Cardioid Envelope of Line Segments
Cardioid Envelope of Line Segments
To create sequence of points on a circle:
Sequence[ (r cos( i 2π/n), r sin(i 2π/n)), i, 0, n-1 ]
The cardioid created using this set of points is sideways, so
Sequence[(r cos(i 2 π / n - π / 2), r sin(i 2 π / n - π / 2)), i, 1, n]
orients it right-side up and rotates it so that it's exactly vertical.
To create a cardioid, numbered points are joined with their doubles, and then repeated in the reverse direction.
Cardioid 1st half = Sequence[Segment[Element[list1, k], Element[list1, 2k]], k, 1, n]
Cardioid 2nd half = Sequence[Segment[Element[list1, n - k], Element[list1, n - 2k]], k, 1, n]