WOLFRAM|DEMONSTRATIONS PROJECT

Transforming an Astroid into a Square

​
a
2
3
a
astroid
diamond
circle
-1.0
-0.5
0.5
1.0
-1.0
-0.5
0.5
1.0

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.