A relaxed and informal presentation conveying the joy of
mathematical discovery and insight. Frequent questions lead readers
to see mathematics as an accessible world of thought, where
understanding can turn opaque formulae into beautiful and
meaningful ideas. The text presents eight topics that illustrate
the unity of mathematical thought as well as the diversity of
mathematical ideas. Drawn from both "pure" and "applied"
mathematics, they include: spirals in nature and in mathematics;
the modern topic of fractals and the ancient topic of Fibonacci
numbers; Pascals Triangle and paper folding; modular arithmetic and
the arithmetic of the infinite. The final chapter presents some
ideas about how mathematics should be done, and hence, how it
should be taught. Presenting many recent discoveries that lead to
interesting open questions, the book can serve as the main text in
courses dealing with contemporary mathematical topics or as
enrichment for other courses. It can also be read with pleasure by
anyone interested in the intellectually intriguing aspects of
mathematics.
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