Here’s the distribution of the first million digits of the…

June 20, 2010

(This article was first published on Human Mathematics, and kindly contributed to R-bloggers)

Here’s the distribution of the first million digits of the square root of two’s decimal expansion.

Number of digits | is:
  0's |  99 818
  1's |  98 926
  2's | 100 442
  3's | 100 191
  4's | 100 031
  5's | 100 059
  6's |  99 885
  7's | 100 012
  8's | 100 347
  9's | 100 126

If each digit had a Bernoulli chance of coming up (like a 10-sided die), you’d expect to see 10 000 ± 30 times.  And going on with that same assumption, the chance of the least-frequent digit coming up less than 99 000 times would be something like one percent.

What does it mean?  I will meditate on this and expand √2 in different bases besides 10.

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