A hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmic spirals or decreasing angles of Archimedean spirals. As this curve widens, it approaches an asymptotic line.

双曲螺线(hyperbolic spiral)是指极径和极角成反比例的动点轨迹。 双曲螺线的极坐标方程是ρ=a/θ，双曲螺线ρ=a/θ以直线y=a为渐近线，曲线有两支，它们关于Y轴对称。

双曲螺线 （Hyperbolic spiral）又称 倒数螺线 （reciprocal spiral）。 极径 与 极角 成反比的点的 轨迹 称为双曲螺线。 有一条平行于极轴的 渐近线。 是 阿基米德螺線 的倒數。 曲线出发于 极点。 其中 c 为常数。 直角坐標系中， 因此可見渐近线为： 。

2025年1月20日 · The hyperbolic spiral, also called the inverse spiral (Whittaker 1944, p. 83), originated with Pierre Varignon in 1704 and was studied by Johann Bernoulli between 1710 and 1713, as well as by Cotes in 1722 (MacTutor Archive). It is also a special case of a Cotes' spiral, i.e., the path followed by a particle in a central orbit with power law

In this paper, we investigate both areas. This paper has three goals. The first is to develop a mathematical theory of hyperbolic spirals. This is done in Section 2 where hyperbolic spirals are compared with their Euclidean analogues. Figures 1 and 2 show an Archimedean spiral in the Euclidean plane and its analogous hyperbolic spiral.

2014年7月26日 · It consists of two branches, which are symmetric with respect to a straight line $d$ (see Fig.). The pole is an asymptotic point. The asymptote is the straight line parallel to …

Hyperbolic spiral is also called reciprocal spiral, because it is the inverse curve of Archemedes' spiral, with inversion center at the center. The inversion curve of all Archemedean spirals with respect to a circle on center is another Archemedean spiral.

阿基米德螺旋画法：（1）先以导程 S 为半径画圆，再将圆周及半径分成相同的 n 等分，图中 n=8； （2）以 O 为圆心，作各同心圆弧于相应数字的半径相交，得交点Ⅰ、Ⅱ、Ⅲ、„ Ⅷ各点，即为阿基米德涡线上的点； （3）依次光滑连接各点，即得阿基米德涡线。 阿基米德螺旋的主要性质有: 1.若点 (ρ,θ)在曲线 ρ= 十 αθ 上,则点 (—ρ,—θ)在曲线 ρ=— +αθ 上。 这两支曲线 关于 π/2 线对称。 特别是 (图 1)当 =0 时,阿基米德螺线 ρ=αθ 可以画出关于 π/2 线的对称两部分。 摘 …

双曲螺线 （Hyperbolic spiral）又称 倒数螺线 （reciprocal spiral）。 极径 与 极角 成反比的点的 轨迹 称为双曲螺线。 有一条平行于极轴的 渐近线。 是 阿基米德螺线 的倒数。 曲线出发于 …

The hyperbolic spiral originated with Pierre Varignon in 1704. It was studied by Johann Bernoulli between 1710 and 1713 and it was also studied by Cotes in 1722 . The roulette of the pole of a hyperbolic spiral rolling on a straight line is a tractrix .