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.