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LITUUS
Curve studied by Cotes and Maclaurin in 1722.
Lituus (Latin word): wand used by Roman augurs, similar to a current bishop's staff. Other name: limaçon spiral. 

Polar equation: .
Curvilinear abscissa: . Radius of curvature: . Transcendental curve. 

The lituus is the locus of the point M on a variable circle centred on O cutting the axis Ox at A such that the area of the circular domain OAM is a constant equal to a^{2}/2.
The inflexion point is obtained for q = 0,5 radians, i.e. around 30°.
The lituus is the inverse with centre O of the Fermat spiral and the radial of the clothoid.
It can be found in the volutes of Ionic capitals:
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© Robert FERRÉOL 2017