perimeter of astroid

The astroid


can be presented in the parametric form


where the polar angle φ gets the values from 0 to 2π. The curve consists of four congruentMathworldPlanetmath arcs, one of which is obtained letting  0φπ2. Thus the whole perimeter of the astroid is


This expression is easily simplified to


giving the result

Title perimeter of astroid
Canonical name PerimeterOfAstroid
Date of creation 2013-03-22 17:14:06
Last modified on 2013-03-22 17:14:06
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Example
Classification msc 26B15
Synonym perimetre of astroid
Related topic Parameter
Related topic ClairautsEquation
Related topic SubstitutionNotation