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World Scientific www.worldscientific.com 6559 hc Kalantari This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations. “Bahman Kalantari has created a beautiful new genre of mathematical visual art, that is quite distinct from Fractal Art, and is just as beautiful. Not only is the art beautiful, but the mathematics and the elegant algorithms that generate it. This book can be read on quite a few levels, all very rewarding, and will inspire lots of future research and new gorgeous art.” Doron Zeilberger Rutgers University Winner of the Steele Prize Polynomial Root-Finding and Polynomiography Polynomial Root-Finding and Polynomiography Polynomial Root-Finding and Polynomiography Bahman Kalantari ,!7IJ8B2-haafjj! ISBN-10 981-270-059-5 ISBN-13 978-981-270-059-9 World Scientific www.worldscientific.com 6265 hc 6265_final.indd 1 10/9/08 12:15:55 PM

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Page 1: Polynomial Root-Finding Polynomiographykalantar/img/BookCover.pdf · of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization

World Scientificwww.worldscientific.com6559 hc

,!7IJ8B0-ccheab!ISBN-10 981-02-2740-XISBN-13 978-981-02-2740-1

Kalantari

This book offers fascinating and modern perspectives into the theory and practice of the historical subject of polynomial root-finding, rejuvenating the field via polynomiography, a creative and novel computer visualization that renders spectacular images of a polynomial equation. Polynomiography will not only pave the way for new applications of polynomials in science and mathematics, but also in art and education. The book presents a thorough development of the basic family, arguably the most fundamental family of iteration functions, deriving many surprising and novel theoretical and practical applications such as: algorithms for approximation of roots of polynomials and analytic functions, polynomiography, bounds on zeros of polynomials, formulas for the approximation of Pi, and characterizations or visualizations associated with a homogeneous linear recurrence relation. These discoveries and a set of beautiful images that provide new visions, even of the well-known polynomials and recurrences, are the makeup of a very desirable book. This book is a must for mathematicians, scientists, advanced undergraduates and graduates, but is also for anyone with an appreciation for the connections between a fantastically creative art form and its ancient mathematical foundations.

“Bahman Kalantari has created a beautiful new genre of mathematical visual art, that is quite distinct from Fractal Art, and is just as beautiful. Not only is the art beautiful, but the mathematics and the elegant algorithms that generate it. This book can be read on quite a few levels, all very rewarding, and will inspire lots of future research and new gorgeous art.”

Doron Zeilberger Rutgers University

Winner of the Steele Prize

PolynomialRoot-Finding and Polynomiography

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Root-Finding and

Polynomiography

Bahman Kalantari

,!7IJ8B2-haafjj!ISBN-10 981-270-059-5ISBN-13 978-981-270-059-9

World Scientificwww.worldscientific.com6265 hc

6265_final.indd 1 10/9/08 12:15:55 PM

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