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A projective plane of order N is a Steiner S(2, N + 1, N 2 + N + 1) system (see Steiner system). Conversely, one can prove that all Steiner systems of this form (λ = 2) are projective planes. The number of mutually orthogonal Latin squares of order N is at most N − 1. N − 1 exist if and only if there is a projective plane of order N.
The six most common shotgun gauges, in descending order of size, are the 10 gauge, 12 gauge, 16 gauge, 20 gauge, 28 gauge, and .410 bore. [7] By far the most popular is the 12 gauge, [7] particularly in the United States. [8] The 20-gauge shotgun is the next most popular size [citation needed], and is popular for upland game hunting. The next ...
12 gauge 20 gauge Italy: 1999 Benelli Raffaello: Benelli Armi: 12 gauge Italy: 1990 Benelli Supernova: Benelli Armi: 12 gauge Italy: 2006 Benelli Vinci: Benelli Armi: 12 gauge Italy: 2009 Beretta 682: Fabbrica d'Armi Pietro Beretta: 12 gauge 20 gauge 28 gauge.410 bore Italy: 1984 Beretta 1201FP: Fabbrica d'Armi Pietro Beretta: 12 gauge Italy ...
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]
Military use of combat shotguns through the 20th century has created a need for ammunition maximizing the combat effectiveness of such weapons within the limitations of international law. 12-gauge has been widely accepted as an appropriate bore diameter to provide an effective number of projectiles within an acceptable recoil.
If P is a finite set, the projective plane is referred to as a finite projective plane. The order of a finite projective plane is n = k – 1, that is, one less than the number of points on a line. All known projective planes have orders that are prime powers. A projective plane of order n is an ((n 2 + n + 1) n + 1) configuration. The smallest ...
Hanfried Lenz gave a classification scheme for projective planes in 1954, [6] which was refined by Adriano Barlotti in 1957. [7] This classification scheme is based on the types of point–line transitivity permitted by the collineation group of the plane and is known as the Lenz–Barlotti classification of projective planes.
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 isomorphism). In general, the projective plane of order n has n 2 + n + 1 points and the same number of lines; each line ...