Geometric Construction 2

Deltoid, Nephroid, Cardioid and Astroid

Construct an animation showing the formation of the deltoid

Construct an animation showing the formation of the nephroid

Construct an animation showing the formation of the cardioid

Construct an animation showing the formation of the astroid

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Show how each of the four curves may be generated in two ways.

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Construct each of the four curves as the envelope of its tangent.

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Construct the osculating circle of each of the four curves.

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Construct circles enveloping both the deltoid and the 3-cusped epicycloid.

Construct circles enveloping both the astroid and the 4-cusped epicycloid.

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Construct this pattern: