The lituus spiral (/ ˈlɪtju.əs /) is a spiral in which the angle θ is inversely proportional to the square of the radius r. This spiral, which has two branches depending on the sign of r, is asymptotic to …

5 days ago · The lituus is the locus of the point P moving such that the area of a circular sector remains constant. The arc length, curvature, and tangential angle are given by s(theta) = (2) …

The lituus was a crooked wand (similar in shape to the top part of some Western European crosiers) used as a cult instrument in ancient Roman religion by augurs [1] to mark out a ritual …

The lituus is a transcendental curve that can be graphed with the polar equation r = k/√θ [1] or, equivalently, r 2 = a 2 /θ. Lituus with k = 5. The inverse of the lituus is Fermat’s spiral — a type …

Lituus is a spiral described by the polar equation r == 1/Sqrt [θ]. The curve is asymptotic to the positive x-axis, and the other end spiral in towards the pole. The above image is a plot from …

The curve consists of two branches, that both approach the pole asymptotically (see Fig.). The line $\phi=0,\phi=\pi$ is an asymptote at $\rho=\pm\infty$, and $(1/2,a\sqrt2)$ and $(-1/2, …

Lituus means a crook, for example a bishop's crosier. Maclaurin gave the curve its name in 1722 . The lituus is the locus of the point P P P moving in such a manner that the area of a circular …

The lituus is a species of the Archimedean spiral. Some authors add (-r, φ) forming a double shape. The curve is formed by the loci of a point P moving in such a way that the area of a …

Click on the Curve menu to choose one of the associated curves. Then click on the diagram to choose a point for the involutes, pedal curve, etc. You can then move the point around and …

Sep 30, 2024 · In mathematics, a lituus is a spiral with polar equation r 2 k where k is any nonzero constant. Thus, the angle is inversely proportional to the square of the radius r. This spiral, …