Geometric Construction 3
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
Martin Gardner: Wheels, Life and Other Mathematical Amusements,
E.H. Lockwood, A Book of Curves, Cambridge University
N.B. Vasilyer and V.L. Gutebmacher, Straight Lines and
Curves, Mir, 1980.
Robert C. Yates, A Handbook on Curves and their Properties,
This is related to the Residue
Curves, see: Graphs of Linear Congruences, Math. Scripta (147) pp.
106-112. Also see pp. 114-115, p. 224, pp. 232-233 of the same issue.