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Cardioid
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Med
Lrg
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Description :
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The cardioid is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of another circle of radius one unit.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (2n + N/2) mod N.
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Nephroid
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Med
Lrg
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Description :
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The nephroid is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius two units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (3n + N/2) mod N.
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Epicycloid 1:3
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius three units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (4n + N/2) mod N.
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Epicycloid 1:4
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius four units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (5n + N/2) mod N.
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Epicycloid 1:5
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius five units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (6n + N/2) mod N.
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Epicycloid 1:6
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius six units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (7n + N/2) mod N.
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Epicycloid 1:8
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius eight units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (9n + N/2) mod N.
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Epicycloid 1:12
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls around the
circumference of a circle of radius twelve units.
It is formed here from its tangents by laying N points equally on a
circle, and joining point n to the point (13n + N/2) mod N.
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Astroid
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Med
Lrg
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Description :
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The astroid is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius four units.
It is formed here from its tangents by choosing a length L
and then joining points on the x-axis to points at distance L on the
y-axis. All the tangent strings in the image have length L.
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Deltoid
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Med
Lrg
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Description :
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The deltoid is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius three units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 2n) mod N.
The strings are extended to an outer circle whose radius is 3 times
the inner circle radius.
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Astroid
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Med
Lrg
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Description :
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The astroid is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius four units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 3n) mod N.
The strings are extended to an outer circle whose radius is 2 times
the inner circle radius.
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Hypocycloid 1:5
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius five units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 4n) mod N.
The strings are extended to an outer circle whose radius is 5/3 times
the inner circle radius.
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Hypocycloid 1:6
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius six units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 5n) mod N.
The strings are extended to an outer circle whose radius is 3/2 times
the inner circle radius.
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Hypocycloid 1:8
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius eight units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 7n) mod N.
The strings are extended to an outer circle whose radius is 4/3 times
the inner circle radius.
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Hypocycloid 1:12
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Med
Lrg
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Description :
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The curve is the path followed by a point on the
circumference of a circle of radius one unit as it rolls inside the
circumference of a circle of radius twelve units.
It is formed here from its tangents by laying N points equally on a
circle (the inner circle), and joining point n to the point (N/2 - 11n) mod N.
The strings are extended to an outer circle whose radius is 6/5 times
the inner circle radius.
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