A curve named after James Watt (17361819), the Scottish engineer who developed the steam engine (MacTutor Archive). The curve is produced by a linkage of rods connecting two wheels of equal diameter. Let the two wheels have radius and let their centers be located a distance apart. Further suppose that a rod of length is fixed at each end to the circumference of the two wheels. Let be the midpoint of the rod. Then Watt's curve is the locus of .
The polar equation of Watt's curve is
(1)

The areas of one of the inner lenses, heartshaped halfregion, and entire enclosed region (which resembles a lemniscate are
(2)
 
(3)
 
(4)

If , then is a circle of radius with a figure of eight inside it.