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 the x axis. Its points of inflexion are at. ± {\displaystyle (\theta ,r)=\left ( …

4 天之前 · 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) kappa(theta)... The lituus is an Archimedean spiral with n=-2, having polar equation r^2theta=a^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 space in the sky (a templum). The passage of birds through this templum indicated divine favor or disfavor for a given undertaking.

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 of Archimedean spiral (the littus is the inverse of Fermat

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 0.1 to 20*Pi. As θ approachs infinity, the curve approaches the origin. Polar equation: r == 1/Sqrt [θ].

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 $(-1/2,-a\sqrt2)$ are points of inflection. The lituus is related to the so-called algebraic spirals. References

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 sector remains constant.

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 circular sector remains constant.

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 watch the associated curve change. For the inverse (wrt a circle) click the mouse and drag to choose a centre and radius. You can then drag the centre of the circle.

2024年9月30日 · 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, which has two branches depending on the sign of r …