# logarithmic spiral

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## logarithmic spiral

[′läg·ə‚rith·mik ′spī·rəl]
(mathematics)
The spiral plane curve whose points in polar coordinates (r,θ) satisfy the equation log r = a θ. Also known as equiangular spiral.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Galaxie[R] Drive System's status as a new gearbox generation is based on the scientific reasoning of the logarithmic spiral - the mathematical function introduced by WITTENSTEIN.
Link points C and D using a smooth curve, and make line CD a logarithmic spiral line.
To simplify the stress analysis, the shear fracture surface of the rock during cutting is treated as a plane whose starting and end points are where the profile of the impact fracture pit (a logarithmic spiral) intersects the cut and uncut surfaces of the lunar rock simulant.
The device used four spring-loaded cams, each shaped like a logarithmic spiral. When placed into a vertical crack in the rock, the cams rest unless the hiker misses a step or slips, causing his or her weight to pull the cams down the crack.
Users are indeed fitting a circle involute when [alpha] = 2 as shown in each figure; Nielsen spiral is fitted when [alpha] = 0 and logarithmic spiral when [alpha] = 1.
Then, if our hypothesis is correct, we deal with the so-called logarithmic spiral (also called exponential spiral)  the equation of which has in the polar coordinates the form
Phi is also expressed in the logarithmic spiral and is the source of the Golden Angle, as well as many other mathematical forms too numerous to mention.
The mass function results in points on a logarithmic spiral lining up under a polar angle [phi] and being separated by the factor [phi].
In articles associated with such diagrams, it is often stated, that the curve thus obtained approximates a logarithmic spiral of golden proportion.
The choice of the models Logarithmic Spiral and Law of Damped Sinusoidal Oscillations (Savelov, 1960) was a personal reductionist approach to the study of forest growth and increment.
* innovative application of a logarithmic spiral, representing the idea of an isomorphic growth, on the charts of stock indexes, to forecast basic trend changes on the market.
The spiral representations of the data reminded us of the Fibonacci sequence and the logarithmic spiral, mathematical forms which can be found throughout nature in objects such as pinecones, pineapples, petals and branches from plant stems (Britannica, 2002).

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