Diagonalele unui hexagon circumscris unei conice

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Cezar Lupu
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Diagonalele unui hexagon circumscris unei conice

Post by Cezar Lupu »

Sa se arate ca in planul proiectiv \( P^{2}(\mathbb{R}) \) diagonalele unui hexagon circumscris unei conice \( \Gamma \) sunt concurente.
An infinite number of mathematicians walk into a bar. The first one orders a beer. The second orders half a beer. The third, a quarter of a beer. The bartender says “You’re all idiots”, and pours two beers.
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Cosmin Pohoata
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Post by Cosmin Pohoata »

Este adevarata si urmatoarea generalizare a teoremei Brianchon: Daca un poligon cu \( 4n+2 \) laturi este circumscris la o conica si \( 2n \) diagonale (din cele \( 2n+1 \)) sunt concurente, atunci si ultima diagonala trece prin punctul respectiv de concurenta al celor \( 2n \).
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