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math logarithmic spiral equation. The constants a and b are adjustable. The natural equation is skr where k1ln a.
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Th is the angle in radians from the horizontal axis. Eg since 1000 10 10 10 10 3 the logarithm base. So its easy to step around the spiral by a given angle but obviously the actual length of any line between two vertices defined by change in angle D th will vary with the radius.
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The logarithmic spiral was first described by Descartes and later extensively investigated by Jacob Bernoulli who called it Spira mirabilis the marvelous spiral. The logarithmic or equiangular spiral was first studied by Rene Descartes in 1638. The general equation of the logarithmic spiral is r aeth cot b in which r is the radius of each turn of the spiral a and b are constants that depend on the particular spiral th is the angle of rotation as the curve spirals and e is the base of the natural logarithm. So the coordinates of a point on the curve in polar coordinates is given by r th.
