# Fano Plane

In finite geometry, the Fano plane (after Gino Fano) is the finite projective plane of order 2, having the smallest possible number of points and lines, 7 each, with 3 points on every line and 3 lines through every point.

### Other articles related to "fano plane, plane, planes, fano":

Bitangents Of A Quartic - Connections To Other Structures
... a, b, and c as the homogeneous coordinates of a point of the Fano plane and d, e, and f as the coordinates of a line in the same finite projective plane the condition that the sum is odd ... The points and lines of the Fano plane that are disjoint from a non-incident point-line pair form a triangle, and the bitangents of a quartic have been considered as being in ... The Levi graph of the Fano plane is the Heawood graph, in which the triangles of the Fano plane are represented by 6-cycles ...
Fire And Ice (board Game)
... Fire and Ice is an abstract strategy game played on Fano plane islands that are themselves part of a larger Fano plane ... island) moves a peg from a spot in one Fano plane island to another spot on the same island or the same spot on another island ... of the board is gained by occupying three of the pegs in one of the lines on the Fano plane ...
Fano Plane - Steiner System
... The Fano plane, as a block design, is a Steiner triple system ... As such, it can be given the structure of a quasigroup ...
Projective Plane - Vector Space Construction - Finite Field Planes
... of this construction are known as "Field planes" ... Taking K to be the finite field of pn elements produces a projective plane of p2 n + pn + 1 points ... The field planes are usually denoted by PG(2,q) where PG stands for projective geometry, the "2" is the dimension and q = pn is called the order of the plane (it is one less than the number of ...
Combinatorial Species - Calculus of Species - A Simple Example - Labeling The Fano Plane
... Let temporarily, just for an easier reading Fano = X^7/PSL(2,7)a the species that correspond to the colineation group of Fano plane and Klein = P4bic = the species that correspond to the Klein group ... then Fano" = X.Klein meaning Since two points determine a line, after labeling any two points in the Fano plane another point is settled ... By differentiation, one obtains Fano"' = X'.Klein + X.Klein' = Klein + X.X.X.X meaning After labeling three distinct points in the Fano plane ...

### Famous quotes containing the word plane:

In time the scouring of wind and rain will wear down the ranges and plane off the region until it has the drab monotony of the older deserts. In the meantime—a two-million-year meantime—travelers may enjoy the cruel beauties of a desert in its youth,....
—For the State of California, U.S. public relief program (1935-1943)