Lituus

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The word lituus originally meant a curved staff ("crozier") or trumpet in the ancient Latin language, and is used with several meanings in English:

[edit] Mathematics

In mathematics, a lituus is a spiral in which the angle is inversely proportional to the square of the radius (as expressed in polar coordinates).

r^2\theta = k \,

This spiral is asymptotic to the line θ = 0.

[edit] Roman ritual

A lituus (reverse, right, over the patera) as cult instrument, in this coin celebrating the pietas of the Roman Emperor Herennius Etruscus.
A lituus (reverse, right, over the patera) as cult instrument, in this coin celebrating the pietas of the Roman Emperor Herennius Etruscus.

The lituus was a crooked wand (similar in shape to the top part of a crosier) used as a cult instrument in Roman religion by augurs to mark out a ritual space in the sky (a templum). The passage of birds through this templum indicated divine favor or disfavor for a given undertaking.

The lituus was also used as a symbol of office for the college of the augurs to mark them out as a priestly group.

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