Limaçon Circle Art 12 images tree :: Geometry > Limaçon Circle Art
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These circle art images illustrate the limaçon obtained as an envelope of circles.

The method of construction is given in a chapter on curves in Geometry and the Visual Arts by Dan Pedoe. The envelope is constructed using a base circle C and a point A. Any circle with centre at some point Q on C with radius QA is a circle of the envelope.

Three types of limaçon are shown

• A on C (a cardioid)
• A outside of C
• A inside of C, which has an interior loop that is not visble if the circle elements are solid

The patterns are

• discs drawn in order round the base circle and with the last placed disc on top.
• discs drawn in order round the base circle and with the last placed disc on top, but alternating between going different directions about the base circle.
• equal height cones.
• rings drawn in order round the base circle and with the last placed ring on top.

 Image List

A on C discs  Med    Lrg
 Description : A on C. Discs drawn in order round the base circle and with the last placed disc on top. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A outside C discs  Med    Lrg
 Description : A outside C. Discs drawn in order round the base circle and with the last placed disc on top. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A in C discs  Med    Lrg
 Description : A in C. Discs drawn in order round the base circle and with the last placed disc on top. The curve has in interior loop hidden by the solid elements. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A on C discs alt  Med    Lrg
 Description : A on C. Discs drawn in order round the base circle and with the last placed disc on top, but alternating between going different directions about the base circle. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A outside C discs alt  Med    Lrg
 Description : A outside C. Discs drawn in order round the base circle and with the last placed disc on top, but alternating between going different directions about the base circle. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A in C discs alt  Med    Lrg
 Description : A in C. Discs drawn in order round the base circle and with the last placed disc on top, but alternating between going different directions about the base circle. The curve has in interior loop hidden by the solid elements. The points mark the other side of the envelope circles across a diameter from point A (the cusp of the curve)

A on C cones  Med    Lrg
 Description : A on C. Equal height cones. The tips of the cones mark the centres of the envelope circles and hence the base circle C.

A outside C cones  Med    Lrg
 Description : A outside C. Equal height cones. The tips of the cones mark the centres of the envelope circles and hence the base circle C.

A in C cones  Med    Lrg
 Description : A in C. Equal height cones. The curve has in interior loop hidden by the solid elements. The tips of the cones mark the centres of the envelope circles and hence the base circle C.

A on C rings  Med    Lrg
 Description : A on C. Rings drawn in order round the base circle and with the last placed ring on top.

A outside C rings  Med    Lrg
 Description : A outside C. Rings drawn in order round the base circle and with the last placed ring on top.

A in C rings  Med    Lrg
 Description : A in C. Rings drawn in order round the base circle and with the last placed ring on top. The interior loop of the curve is visble in this image as the circle elements are just the outlines of the circles, rather than solid.