"Spira mirabilis" redirects here. For the orchestra, see Spira Mirabilis (orchestra). For the Italian film, see Spira Mirabilis (film).
Logarithmic spiral (pitch 10°)A section of the Mandelbrot set following a logarithmic spiral
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 spiral was Albrecht Dürer (1525) who called it an "eternal line" ("ewige Linie").[1][2] More than a century later, the curve was discussed by Descartes (1638), and later extensively investigated by Jacob Bernoulli, who called it Spira mirabilis, "the marvelous spiral".
The logarithmic spiral can be distinguished from the Archimedean spiral by the fact that the distances between the turnings of a logarithmic spiral increase in geometric progression, while in an Archimedean spiral these distances are constant.
^Albrecht Dürer (1525). Underweysung der Messung, mit dem Zirckel und Richtscheyt, in Linien, Ebenen unnd gantzen corporen.
^Hammer, Øyvind (2016). "Dürer's dirty secret". The Perfect Shape: Spiral Stories. Springer International Publishing. pp. 173–175. doi:10.1007/978-3-319-47373-4_41. ISBN 978-3-319-47372-7.
and 27 Related for: Logarithmic spiral information
A logarithmicspiral, 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 logarithmicspiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from...
in 1956. Archimedean spiral antennas are the most popular, while logarithmicspiral antennas are independent of frequency: the driving point impedance...
hexecontahedron. Logarithmicspirals are self-similar spirals where distances covered per turn are in geometric progression. A logarithmicspiral whose radius...
measured in radians), hence the name "arithmetic spiral". In contrast to this, in a logarithmicspiral these distances, as well as the distances of the...
A logarithmicspiral 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...
Eric W. "LogarithmicSpiral". mathworld.wolfram.com. Wolfram Research, Inc. Retrieved 18 February 2019. Weisstein, Eric W. "Nielsen's Spiral". mathworld...
of the next one, scaled by a constant factor. This gives rise to a logarithmicspiral. Benford's law on the distribution of leading digits can also be explained...
patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmicspirals of three different...
tension in shaping soap films and similar structures such as cells; the logarithmicspiral as seen in mollusc shells and ruminant horns; the arrangement of leaves...
projection is a logarithmicspiral, 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 Logarithmicspiral, Logarithmic growth Logarithmic distribution, a discrete probability distribution...
} denotes the golden ratio; logarithmicspirals with other angles are not golden spirals. Spirals that are not logarithmic have pitch angles that vary...
hyperbolic spiral is a type of spiral with a pitch angle that increases with distance from its center, unlike the constant angles of logarithmicspirals or decreasing...
as a logarithmicspiral. However, spiral arms may also be described as an Archimedean or hyperbolic spiral. In the case of the logarithmicspiral, the...
closed-form solutions for arc length include the catenary, circle, cycloid, logarithmicspiral, parabola, semicubical parabola and straight line. The lack of a closed...
self-similar in character, with the branched meristems making up a logarithmicspiral, giving a form approximating a natural fractal; each bud is composed...
Milky Way's spiral structure is uncertain, and there is currently no consensus on the nature of the Milky Way's arms. Perfect logarithmicspiral patterns...
Logarithmic identities Logarithmic number system Logarithmic scale LogarithmicspiralLogarithmic timeline Logit LogSumExp Mantissa is a disambiguation page;...
that stars do move along spiral arms, and described how mutual gravity between stars causes orbits to align on logarithmicspirals. When the theory is applied...
a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmicspiral. Conchospirals are used in...
chambered nautilus grows at a constant rate and so its shell forms a logarithmicspiral to accommodate that growth without changing shape. Also, honeybees...
lifetime, titled Logometria, in which he successfully constructs the logarithmicspiral. After his death, many of Cotes's mathematical papers were edited...
presents one of the finest natural examples of a logarithmicspiral, although it is not a golden spiral. The use of nautilus shells in art and literature...
particular he studied these associated curves of the parabola, the logarithmicspiral and epicycloids around 1692. The lemniscate of Bernoulli was first...
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