Visible Structures in Number Theory

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

  ABSTRACT 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

• Introduction
• In Pursuit of Patterns
• In Support of Proof
• The Structure of Numbers
  • Binary Expansions
  • Sequences of Polynomials
  • Quasi-Rationals
  • Complex Zeros
• Conclusion
  • Acknowledgements
• References
• About this document ...