Shikin, Eugene V., Handbook and Atlas of Curves, CRC Press, 1995. McQuarrie, Donald A., Mathematical Methods for Scientists and Engineers, University Science Books, 2003. H., A Book of Curves,Cambridge University Press, 1961. A plane curve whose equation is r a in polar coordinates, meaning that the length of the curves radius r from its centre is always a constant ratio of. 1 Notably, Archimedes employed the Archimedean spiral in this book to square the circle and trisect an angle. Katz, Victor J., A History of Mathematics, PEARSON - Addison Wesley, 2004. On Spirals ( Greek: ) is a treatise by Archimedes, written around 225 BC. Gray, Alfred, Modern Differential Geometry of Curves and Surfaces with MATHEMATICA ®, 2nd ed., CRC Press, 1998. Merzbach, A History of Mathematics, 2nd ed., John Wiley and Sons, 1991.Įves, Howard, An Introduction to theHistory of Mathematics, 6th ed. In nature, the spiraled chambered nautilus is associated with the Golden Ratio, which again is associated with the Fibonacci Sequence.īoyer, Carl B., revised by U. In architecture there is the Ionic capital on a column. The Archmedean spiral is the spiral created by an object which moves away from a fixed point at a constant speed while rotating with a constant velocity. Maclaurin, best known for hiswork on series, discusses spirals in Harmonia Mensurarum (1722). We find Cayley's Sextic, Tschirnhausen's Cubic, and Lituus' shepherd's (or a bishop's) crook. The name spiral, where a curve winds outward from a fixed point, has been extended to curves where the tracing point moves alternately toward and away from the pole, the so-called sinusoidal type. Among the more famous are Archimedes, Descartes, Bernoulli, Euler, and Fermat, but there are many more whose work has enormously influenced pure mathematics, science and engineering. From the legendary Delian problem in antiquity to modern freeway construction, spirals have attracted great mathematical talent.
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