SAS HONORS SEMINARFALL SEMESTER 2011

Polynomials are Too Beautiful to be Limited to Math(The Fine Art and Science of Polynomiography)

You Don’t Have to be a Mathematician to do Polynomiography

POLYNOMIOGRAPHY

Bahman KalantariProfessor of Computer Science, Rutgers University

Email: kalantari@cs.rutgers.edu, Web: www.polynomiography.com

Course Number: 01:090:265Meeting day & time: TH 03:20-06:20 PM

Location: ARC (Allison Road Classroom Building), Rm 118 - BUSCH CampusCredit: 3

Join Dr Bahman Kalantari as he explains and helps you explore his creation, Polynomiog-raphy. Dr Kalantari welcomes artists and students from all fields. Through Dr Kalantari’sunique software, students will be introduced to a fantastic and very powerful medium, easy touse, where polynomials turn into objects that can be used to create artwork of diverse types,invent games,and discover many new concepts and creative ideas. Working with Polynomiog-raphy software is similar to learning to work with a sophisticated camera: one needs to learnthe basics, the rest is up to the photographer.

Course Description

1

This seminar will introduce students to a novel and interdisciplinary field, called Poly-nomiography, the fine art and science of visualizing a polynomial equation through computer-generated images rendered via a corresponding software to be made available to students.

Polynomials are the most fundamental entities in all of math and sciences and Polynomiogra-phy is a significant medium that can teach many mathematical properties, even beyond conceptscovered in typical math or science courses. However, the goal of this particular course is not toteach mathematics or algorithms. While working with the software, students will discover thebasics of the underlying mathematical and algorithmic foundation of polynomiography aimedat solving a polynomial equation, a task present in every branch of science and mathematics.However, through polynomiography and its software students will learn to create art and designby turning the polynomial root-finding problem upside down. That is, through the ease of soft-ware students will be able to experiment with polynomials and root-finding algorithms as thebasis for creating intricate designs and patterns, even animations. Not only polynomiographyand individual student’s creativity could result in art and design analogous to the most sophis-ticated human creations, but artwork of a degree of complexity and sophistication not possiblewithout the use of polynomiography and its software. Polynomiography allows virtual paintingusing the computer screen as its canvas. It could also inspire new artistic styles and actualpaintings, originated directly from polynomiography software, or indirectly from its concepts.

The seminar introduces the students to a range of possible course projects to be carriedout either individually or in small groups. Sample projects consist of: Creating quality andnovel 2D or 3D artwork using polynomiography software, e.g. as prints or video productions.Novel visualization or animations, as art or as means in conveying a mathematical propertyor concept. Comparison of polynomiographic images and traditional human art and design,e.g. discovering parallels between classes of polynomiographs and artworks of known artists, orcomparison with particular styles of painting. Using polynomiography to produce interestingdesigns or paintings. Using polynomiography to make a noteworthy mathematical conjecture,possibly even its proof. Exploring potentials in cryptography and encryption of numbers, as art,as math, or otherwise. Discovering novel and useful applications of polynomiography at anylevel of K-16 education, discovering or designing games based on polynomiography. Exploringthe usage of polynomiography in science. In additional to the above, students may proposetheir own creative projects.

GRADING and PREREQUISITES: Grading will be based on classroom participation (20%), oral presentation of their project (20 %), followed at the end by a hand-written versionof the presentation (10 - 15 pages), as well as supplementary images, artworks, animations, oronline links (60 %). By mid-semester students must be able to make a short presentation onthe goals of their project and at the end of the course a longer presentation about the projectand the findings. Prerequisite for the course are algebra, calculus, interest to explore, or theconsent of the instructor.

Actual student projects demonstrate diversity and richness in the use of Polynomiography:• Ecology and Polynomiography: Nature and Technology• Bridging the Brains Hemisphere through Polynomiography.• Simulating Neuroscience Through Visualization with Polynomiography• The Transformation of the Julia Set in Polynomial Root-Finding• Making Math Fun: Potential Uses for Polynomiography in Special Education• Calculating Bach by Appreciating Polynomiography

2

• Art Inspired by Math?! Are You Kidding Me?• Integrating Polynomiography into the World of Games• Polynomiography: Shedding Light on Complementarism• An Experimental Fusion of Music and Polynomiography• Polynomiography and Electric Fields• God, Christ, and Mathematics: Exploring Genesis and the New Testament through Poly-

nomiography

RECOMMENDED TEXTBOOK “Polynomial Root-Finding and Polynomiography,” WorldScientific, Hackensack, NJ, 2008, Bahman Kalantari .

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

Doron Zeilberger Rutgers University, Winner of the Steele Prize

Polynomiography is a fascinating meeting of polynomials, iterative systems, and artistry -a great way to explore the marriage of visual and intellectual beauty.

Ken Perlin New York University, Winner of the Oscar Prize

This book truly is a textbook... This is because the author always has the reader in mind, andcarefully explains what is going on... Although the book is not explicitly addressed to high schoolteachers or undergraduate students, many chapters are suitable for this readership. Researchersin this topic might enjoy finding the long lists of references and the many historical remarks,both giving ample suggestions for further readings.

Mathematical Reviews

BAHMAN KALANTARI is a professor of computer science and the inventor of the U.S.patented technology of Polynomiography. His research interests lie in theory, algorithms,and applications in a wide range of topics that include mathematical programming; discreteand combinatorial optimization; polynomial root-finding and approximation theory; and Poly-nomiography and its applications in art and eduction. Kalantari’s Polynomiography has re-ceived national and international media recognition that include the Star-Ledger, New JerseySavvy Living Magazine, Science News, DISCOVER Magazine, Tiede (popular science magazineof Finland), Muy Interesante (popular science magazine of Spain) and more. His artworks havebeen exhibited in such venues as a traveling art-math exhibition in France, SIGGRAPH ArtGallery in LA, as well as at Rutgers and around New Jersey. His artworks have also appearedon the cover of publications such as Computer Graphics Quarterly, Princeton University Press,art-math conference proceedings, and in science magazines. He has delivered numerous lec-tures on Polynomiography and to various audiences, including invited presentations in France,Germany, Austria, Italy, Japan, Belgium, as well as in middle and high schools in New Jersey,and K-12 teacher conferences. He hopes to internationalize Polynomiography as a medium forart, math, science, and education, and at many different levels. He is the author of, “Poly-nomial Root-Finding and Polynomiography.” For more information on Polynomiography visitwww.polynomiography.com

3