Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
- Additional Readings
A type of plane curve that consists of loops (leaves, petals) emanating from a common point and that has a roselike appearance. Taking the common point O as the pole of a polar coordinate system (see illustration), these curves have equations of the form ρ = a · sin nθ, where a > 0 and n is a positive integer (also ρ = a · cos nθ, with a different choice of the initial line of the coordinate system). The curve is a circle of diameter a for n = 1. It has n or 2n leaves, according to whether n is an odd or even integer, respectively. The area enclosed by one leaf is ; therefore the entire area of the three-leaved rose ρ = a sin 3θ is , and that of the four-leaved rose ρ = a sin 2θ is . The lemniscate is sometimes called a two-leaved rose, though its equation, ρ2 = a2 cos 2θ, is not of the form given above. See also: Lemniscate of Bernoulli
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