### On the coexistence of various geometries

Marek Kordos (1989)

Colloquium Mathematicae

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Marek Kordos (1989)

Colloquium Mathematicae

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Boskoff, Wladimir G., Suceavă, Bogdan D. (2008)

Beiträge zur Algebra und Geometrie

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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],...

Andrzej Miernowski, Witold Mozgawa (1997)

Collectanea Mathematica

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Grassmannians of higher order appeared for the first time in a paper of A. Szybiak in the context of the Cartan method of moving frame. In the present paper we consider a special case of higher order Grassmannian, the projective space of second order. We introduce the projective group of second order acting on this space, derive its Maurer-Cartan equations and show that our generalized projective space is a homogeneous space of this group.

Mathias Peternell (1987)

Mathematische Zeitschrift

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Klaus Kaiser (1973)

Colloquium Mathematicae

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Gallo, Daniel M. (1997)

Annales Academiae Scientiarum Fennicae. Mathematica

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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...

Keppens, Dirk, Van Maldeghem, Hendrik (2009)

Beiträge zur Algebra und Geometrie

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Leendert van Gastel (1990)

Banach Center Publications

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Erich W. Ellers (1982)

Aequationes mathematicae

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Sebastian Klein, Helmut Reckziegel (2005)

Banach Center Publications

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Jaroslava Jachanová, Helena Žáková (1976)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

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