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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.
A projective geometry of dimension 1 consists of a single line containing at least 3 points. The geometric construction of arithmetic operations cannot be performed in either of these cases. For dimension 2, there is a rich structure in virtue of the absence of Desargues' Theorem. The Fano plane is the projective plane with the fewest points ...
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.
The projective plane of order 2 is called the Fano plane. See also the article on finite geometry. Using the vector space construction with finite fields there exists a projective plane of order N = p n, for each prime power p n. In fact, for all known finite projective planes, the order N is a prime power. [citation needed]
The Fano plane. This particular projective plane is sometimes called the Fano plane. If any of the lines is removed from the plane, along with the points on that line, the resulting geometry is the affine plane of order 2. The Fano plane is called the projective plane of order 2 because it is unique (up to
Fano Plane (7 points and 7 lines) Fano went on to describe finite projective spaces of arbitrary dimension and prime orders. In 1907 Gino Fano contributed two articles to Part III of Klein's encyclopedia. The first (SS. 221–88) was a comparison of analytic geometry and synthetic geometry through their historic development in the
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]
In finite geometry, PG(3, 2) is the smallest three-dimensional projective space.It can be thought of as an extension of the Fano plane.It has 15 points, 35 lines, and 15 planes. [1]