Polar equation:
r2 = a2/θ

Click below to see one of the Associated curves.

Definitions of the Associated curves Evolute
Involute 1 Involute 2
Inverse curve wrt origin Inverse wrt another circle
Pedal curve wrt origin Pedal wrt another point
Negative pedal curve wrt origin Negative pedal wrt another point
Caustic wrt horizontal rays Caustic curve wrt another point

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The lituus curve originated with Cotes in 1722. Lituus means a crook, for example a bishop's crosier. Maclaurin used the term in his book Harmonia Mensurarumin 1722. The lituus is the locus of the point P moving in such a manner that the area of a circular sector remains constant.

Roger Cotes (1682-1716) died at the age of 34 having only published two memoirs during his lifetime. Appointed professor at Cambridge at the age of 24 his work was published only after his death.

Cotes discovered an important theorem on the nth roots of unity; anticipated the method of least squares and discovered a method of integrating rational fractions with binomial denominators.

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JOC/EFR/BS January 1997

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