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Visible Structures in Number Theory

Peter Borwein Loki Jörgenson
Centre for Experimental
& Constructive Mathematics
Department of Mathematics & Statistics

Simon Fraser University, Burnaby, B.C. CANADA V5L 2T7

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

Number theorists have been interested in the characteristics of numerical constants like $\pi, e$ and $\log{(2)}$ for centuries. These numbers, real irrationals, are composed of an unending string of digits in a specific but seemingly random order. As statistical methods and traditional analysis have revealed very little, it has been proposed that the natural visual capacities of human perception be employed to search for complex correlations in the numerical distributions.

Keywords irrationality, continued fractions, zero/one polynomi als, visualization