Family of curves

Family of curves

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. Sets of curves given by an implicit relation may also represent families of curves.

Families of curves appear frequently in solutions of differential equations; when an additive constant of integration is introduced, it will usually be manipulated algebraically until it no longer represents a simple linear transformation.

Families of curves may also arise in other areas. For example, all non-degenerate conic sections can be represented using a single polar equation with one parameter, the eccentricity of the curve:

:r( heta) = {e over 1+e cos heta}

as the value of e changes, the appearance of the curve varies in a relatively complicated way.

Families of curves may arise in various topics in geometry, including the envelope of a set of curves and the caustic of a given curve.


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  • Family of curves — Family Fam i*ly, n.; pl. {Families}. [L. familia, fr. famulus servant; akin to Oscan famel servant, cf. faamat he dwells, Skr. dh[=a]man house, fr. dh[=a]to set, make, do: cf. F. famille. Cf. {Do}, v. t., {Doom}, {Fact}, {Feat}.] 1. The… …   The Collaborative International Dictionary of English

  • family of curves — kreivių šeima statusas T sritis fizika atitikmenys: angl. family of curves vok. Kurvenschar, f rus. семейство кривых, n pranc. famille de courbes, f …   Fizikos terminų žodynas

  • family of curves — Math. a collection of curves whose equations differ only by values assigned a parameter or parameters. * * * …   Universalium

  • family of curves — Math. a collection of curves whose equations differ only by values assigned a parameter or parameters …   Useful english dictionary

  • Family — Fam i*ly, n.; pl. {Families}. [L. familia, fr. famulus servant; akin to Oscan famel servant, cf. faamat he dwells, Skr. dh[=a]man house, fr. dh[=a]to set, make, do: cf. F. famille. Cf. {Do}, v. t., {Doom}, {Fact}, {Feat}.] 1. The collective body… …   The Collaborative International Dictionary of English

  • Family circle — Family Fam i*ly, n.; pl. {Families}. [L. familia, fr. famulus servant; akin to Oscan famel servant, cf. faamat he dwells, Skr. dh[=a]man house, fr. dh[=a]to set, make, do: cf. F. famille. Cf. {Do}, v. t., {Doom}, {Fact}, {Feat}.] 1. The… …   The Collaborative International Dictionary of English

  • Family man — Family Fam i*ly, n.; pl. {Families}. [L. familia, fr. famulus servant; akin to Oscan famel servant, cf. faamat he dwells, Skr. dh[=a]man house, fr. dh[=a]to set, make, do: cf. F. famille. Cf. {Do}, v. t., {Doom}, {Fact}, {Feat}.] 1. The… …   The Collaborative International Dictionary of English

  • Family of surfaces — Family Fam i*ly, n.; pl. {Families}. [L. familia, fr. famulus servant; akin to Oscan famel servant, cf. faamat he dwells, Skr. dh[=a]man house, fr. dh[=a]to set, make, do: cf. F. famille. Cf. {Do}, v. t., {Doom}, {Fact}, {Feat}.] 1. The… …   The Collaborative International Dictionary of English

  • Curves International — Type Private company Industry Fitness Founded Harlingen, Texas (1992) …   Wikipedia

  • family — [fam′ə lē, fam′lē] n. pl. families [ME familie < L familia, household establishment, akin to famulus, servant < ? IE * dhe mo , house (< base * dhē : see DO1) > Sans dhāman, household] 1. Obs. all the people living in the same house;… …   English World dictionary

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