Chapter 4: Systems Based on Numbers

Section 5: Mathematical Constants

Rational numbers

The pictures below show the base 2 digit sequences of numbers m/n for successive m.

The digits of 1/n in base b repeat with period


which is equal to MultiplicativeOrder[b, n] for prime n, and is at most n-1. Each repeating block of digits typically seems quite random, and has properties such as all possible subblocks of digits up to a certain length appearing (see page 1084).

Rational numbers image 1

Image Source Notebooks:

From Stephen Wolfram: A New Kind of Science [citation]