Search results
Results from the WOW.Com Content Network
In finite geometry, the Fano plane (named after Gino Fano) is a finite projective plane with the smallest possible number of points and lines: 7 points and 7 lines, with 3 points on every line and 3 lines through every point.
In algebraic geometry, a Fano variety, introduced by Gino Fano (Fano 1934, 1942), is an algebraic variety that generalizes certain aspects of complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient projective space.
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 [ 2 ] family in Mantua , in Italy and died in Verona , also in Italy.
The first axiomatic treatment of finite projective geometry was developed by the Italian mathematician Gino Fano. In his work [ 2 ] on proving the independence of the set of axioms for projective n -space that he developed, [ 3 ] he considered a finite three dimensional space with 15 points, 35 lines and 15 planes (see diagram), in which each ...
The field planes are usually denoted by PG(2, q) where PG stands for projective geometry, the "2" is the dimension and q is called the order of the plane (it is one less than the number of points on any line). The Fano plane, discussed below, is denoted by PG(2, 2). The third example above is the projective plane PG(2, 3). The Fano plane.
The Fano plane has no such line (that is, it is a Sylvester–Gallai configuration), so it is not realizable. [12] A complete quadrangle consists of four points, no three of which are collinear. In the Fano plane, the three points not on a complete quadrangle are the diagonal points of that quadrangle and are collinear.
Fano Varieties and Extremal Laurent Polynomials A collaborative research blog for the project. 'Periodic Table of Shapes' to Give a New Dimension to Math; Atoms ripple in the periodic table of shapes; Nature's building blocks brought to life; Databases of quantum periods for Fano manifolds by Tom Coates and Alexander M. Kasprzyk
The Fano plane, the projective plane over the field with two elements, is one of the simplest objects in Galois geometry.. Galois geometry (named after the 19th-century French mathematician Évariste Galois) is the branch of finite geometry that is concerned with algebraic and analytic geometry over a finite field (or Galois field). [1]