Geometric Construction 4


Construct the astroid.


Construct the deltoid.


Construct the nephroid.


Construct the cardioid.


Construct an animation showing a rod of fixed length slides with its ends upon two fixed perpendicular lines.
Construct the cardioid as the envelop of circles. Find the point of tangency.
Reference: Herman Baravalle, Dynamic Beauty of Geometrical Forms, Math. Scripta (1948) p.294.

Construct the nephroid as the envelope of circles. Find the point of tangency.


Two persons walk at constant speed around a circle. The ratio of their angular velocity is k ( k is not 0, 1 or -1). Find the envelope of all the straight lines joining them for k = 2, 3, -2, -3. Find the point of tangency.