Comments on: The Family of Curves
http://www.axiomaudio.com/blog/the-family-of-curves/
Axiom Home Theater BlogWed, 13 Jan 2016 11:10:36 +0000hourly1https://wordpress.org/?v=4.5.3By: Fred Heinzler
http://www.axiomaudio.com/blog/the-family-of-curves/comment-page-1/#comment-23955
Wed, 18 Sep 2013 12:31:51 +0000http://www.axiomaudio.com/blog/?p=1641#comment-23955Come into Avery Audio and listen to Axiom's 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when an additive constant of integration is introduced, it will usually be manipulated algebraically until it no longer represents a simple linear transformation.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(theta) = {e over 1+e cos theta}
as the value of e changes, the appearance of the curve varies in a relatively complicated way. Listen to Axiom's explanation here:
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