Two perspective triangles, and their center and axis of perspectivity
In geometry, the Desargues configuration is a configuration of ten points and ten lines, with three points per line and three lines per point. It is named after Girard Desargues.
The Desargues configuration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in three dimensions from five planes in general position, or in four dimensions from the 5-cell, the four-dimensional regular simplex. It has a large group of symmetries, taking any point to any other point and any line to any other line. It is also self-dual, meaning that if the points are replaced by lines and vice versa using projective duality, the same configuration results.
Graphs associated with the Desargues configuration include the Desargues graph (its graph of point-line incidences) and the Petersen graph (its graph of non-incident lines). The Desargues configuration is one of ten different configurations with ten points and lines, three points per line, and three lines per point, nine of which can be realized in the Euclidean plane.
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after Girard Desargues. The Desarguesconfiguration can be constructed in two dimensions from the points and lines occurring in Desargues's theorem, in...
projective geometry. Desargues' theorem, the Desargues graph, and the crater Desargues on the Moon are named in his honour. Born in Lyon, Desargues came from a...
graph theory, the Desargues graph is a distance-transitive, cubic graph with 20 vertices and 30 edges. It is named after Girard Desargues, arises from several...
lines of the Desarguesconfiguration, and its edges represent pairs of lines that do not meet at one of the ten points of the configuration. Donald Knuth...
even though the plane is too small to contain a non-degenerate Desarguesconfiguration (which requires 10 points and 10 lines). The lines of the Fano...
equivalent hypergraph, and vice versa. The Desargues graph is the Levi graph of the Desarguesconfiguration, composed of 10 points and 10 lines. There...
Like the Pappus configuration, the Desarguesconfiguration can be defined in terms of perspective triangles, and the Reye configuration can be defined...
consequences of incidence of lines in geometric configurations. David Hilbert showed that the Desarguesconfiguration played a special role. Further work was...
projective spaces; such embeddability is a consequence of a property known as Desargues' theorem, not shared by all projective planes. A projective plane consists...
semiregular polytopes in 6, 7, and 8 dimensions Some Johnson solids Desarguesconfiguration Two of the Catalan solids Classical and exceptional root systems...
Kepler (1571–1630) and Girard Desargues (1591–1661) independently developed the concept of the "point at infinity". Desargues developed an alternative way...
Berger, Marcel (2010), "I.4 Three configurations of the affine plane and what has happened to them: Pappus, Desargues, and Perles", Geometry revealed,...
through A, there is at most one line through A which does not meet r. (Desargues) Given seven distinct points A, A', B, B', C, C', O, such that AA', BB'...
this period was the systematic study of projective geometry by Girard Desargues (1591–1661). Projective geometry studies properties of shapes which are...
include: Projective geometry, introduced in the 16th century by Girard Desargues, extends Euclidean geometry by adding points at infinity at which parallel...
1-factorization. The theorem was stated earlier in terms of projective configurations and was proven by Ernst Steinitz. For multigraphs, in which multiple...
paper and also allowed to confront, as digraphs, the Pappus graph to the Desargues graph. These applications as well as the reference use the following definition...
SAT. Master Thesis, University of Tübingen, 2018 Kagno, I. N. (1947), "Desargues' and Pappus' graphs and their groups", American Journal of Mathematics...
maintain proper orientation of the books. French mathematician and engineer Desargues designed and constructed the first mill with epicycloidal teeth c. 1650...
The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism. It echoes the rationale and construction...
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