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

In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from...

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

A logarithmic spiral beach is a type of beach which develops in the direction under which it is sheltered by a headland, in an area called the shadow zone...

of golden triangles. A logarithmic spiral can be drawn through the vertices. This spiral is also known as an equiangular spiral, a term coined by René...

hexecontahedron. Logarithmic spirals are self-similar spirals where distances covered per turn are in geometric progression. A logarithmic spiral whose radius...

of the next one, scaled by a constant factor. This gives rise to a logarithmic spiral. Benford's law on the distribution of leading digits can also be explained...

in 1956. Archimedean spiral antennas are the most popular, while logarithmic spiral antennas are independent of frequency: the driving point impedance...

distance from the spiral center, contrasting with the Archimedean spiral (for which this distance is invariant) and the logarithmic spiral (for which the...

projection is a logarithmic spiral, it is called conchospiral (from conch). In the x {\displaystyle x} - y {\displaystyle y} -plane a spiral with parametric...

the logarithmic function to describe measurements Logarithmic spiral, Logarithmic growth Logarithmic distribution, a discrete probability distribution...

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...

Milky Way's spiral structure is uncertain, and there is currently no consensus on the nature of the Milky Way's arms. Perfect logarithmic spiral patterns...

patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmic spirals of three different...

measured in radians), hence the name "arithmetic spiral". In contrast to this, in a logarithmic spiral these distances, as well as the distances of the...

tension in shaping soap films and similar structures such as cells; the logarithmic spiral as seen in mollusc shells and ruminant horns; the arrangement of leaves...

Eric W. "Logarithmic Spiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019. Weisstein, Eric W. "Nielsen's Spiral". mathworld...

closed-form solutions for arc length include the catenary, circle, cycloid, logarithmic spiral, parabola, semicubical parabola and straight line. The lack of a closed...

Logarithmic identities Logarithmic number system Logarithmic scale Logarithmic spiral Logarithmic timeline Logit LogSumExp Mantissa is a disambiguation page;...

decorations of the mediæval Mosque of Córdoba, Andalusia. A silver spiral is a logarithmic spiral that gets wider by a factor of ⁠ σ {\displaystyle \sigma } ⁠...

self-similar in character, with the branched meristems making up a logarithmic spiral, giving a form approximating a natural fractal; each bud is composed...

squares form an infinite sequence of points on the golden spiral, the unique logarithmic spiral with this property. Diagonal lines drawn between the first...

lifetime, titled Logometria, in which he successfully constructs the logarithmic spiral. After his death, many of Cotes's mathematical papers were edited...

} denotes the golden ratio; logarithmic spirals with other angles are not golden spirals. Spirals that are not logarithmic have pitch angles that vary...

that the logarithmic spirals are self-similar, meaning that upon applying any similarity transformation to the spiral, the resulting spiral is congruent...

that stars do move along spiral arms, and described how mutual gravity between stars causes orbits to align on logarithmic spirals. When the theory is applied...

logarithmic spiral. Although many references assert that the instrument scroll closely follows the golden spiral (a specific form of the logarithmic spiral)...

presents one of the finest natural examples of a logarithmic spiral, although it is not a golden spiral. The use of nautilus shells in art and literature...

Rectangular hyperbola Center Lemniscate of Bernoulli Logarithmic spiral Pole Logarithmic spiral Sinusoidal spiral r n = a n cos ⁡ n θ {\displaystyle r^{n}=a^{n}\cos...

calculates the Z transform at a finite number of points zk along a logarithmic spiral contour, defined as: X k = ∑ n = 0 N − 1 x ( n ) z k − n {\displaystyle...