Handbook of Famous Plane Curves Using Mathematica
Description:... Inspired by the Famous Curves Index of the award-winning website by MacTutor History of Mathematics archive maintained by John J. O'Connor and Edmund F. Robertson and hosted by the University of St Andrews, the author wrote this handbook of famous plane curves using Mathematica® as a tool to graph, animate, calculate and to construct derived curves from given ones. Some constructions are extremely difficult to draw by hands, especially those involve numerical integration can be performed with ease with Mathematica®. Even for some simple curves before the invention of computer, drawing them by hands might take a long time. To borrow the words of Rudy Rucker (author of The Fourth Dimension): "if the only thing you're going to be remembered for in 300 years is one single curve, then you don't mind spending a year or two in getting it right!"
Plane curves had been studied since antiquity. However, the general theory of plane curves began to be developed only after the invention of Cartesian coordinates by Descartes in the early 1600s. The discovery of calculus in the 17th century led to the study of more complicated plane curves. The methods of calculus, in particular integration, provides solution of finding the arc length and area of a plane curve.
Plane curves are of historical interest. It could be said that significant part of classical mathematics deal with them. Most books on history of mathematics include information on various plane curves. Plane curves remain a source of inspiration and a topic of research to this day. Whenever it is applicable the author mentions some research papers in which the curves are used for applications in modern science and technology.
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