examples of Desarguesian projective planes. The projective planes that can not be constructed in this manner are called non-Desarguesian planes, and the...

a non-Desarguesian plane is a projective plane that does not satisfy Desargues' theorem (named after Girard Desargues), or in other words a plane that...

and infinite affine planes. As well as affine planes over fields (and division rings), there are also many non-Desarguesian planes, not derived from coordinates...

and writing the line as an intersection of two planes. As there are non-Desarguesian projective planes in which Desargues's theorem is not true, some...

In mathematics, a Hughes plane is one of the non-Desarguesian projective planes found by Hughes (1957). There are examples of order p2n for every odd prime...

Géometre (proposed by Henri Brocard). He died in Lyon. Desarguesian plane, non-Desarguesian plane Desargues' theorem Desargues graph Desargues configuration...

two has affine and projective planes that are not isomorphic to Galois geometries, namely the non-Desarguesian planes. Similar results hold for other...

real numbers. The first non-Desarguesian plane was noted by David Hilbert in his Foundations of Geometry. The Moulton plane is a standard illustration...

Moulton (surname) Moulton Bicycle Moulton lunar crater Moulton plane, a non-desarguesian plane geometry Moulton (horse), a Thoroughbred racehorse Molten (disambiguation)...

On the other hand, axiomatic studies revealed the existence of non-Desarguesian planes, examples to show that the axioms of incidence can be modelled...

In mathematics, a Hall plane is a non-Desarguesian projective plane constructed by Marshall Hall Jr. (1943). There are examples of order p2n for every...

is Desarguesian, but some infinite Moufang planes are non-Desarguesian planes. In particular, the Cayley plane, an infinite Moufang projective plane over...

Pappus's theorem does not hold are Desarguesian projective planes over noncommutative division rings, and non-Desarguesian planes. The proof is invalid if C ...

this construction, the Fano plane is considered to be a Desarguesian plane, even though the plane is too small to contain a non-degenerate Desargues configuration...

Moulton plane is an affine plane in which Desargues' theorem does not hold. The associated projective plane is consequently non-desarguesian as well....

Desarguesian planes of finite order are always self-dual. However, there are non-Desarguesian planes which are not self-dual, such as the Hall planes...

Cremona–Richmond configuration Kummer configuration Klein configuration Non-Desarguesian planes Combinatorial designs Finite geometry Intersection theorem Levi...

translation planes are among the most well-studied of the known non-Desarguesian planes, and the vast majority of known non-Desarguesian planes are either...

projective linear transform. However, with the exception of the non-Desarguesian planes, all projective spaces are the projectivization of a linear space...

However, there do exist non-Desarguesian planes and the choice of point to remove in them may result in non-isomorphic dual affine planes having the same parameters...

André planes are a class of finite translation planes found by André. The Desarguesian plane and the Hall planes are examples of André planes; the two-dimensional...

theorem and are projective planes over division rings, but there are many non-Desarguesian planes. Dimension at least 3: Two non-intersecting lines exist...

which leaves Ω invariant. If Ω is an oval in a finite Desarguesian (pappian) projective plane of odd order, PG(2, q), then Ω is a conic by Segre's theorem...

topological projective planes that are not smooth. On the other hand, the following construction yields real analytic non-Desarguesian planes of dimension 2,...

a non-absolute line. In summary, von Staudt conics are not ovals in finite projective planes (desarguesian or not) of even order. In a pappian plane (i...

Zappa and Beniamino Segre, and wrote important works concerning the Non-Desarguesian plane. He was also a leading member of the Italian Communist Party and...

unavailable in non-Desarguesian contexts. Thus, the simplest analytic way to construct a projective plane is to start with an affine plane and extend it...

is a non-Desarguesian plane, where Desargues' theorem does not hold. More precisely, as of 2005, there are two objects called Cayley planes, namely the...

Desargues Desarguesian plane Line at infinity Point at infinity Plane at infinity Hyperplane at infinity Projective line Projective plane Oval (projective...

for the unique non-Desarguesian translation plane of order 9. These differ in the fundamental quadrilateral used to construct the plane (see Weibel 2007)...