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The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's theorem, with each line meeting 3 of the points and each point meeting 3 lines. In general, the Pappus line does not pass through the point of intersection of A B C {\displaystyle ABC} and a b c {\displaystyle abc} . [ 3 ]
The Pappus graph. The Levi graph of the Pappus configuration is known as the Pappus graph.It is a bipartite symmetric cubic graph with 18 vertices and 27 edges. [3]Adding three more parallel lines to the Pappus configuration, through each triple of points that are not already connected by lines of the configuration, produces the Hesse configuration.
Pappus of Alexandria (/ ˈ p æ p ə s / ⓘ; Ancient Greek: Πάππος ὁ Ἀλεξανδρεύς; c. 290 – c. 350 AD) was a Greek mathematician of late antiquity known for his Synagoge (Συναγωγή) or Collection (c. 340), [1] and for Pappus's hexagon theorem in projective geometry. Almost nothing is known about his life except for ...
This is one of the equivalent forms of Pappus's (hexagon) theorem. [5] When this happens, the nine associated points (six triangle vertices and three centers) and nine associated lines (three through each perspective center) form an instance of the Pappus configuration.
Hessenberg received his Ph.D. from the University of Berlin in 1899 under the guidance of Hermann Schwarz and Lazarus Fuchs.. His name is usually associated with projective geometry, where he is known for proving that Desargues' theorem is a consequence of Pappus's hexagon theorem, [1] and differential geometry where he is known for introducing the concept of a connection.
Pappus 1. Pappus of Alexandria. 2. The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's hexagon theorem. parabolic point A point of a variety that also lies in the Hessian. parallel 1. Meeting at the line or plane at infinity, as in parallel lines 2.
Pappus's hexagon theorem ; Paris–Harrington theorem (mathematical logic) Parovicenko's theorem ; Parallel axis theorem ; Parseval's theorem (Fourier analysis) Parthasarathy's theorem (game theory) Pascal's theorem ; Pasch's theorem (order theory) Peano existence theorem (ordinary differential equations) Peeling theorem
In these spaces, the Pappus hexagon theorem holds. Conversely, if the Pappus hexagon theorem is included in the axioms of a plane geometry, then one can define a field k such that the geometry is the same as the affine or projective geometry over k.