Geometric Construction 4
Further Geometric Properties of the Cycloids
Construct the animation displaying the deltoid sliding inside the 5-cusped hypocycloid.
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Construct the animation displaying the astroid sliding inside the 3-cusped epicycloid.
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Construct the animation displaying the deltoid being enveloped by a family of 3-cusped trochoids.
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Construct an animation from this figure:
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Show that nephroid may be regarded as a catacaustic of the cardioid:
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Show that cardioid may be regarded as a catacaustic of the circle:
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Construct this animation displaying a pair of orthogonal cardioids sharing the same cusp:
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Given two cardioids sharing the same cusp, construct a circle passing through the cusp and tangent to both of them.
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Construct this gear-tooth coupling among a deltoid, an astroid. a cardioid and a nephroid.
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Construct two rotating cardioids meeting orthogonally.
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Construct two rotating cardioids meeting tangentially as thus:
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Construct a rotating cardioid and a rotating nephroid meeting tangentially.
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Construct two orthogonal cardioids meeting on a deltoid.
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Construct this animation containing all the interesting epi- and hypocycloids.