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The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
A partial linear space = (,,) of order , is called a semipartial geometry if there are integers, such that: . If a point and a line are not incident, there are either or exactly pairs (,) , such that is incident with and is incident with .
Analytic geometry associates to each point in the Euclidean plane an ordered pair. The red ellipse is associated with the set of all pairs ( x , y ) such that x 2 / 4 + y 2 = 1 . In mathematics , an ordered pair , denoted ( a , b ), is a pair of objects in which their order is significant.
The edges of this graph correspond to the flags (incident point/line pairs) of the incidence structure. The original Levi graph was the incidence graph of the generalized quadrangle of order two (example 3 above), [10] but the term has been extended by H.S.M. Coxeter [11] to refer to an incidence graph of any incidence structure. [12]
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
A partial linear space is an incidence structure for which the following axioms are true: [3] Every pair of distinct points determines at most one line. Every line contains at least two distinct points. In a partial linear space it is also true that every pair of distinct lines meet in at most one point.
In Euclidean geometry, linear separability is a property of two sets of points. This is most easily visualized in two dimensions (the Euclidean plane ) by thinking of one set of points as being colored blue and the other set of points as being colored red.
A linear system of divisors algebraicizes the classic geometric notion of a family of curves, as in the Apollonian circles.. In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.