catacaustic
Given a plane curve , its catacaustic (Greek ‘burning along’) is the envelope of a family of rays reflected from after having emanated from a point (which may be infinitely far, in which case the rays are initially parallel).
For example, the catacaustic of a logarithmic spiral reflecting the rays emanating from the origin is a congruent spiral. The catacaustic of the exponential curve (http://planetmath.org/ExponentialFunction) reflecting the vertical rays is the catenary .
Title | catacaustic |
Canonical name | Catacaustic |
Date of creation | 2013-03-22 18:52:56 |
Last modified on | 2013-03-22 18:52:56 |
Owner | pahio (2872) |
Last modified by | pahio (2872) |
Numerical id | 10 |
Author | pahio (2872) |
Entry type | Definition |
Classification | msc 53A04 |
Classification | msc 51N20 |
Classification | msc 26B05 |
Classification | msc 26A24 |
Synonym | caustic |
Related topic | HeronsPrinciple |
Related topic | ExampleOfFindingCatacaustic |