Searching $latex \pi$

Take a look at the Pi Search Page. You can type in a bunch of digits and it tries to find them somewhere in the first 3.2 billion digits of the decimal expansion of \pi.

\pi, of course, is the ratio of any circle’s circumference to its diameter, and is approximately equal to

\pi \approx 3.14159265358979323846264\dots

The digits never repeat since \pi is irrational. Try searching for your 7-digit phone number. Surprised that it was found? Even more surprised that I was so sure your phone number would be found?

Well, let’s think about it for a minute. Assuming the digits of \pi are essentially random, the chance of a particular digit having a particular value is 1 in 10; in other words, the probability of a particular digit having a particular value is 1/10. So the probability that 7 digits in a row will all have certain values (such as your phone number) is (1/10)^7, or one chance in ten million. This might sound like a very small chance, but remember, we are talking about 3.2 billion digits in which to search. So in fact, we would expect that your phone number occurs about 3.2 \times 10^9 / 10^7 = 320 times in the first 3.2 billion digits of \pi! This also means that you have a good chance of finding any eight-digit sequence of numbers, and a fairly good chance of finding any nine-digit sequence of numbers, but your chances of finding any particular sequence of ten or more digits are not so good. Try it and see!


About Brent

Assistant Professor of Computer Science at Hendrix College. Functional programmer, mathematician, teacher, pianist, follower of Jesus.
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