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.

To leave a comment for the author, please follow the link and comment on their blog: Human Mathematics. offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , ,

Comments are closed.


Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)