Further Geometric Properties of the Cycloids

Geometric Construction 4

Further Geometric Properties of the Cycloids

Construct the animation displaying the deltoid sliding inside the 5-cusped hypocycloid.

Construct the animation displaying the astroid sliding inside the 3-cusped epicycloid.

Construct the animation displaying the deltoid being enveloped by a family of 3-cusped trochoids.

Construct an animation from this figure:

Show that nephroid may be regarded as a catacaustic of the cardioid:

Show that cardioid may be regarded as a catacaustic of the circle:

Construct this animation displaying a pair of orthogonal cardioids sharing the same cusp:

Given two cardioids sharing the same cusp, construct a circle passing through the cusp and tangent to both of them.

Construct this gear-tooth coupling among a deltoid, an astroid. a cardioid and a nephroid.

Construct two rotating cardioids meeting orthogonally.

Construct two rotating cardioids meeting tangentially as thus:

Construct a rotating cardioid and a rotating nephroid meeting tangentially.

Construct two orthogonal cardioids meeting on a deltoid.

Construct this animation containing all the interesting epi- and hypocycloids.