Displaying similar documents to “Homography in ℝℙ”

Pascal’s Theorem in Real Projective Plane

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...

Group of Homography in Real Projective Plane

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)...

Combinatorial Grassmannians

Andrzej Owsiejczuk (2007)

Formalized Mathematics

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In the paper I construct the configuration G which is a partial linear space. It consists of k-element subsets of some base set as points and (k + 1)-element subsets as lines. The incidence is given by inclusion. I also introduce automorphisms of partial linear spaces and show that automorphisms of G are generated by permutations of the base set.