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Visible Structures in Number Theory

by Peter Borwein and Loki Jörgenson

Year of Award: 2002

Publication Information: The American Mathematical Monthly, vol. 108, no. 5, 2002, pp. 897-910

Summary: Computer graphics offers magnitudes of improvement in resolution and speed over hand-drawn images and provides increased utility through color, animation, image processing, and user interactivity, and to some degree, mathematics has evolved to exploit these new tools and techniques. This paper explores some subtle uses of interactive graphical tools that help us "see" the mathematics more clearly. In particular, it focuses on cases where the right picture suggests the "right theorem", indicates structure where none was expected, or reveals the possibility of "visual proof".

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About the Authors: (from The American Mathematical Monthly,Vol. 108 No. 5, (2001))

Peter Borwein is a Professor of Mathematics at Simon Fraser University, Vancouver, British Columbia. His Ph.D. is from the University of British Columbia under the supervision of David Boyd. After a postdoctoral year in Oxford and a dozen years at Dalhousie University in Halifax, Nova Scotia, he took up his current position. He has authored five books and over a hundred research articles. His research interests span diophantine and computational number theory, classical analysis, and symbolic computation. He is co-recipient of the Chauvenet Prize and the Hasse Prize, both for exposition in mathematics

Loki Jörgenson is an Adjunct Professor of Mathematics at Simon Fraser University, Vancouver, British Columbia. Previously the Research Manager for the Centre for Experimental and Constructive Mathematics, he is a senior scientist at Jaalam Research. He maintains his involvement in mathematics as the digital editor for the Canadian Mathematical Society. His Ph.D. is in computational physics from McGill University, and he has been active in visualization, simulation, and computation for over 15 years. His research has included forays into philosophy, graphics, educational technologies, high performance computing, statistical mechanics, high energy physics, logic, and number theory.


Subject classification(s): Number Theory
Publication Date: 
Tuesday, September 23, 2008