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 ?
Next, based on equation of state for the stress on any microelement in an object under external load and (14) and (15), the shear stress, [[tau].sub.p], and the normal stress, [[sigma].sub.p], at any point on the logarithmic spiral are
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.
Assume uniformly distributed force, q, in logarithmic spiral AB satisfies the following condition:
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.
The logarithmic spiral (far left) maintains a constant angle, the camming angle, between its tangent and its radial line.
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.
(26) Interestingly, the shell of the Murex trunculus, the snail from which tekhelet dye is made, appears to follow the phi-based logarithmic spiral.
The general equation of a logarithmic spiral, attributed to Descartes, is given in polar form by
In order to find c, use is made of a diagram in which part of a logarithmic spiral is enclosed by a rectangle of golden proportion; the sides of which are tangential to the spiral (see Figure 2).
181), one can construct a logarithmic spiral (a spiral in which the logarithm of the radial distance from the center increases in proportion to the total angle traversed along the spiral).