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Geometric Construction 11

Construct an animation showing the cardioid has three parallel tangents
in any direction.

Construct an animation displaying the largest deltoid that can be inscribed
in a nephroid.

Given the rose curve, construct its escribed deltoid.

Construct an animation showing that the cardioid is the caustic of a circle
with radient-point at the circumference.

Construct an animation showing that the nephroid is the caustic of a cardioid
with radient-point at the cusp.

Construct an animation displaying the principle behind the cardioid condensor.

Show that is the cardioid is pivoted at the cusp and rotated with constant
angular velocity, a pin, constrained to a fixed line and bearing on the
cardioid, will move with simple harmonic motion.

Combine two anti-parallelograms to generate the cardioid as thus: