Cardioid

Med
Lrg

Description :

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.





Nephroid

Med
Lrg

Description :

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.





Epicycloid 1:3

Med
Lrg

Description :

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.





Epicycloid 1:4

Med
Lrg

Description :

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.





Epicycloid 1:5

Med
Lrg

Description :

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.





Epicycloid 1:6

Med
Lrg

Description :

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.





Epicycloid 1:8

Med
Lrg

Description :

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.





Epicycloid 1:12

Med
Lrg

Description :

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.





Astroid

Med
Lrg

Description :

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 xaxis to points at distance L on the
yaxis. All the tangent strings in the image have length L.





Deltoid

Med
Lrg

Description :

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.





Astroid

Med
Lrg

Description :

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.





Hypocycloid 1:5

Med
Lrg

Description :

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.





Hypocycloid 1:6

Med
Lrg

Description :

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.





Hypocycloid 1:8

Med
Lrg

Description :

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.





Hypocycloid 1:12

Med
Lrg

Description :

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.




