WOLFRAM|DEMONSTRATIONS PROJECT

Transforming an Astroid into a Square

​
a
2
3
a
astroid
diamond
circle
This Demonstration shows that it is possible to parameterize a function that transforms an astroid into a square.
When
a=2/3,1,2
, the curve is an astroid, a diamond, or a unit circle, respectively; for larger values, the curve is a square with rounded corners.