March 14, 2005

Happy Pi (π) Day!

Today, we celebrate that rascally, irrational mathematical constant, Pi. It primarily describes the relationship between the circumference of a circle and its diameter, but Pi also surfaces in various other regions of mathematics -- in ways that seem magical!

What do you do on Pi Day to celebrate? Well, the ball drops at 1:59 (AM or PM is up to you). For games, you might try searching for your name or some other meaningful text in the first 4 billion binary digits! It can be like a magic eight-ball! If you're feeling more contemplative, you can gaze upon the digits for a while. And if you're hungry... well... you know.


Posted March 14, 2005 12:50 PM

So what name do you think has the smallest index? Brian is at 3102736908. Dave, you've got me beat at 2633269076. The interesting thing is that "slacker" can't be found!

search string = "slacker"
35-bit binary equivalent = 10011011000000100011010110010110010

string does not occur in first 4 billion binary digits of pi

Oh well!

Posted by: Anonymous at March 14, 2005 1:58 PM

Amazing. Who knew there was such a day. We should all be so lucky as to celebrate such a day. Now, if you're ready for something really interesting, how about helping me solve Goldbach's conjecture? 'Every even integer greater than 2 can be written as the sum of two primes'. I've already gone through Lagrange's theorem, that every non-negative integer can be written as the sum of four cubes (0 counts as one of the possible cubes).

7 = 2^2 + 1^2 +1^2 + 1^2

27 = 4^2 + 3^2 + 1^2 + 1^2


The proof is slick.

So, about that Goldbach conjecture...

Posted by: Jesse at March 15, 2005 7:04 PM

Jesse, proving Goldbach's conjecture is a piece of cake! You just start from the definitions, yadda yadda yadda, ... I forget exactly how I did it, and somehow lost the notebook I wrote it in. Why all the excitement? Does it have any important implications?

Posted by: Dave Lemen at March 16, 2005 10:29 AM


Since when does a problem need important implications? Actually, I don't think it does. Although I believe if the RH is proved, Goldbach's conjecture is almost proved by default.
Seriously though, I never thought I'd get excited about number theory. I mean, the definitions aren't very abstract, it's all very blue collar, as far as mathematics goes. But I'll be damned if they aren't the hardest problems in the world to solve. That's what makes them so exciting. My grandmother could understand the problem (as opposed to any problem you could state in any other branch of mathematics), she'd probably even realize how intuitively true the problems were. But solve them? It's been hundreds of years for many of these problems and it may be several hundred more.

So you lost the notebook with the proof huh?

Posted by: Jesse at March 17, 2005 1:12 PM

Yes, number theory is very interesting to me too, but perhaps because I can't understand any of the other stuff. You could say I'm much like your grandmother that way. Yeah. Go ahead. Say it. SAY IT!!!

Speaking of the notebook... Wouldn't you like to get your hands on Riemann's housekeeper?

Posted by: Dave Lemen at March 17, 2005 2:19 PM