tools in its study. In a separate usage, a Fano plane is a projective plane that never satisfies Fano's axiom; in other words, the diagonal points of a...

of the Fano plane, a finite geometry in which the diagonal points of a complete quadrangle are collinear, some authors have augmented the axioms of projective...

structures. An alternative to adding the axiom is to refer to incidence structures that do not satisfy the axiom as being trivial and those that do as non-trivial...

authors give a treatment that embraces the Fano plane PG(2, 2) as the smallest finite projective plane. An axiom system that achieves this is as follows:...

Gino Fano (5 January 1871 – 8 November 1952) was an Italian mathematician, best known as the founder of finite geometry. He was born to a wealthy Jewish...

defined over a field that does not have even characteristic include Fano's axiom; The three diagonal points of a complete quadrangle are never collinear...

developed by the Italian mathematician Gino Fano. In his work on proving the independence of the set of axioms for projective n-space that he developed,...

example of a matroid defined in this way is the Fano matroid, a rank three matroid derived from the Fano plane, a finite geometry with seven points (the...

the study of geometries as axiomatic systems. There are several sets of axioms which give rise to Euclidean geometry or to non-Euclidean geometries. These...

not be these geometric objects. Some examples of incidence structures 1. Fano plane 2. Non-uniform structure 3. Generalized quadrangle 4. Möbius–Kantor...