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A general straight-line thread connects the two points (0, k−t) and (t, 0), where k is an arbitrary scaling constant, and the family of lines is generated by varying the parameter t. From simple geometry, the equation of this straight line is y = −( k − t ) x / t + k − t .
In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...
Then is the partition in which each block C is the union of a family of blocks connected by this relation. Based on the equivalence between geometric lattices and matroids , this lattice of partitions of a finite set corresponds to a matroid in which the base set of the matroid consists of the atoms of the lattice, namely, the partitions with n ...
In geometry, a family of curves is a set of curves, each of which is given by a function or parametrization in which one or more of the parameters is variable. In general, the parameter(s) influence the shape of the curve in a way that is more complicated than a simple linear transformation .
A set of polygons in an Euler diagram This set equals the one depicted above since both have the very same elements.. In mathematics, a set is a collection of different [1] things; [2] [3] [4] these things are called elements or members of the set and are typically mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other ...
This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), ... Line; Degree 2 ...
The line of centers is perpendicular to the radical plane, which is a real plane in the pencil containing the imaginary circle. If the spheres intersect in a point A, all the spheres in the pencil are tangent at A and the radical plane is the common tangent plane of all these spheres. The line of centers is perpendicular to the radical plane at A.
Examples of hereditary graph classes are independent graphs (graphs with no edges), which is a special case (with c = 1) of being c-colorable for some number c, being forests, planar, complete, complete multipartite etc. Sometimes the term "hereditary" has been defined with reference to graph minors; then it may be called a minor-hereditary ...