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In mathematics, a ternary operation is an n-ary operation with n = 3. A ternary operation on a set A takes any given three elements of A and combines them to form a single element of A . In computer science , a ternary operator is an operator that takes three arguments as input and returns one output.
A planar ternary ring (PTR) or ternary field is special type of ternary system used by Marshall Hall [1] to construct projective planes by means of coordinates. A planar ternary ring is not a ring in the traditional sense, but any field gives a planar ternary ring where the operation T {\displaystyle T} is defined by T ( a , b , c ) = a b + c ...
The archetypical example is the real projective plane, also known as the extended Euclidean plane. [1] This example, in slightly different guises, is important in algebraic geometry , topology and projective geometry where it may be denoted variously by PG(2, R ) , RP 2 , or P 2 ( R ), among other notations.
A plane duality is a map from a projective plane C = (P, L, I) to its dual plane C ∗ = (L, P, I ∗) (see § Principle of duality above) which preserves incidence. That is, a plane duality σ will map points to lines and lines to points (P σ = L and L σ = P) in such a way that if a point Q is on a line m (denoted by Q I m) then Q I m ⇔ m ...
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured.
Configurations (4 3 6 2) (a complete quadrangle, at left) and (6 2 4 3) (a complete quadrilateral, at right).. In mathematics, specifically projective geometry, a configuration in the plane consists of a finite set of points, and a finite arrangement of lines, such that each point is incident to the same number of lines and each line is incident to the same number of points.
The Upper and Lower Dimension axioms together require that any model of these axioms have dimension 2, i.e. that we are axiomatizing the Euclidean plane. Suitable changes in these axioms yield axiom sets for Euclidean geometry for dimensions 0, 1, and greater than 2 (Tarski and Givant 1999: Axioms 8 (1), 8 (n), 9 (0), 9 (1), 9 (n)).