, Pappus' Theorem, Steiner triple system, two squares equality
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## Representing the Fano matroid

In my lecture today I proved that the Fano matroid is representable over a field F if and only the characteristic of F is 2. There is a proof of this using only the classical theorems of Ceva and Menelaus … Continue reading

Posted in exposition
Tagged Ceva's theorem, Euclidean geometry, Fano plane, matroid, Menelaus' theorem, representation
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