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Search for your name in pi

dr-mikes-maths.com

42 pointstokenadult20 comments

Because the number "10" keeps appearing in the denominator, we say this is pi in "base 10". It is also why we have 10 different digits.

I thought we have 10 digits so we can count our fingers.

Also, every number system is base "10" in its own system :-)

That's profound.

I believe there is a tribe in South America that uses an octal system because instead of their fingers to count they use the indents between their knuckles.

This is indeed the coolest thing:

The first English word in pi is... wait for it... PI, coming in at position 18. Now isn't that cute?

That argues for using base 27 better than the article does.

This is one of those silly things that you just can't stop playing with.

  * "allah" isn't there but "jesus" is found twice!
  * "hate occurs more than "love"

Just as I was really excited about the mystical possibilities here, I came across this party pooper: http://math.stackexchange.com/questions/20566/prove-there-ar...

To accompany this, a link to a wonderful article about π by one of the leading researchers on the number π, an article I share with my students each year on π day.

http://www.nieuwarchief.nl/serie5/deel01/sep2000/pdf/borwein...

I am now going to lock myself in the bathroom until I can prove that pi + e is irrational. I mean, how hard can it be?

I think you win the nerd award for 2011.

Very, very, very hard.

You almost certainly know that already, so here are a couple more remarks just for fun:

One useful technique when making pseudorandom number generators is to take two not-so-good RNGs and combine their outputs (e.g., adding them or XORing them). If the two RNGs have different enough "structure", the combined generator can have much better statistical properties than either of its two components. The fact that it's much harder to prove anything about pi+e than about pi or e individually is rather like that.

But even proving that pi is irrational is highly nontrivial. (Proving that e is irrational, on the other hand, is a fairly easy exercise. Sketch: suppose e = p/q; then q!e is an integer; but q!e is the sum of a series whose terms are initially integers and then abruptly positive numbers small enough that their sum has to be between 0 and 1; contradiction.)

How awesome would it be if pi + e were found to be rational? Maybe everything starts cancelling out past the zillionth digit...

  > Your chances:
  >   3 or fewer letters: about 100% 
  >   7 or more letters: about 0%.

While this might be true for the set he's calculated, doesn't an infinite sequence of non-repeating digits suggest the likelihood of every sequence approaches one as the number of digits are calculated approaches infinity?

Yes.

No! Consider this number:

0.101001000100001..... (continue the obvious pattern)

This number is irrational but there is an obvious pattern to the digits. The pattern is not random. It's an open question on whether or not the digits of pi are randomly distributed. If so then what you write is correct.

Doesn't the difference between just being irrational (e.g., sqrt(2)) and being transcendental (e.g., \pi, e) matter here?

The claim I responded to had to do with the randomness of the digits of a number. The person appeared to have the belief that irrational numbers have to have random digits. This isn't true. This isn't true for transcendental numbers either. The number I gave is transcendental but doesn't have random digits.

I immediately thought that same thing. Someone else posted this link (http://math.stackexchange.com/questions/20566/prove-there-ar...) which answers the question: if Pi is a "normal number" -- a number whose expansion in base b asymptotically contains each digit 0, 1, ..., b-1 with equal frequency, for any give b -- then within that numbers expansion (in any base) you'll find every finite string composed of those digits infinitely many times. So normal numbers will not only contain any person's name, but every book ever written, every law of nature, etc.

Wikipedia says that Pi is widely believed to be normal, but that it's not been proved. It's interesting that almost every real number has this normality property (in the sense that the set of real numbers that are not normal has Lebesgue measure zero), as it sounds like a very restrictive criteria.

That site has 30 million (base 27) digits of Pi. I used a dump of the first 5 trillion digits, and am now submitting prior art to all software patent trolls.

This is, of course, bizarrely arbitrary, since its assuming there's any underlying meaning to the ordering of the English alphabet (since, ya know, there isn't).

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