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...

Archimedean spiral hyperbolic spiral Fermat's spiral lituus logarithmic spiral Cornu spiral spiral of Theodorus Fibonacci Spiral (golden spiral) The involute...

4) Example 4 is based on a hyperbolic spiral r ( φ ) = a / φ {\displaystyle \;r(\varphi )=a/\varphi \;} . Such a spiral has an asymptote (black line)...

logarithmic spirals, Archimedean spirals, or hyperbolic spirals, their pitch angles vary with distance from the galactic center, unlike logarithmic spirals (for...

1. Other spirals falling into this group include the hyperbolic spiral (c = −1), Fermat's spiral (c = 2), and the lituus (c = −2). One method of squaring...

In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just...

from the center of the spiral. For an Archimedean spiral the angle decreases with the distance, while for a hyperbolic spiral the angle increases with...

logarithmic spiral. However, spiral arms may also be described as an Archimedean or hyperbolic spiral. In the case of the logarithmic spiral, the pitch...

Spirals Archimedean spiral Cornu spiral Cotes' spiral Fermat's spiral Galileo's spiral Hyperbolic spiral Lituus Logarithmic spiral Nielsen's spiral Golden...

spiral, equiangular spiral, or growth spiral is a self-similar spiral curve that often appears in nature. The first to describe a logarithmic spiral was...

list of spirals includes named spirals that have been described mathematically. Mathematics portal Catherine wheel (firework) List of spiral galaxies...

complete Fermat's spiral (both branches) is a smooth double point free curve, in contrast with the Archimedean and hyperbolic spiral. Like a line or circle...

first and third forms are Poinsot's spirals; the second is the equiangular spiral; the fourth is the hyperbolic spiral; the fifth is the epispiral. For more...

of the oldest structures in architectural history. The oldest example of spiral stairs dates back to the 400s BC. Medieval architecture saw experimentation...

Syntractrix Tractrix Trochoid Archimedean spiral Cornu spiral Fermat's spiral Hyperbolic spiral Lituus Logarithmic spiral Maurer rose Reuleaux triangle Blancmange...

\operatorname {sech} (n\theta )} where csch is the hyperbolic cosecant, and sech is the hyperbolic secant. They are named after the French mathematician...

regarded in a multitude of ways: It is the locus of the center of a hyperbolic spiral rolling (without skidding) on a straight line. It is the involute...

Sinusoid Spirals Archimedean spiral Cornu spiral Cotes' spiral Fermat's spiral Galileo's spiral [3] Hyperbolic spiral Lituus Logarithmic spiral Nielsen's...

{\frac {rp_{c}}{p}}\right)=0.} As an example take the logarithmic spiral with the spiral angle α: r = a e cos ⁡ α sin ⁡ α θ . {\displaystyle r=ae^{{\frac...

treat Cin as the primary function, and derive Ci in terms of Cin. The hyperbolic sine integral is defined as Shi ⁡ ( x ) = ∫ 0 x sinh ⁡ ( t ) t d t . {\displaystyle...

{\displaystyle C=1} , the solution is the hyperbolic spiral. When C > 1 {\displaystyle C>1} the solution is Poinsot's spiral. Although the Binet equation fails...

known as density of hyperbolicity, is one of the most important open problems in complex dynamics. Hypothetical non-hyperbolic components of the Mandelbrot...

(that is, the pitch surface of the hypoid gear is a hyperbolic surface), whereas the shape of a spiral bevel gear is normally conical. The hypoid gear places...

This article lists the regular polytopes in Euclidean, spherical and hyperbolic spaces. This table shows a summary of regular polytope counts by rank....

Archimedean spiral and hyperbolic spiral are inverse curves. Similarly, the Fermat spiral and the lituus are inverse curves. The logarithmic spiral is its...

gear, the basic geometry of hypoid gear is hyperbolic. The spiral angle of the pinion is larger than the spiral angle of the gear in a hypoid gearbox, so...

orientation-preserving isometries of hyperbolic 3-space and therefore plays an important role when studying hyperbolic 3-manifolds. In physics, the identity...

going to zero yields the third form of a Cotes's spiral, the so-called reciprocal spiral or hyperbolic spiral, as a solution 1 r = A θ 2 + ε {\displaystyle...

In mathematics, the Gudermannian function relates a hyperbolic angle measure ψ {\textstyle \psi } to a circular angle measure ϕ {\textstyle \phi } called...

Voderberg tiling, a spiral, monohedral tiling made of enneagons Alternated octagonal or tritetragonal tiling is a uniform tiling of the hyperbolic plane Topological...