Promenade around Pascal triangle number motives

Cristian Cobeli, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

We survey classical results and recent developments, old and new problems, conjectures and ideas selected from the endless theme of iterated application of the fundamental rule of addition. The multitude of forms created by this spring, like the commandment "Let there be light" from the first day of creation, is emphasized by the role played by the prime numbers. The subject sounds harmoniously between poetry and astronomy or geometry, finding its origin in the East at Pingala (4-2nd century BC) and in the West at Apollonius of Perga (3rd century BC). Our work is divided in two parts: the present paper is mostly dedicated to playing with numbers, while the second one, which will follow in a companion paper, is based on geometrical motives.

Original languageEnglish (US)
Pages (from-to)73-98
Number of pages26
JournalBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Volume56
Issue number1
StatePublished - 2013

Keywords

  • Absolute differences
  • Collatz conjecture
  • Continued fractions
  • Ducci game
  • Fractals
  • Gilbreath conjecture
  • Greatest prime factor
  • Pascal triangle
  • Sierpinski gasket
  • Thwaites conjectures

ASJC Scopus subject areas

  • Mathematics(all)

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