John Bernoulli (1667 - 1748)

A World of Curves: All in One

by Ravinder Kumar

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Best Linear Fit Book Description:

Graphing is a very important aspect of learning of mathematics at all levels, particularly at the undergraduate level. The world of curves is full of wonders. But, with the advent of technology, we find ironically, that the culture of studying this beautiful world is getting pushed into oblivion. This is despite the fact that these days books, particularly calculus books, emphasize the graphical aspect of concepts. Books, however, often do not talk about envelopes, evolutes, involutes, pedals, negative pedals etc., any more. Historically, these and other ways of determining curves not only shed light on the curves and their characteristic properties, but also produce some fantastic curves, otherwise difficult to create and visualize.

It is the objective of this 14 page microworld to provide some ways of gaining insight into the world of curves. This effort is by no means exhaustive or comprehensive. Here, we explore curves defined by parametric equations only. We also provide mechanism to understand and explore the envelope, pedal, negative pedal, and contrapedal. For a list of historically famous curves and their properties we refer to the website: MacTutor of History of Mathematics.

This book may be used for

1. Calculus I
2. Calculus II

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