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p. 525. Numbers that countlocked

  • Peter M. Higgins


‘Numbers that count examines numbers that arise of their own accord in counting problems. Arithmetic and geometric series rely on a common difference and common ratio between terms respectively. Triangular numbers arise from summing all the terms from 1 to n. However, if one multiplies instead of adding, the resulting number is a factorial. Binomial coefficients can be found using either the binomial expression or the Arithmetic Triangle. Fibonacci numbers follow the Golden Ratio, and can be seen throughout nature. Partition and Stirling numbers are used to partition objects into blocks, and hailstone numbers rise and fall erratically before ultimately falling to 1.

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