Notes

Chapter 4: Systems Based on Numbers

Section 5: Mathematical Constants


Rational numbers

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

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

MultiplicativeOrder[b,FixedPoint[#/GCD[#,b]&,n]]

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).


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