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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 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 .
The family of lines formed by the sides of a regular polygon together with its axes of symmetry, and; The sides and axes of symmetry of an even regular polygon, together with the line at infinity. Additionally there are many other examples of sporadic simplicial arrangements that do not fit into any known infinite family. [22]
More generally, a collection of any sets whatsoever is called a family of sets, set family, or a set system. Additionally, a family of sets may be defined as a function from a set I {\displaystyle I} , known as the index set, to F {\displaystyle F} , in which case the sets of the family are indexed by members of I {\displaystyle I} . [ 1 ]
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