On a dependence between polarities and an order of a projective plane
Jaroslava Jachanová, Helena Žáková (1976)
Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika
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Jaroslava Jachanová, Helena Žáková (1976)
Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika
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Marek Jukl (1997)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
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Pfeiffer, Thorsten (1998)
Beiträge zur Algebra und Geometrie
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Roland Coghetto (2017)
Formalized Mathematics
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In this article we check, with the Mizar system [2], Pascal’s theorem in the real projective plane (in projective geometry Pascal’s theorem is also known as the Hexagrammum Mysticum Theorem)1. Pappus’ theorem is a special case of a degenerate conic of two lines. For proving Pascal’s theorem, we use the techniques developed in the section “Projective Proofs of Pappus’ Theorem” in the chapter “Pappus’ Theorem: Nine proofs and three variations” [11]. We also follow some ideas from Harrison’s...
Oswald Gschnitzer (1996)
Manuscripta mathematica
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Václav Havel (1974)
Czechoslovak Mathematical Journal
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Roland Coghetto (2016)
Formalized Mathematics
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The real projective plane has been formalized in Isabelle/HOL by Timothy Makarios [13] and in Coq by Nicolas Magaud, Julien Narboux and Pascal Schreck [12]. Some definitions on the real projective spaces were introduced early in the Mizar Mathematical Library by Wojciech Leonczuk [9], Krzysztof Prazmowski [10] and by Wojciech Skaba [18]. In this article, we check with the Mizar system [4], some properties on the determinants and the Grassmann-Plücker relation in rank 3 [2], [1], [7],...