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Encyclopedia > Lituus

A lituus (Latin for "crozier") is a spiral in which (in polar coordinates) the angle is inversely proportional to the square of the radius.


image:lituus.png


The lituus is asymptotic to the line θ=0.


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Lituus (0 words)
According to Robert C. Yates 1952, the Lituus curve is studied by Roger Cotes in 1722.
Lituus is a spiral described by the polar equation r == 1/Sqrt[θ].
That is, suppose P is a point on the curve, and X a point on the asymptote OP distance from the origin O. Suppose the area of the circular sector OPX is A. As P moves towards the center on the curve, the area remains the same.
Lituus (0 words)
The lituus curve originated with Cotes in 1722.
Lituus means a crook, for example a bishop's crosier.
The lituus is the locus of the point P moving in such a manner that the area of a circular sector remains constant.
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