释义 |
StrophoidLet be a curve, let be a fixed point (the Pole), and let be a second fixed point. Let and bepoints on a line through meeting at such that . The Locus of and is called thestrophoid of with respect to the Pole and fixed point . Let be represented parametrically by , and let and . Then the equation of the strophoid is
where
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The name strophoid means ``belt with a twist,'' and was proposed by Montucci in 1846 (MacTutor Archive). The polar form for a general strophoid is
 | (4) |
If , the curve is a Right Strophoid. The following table gives the strophoids of some commoncurves.Curve | Pole | Fixed Point | Strophoid | line | not on line | on line | oblique strophoid | line | not on line | foot of Perpendicular origin to line | Right Strophoid | Circle | center | on the circumference | Freeth's Nephroid |
See also Right Strophoid References
Lawrence, J. D. A Catalog of Special Plane Curves. New York: Dover, pp. 51-53 and 205, 1972.Lockwood, E. H. ``Strophoids.'' Ch. 16 in A Book of Curves. Cambridge, England: Cambridge University Press, pp. 134-137, 1967. MacTutor History of Mathematics Archive. ``Right.''http://www-groups.dcs.st-and.ac.uk/~history/Curves/Right.html. Yates, R. C. ``Strophoid.'' A Handbook on Curves and Their Properties. Ann Arbor, MI: J. W. Edwards, pp. 217-220, 1952.
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