Microworld: A
World of Curves: (All in One)
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above to visit the Microworld.
Author:
Ravinder
Kumar
Graphing
is a very important aspect of the teaching and 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 practice of exploring 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
constructions. 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 approaches to
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
- Calculus I
- Calculus II
Number
of Pages: 14
Animation: Yes
Grade Level: 11-15
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