General projective differential geometry of paths
A. D. Michal, A. B. Mewborn (1951)
Compositio Mathematica
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A. D. Michal, A. B. Mewborn (1951)
Compositio Mathematica
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Cătălin Tigăeru (1998)
Archivum Mathematicum
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We prove that the set of the -projective symmetries is a Lie algebra.
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.
Marek Kordos (1989)
Colloquium Mathematicae
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Udrişte, C., Hirică, I.E. (1997)
Balkan Journal of Geometry and its Applications (BJGA)
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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],...
Boskoff, Wladimir G., Suceavă, Bogdan D. (2008)
Beiträge zur Algebra und Geometrie
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Roland Coghetto (2017)
Formalized Mathematics
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Using the Mizar system [2], we formalized that homographies of the projective real plane (as defined in [5]), form a group. Then, we prove that, using the notations of Borsuk and Szmielew in [3] “Consider in space ℝℙ2 points P1, P2, P3, P4 of which three points are not collinear and points Q1,Q2,Q3,Q4 each three points of which are also not collinear. There exists one homography h of space ℝℙ2 such that h(Pi) = Qi for i = 1, 2, 3, 4.” (Existence Statement 52 and Existence Statement 53)...
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...
Mihăilescu, Viorel, Udrişte, Constantin (1998)
Balkan Journal of Geometry and its Applications (BJGA)
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