today's cool mathematics fact

[aryanhwy]

I just found out that you can represent pi as a continued fraction with 4 in the numerator and then the denominator constructed out of odd numbers and increasing, successive squares. See http://www.petrospec-technologies.com/Herkommer/contfrac.htm, and look for "a continued fraction representation for pi".

It's things like this that really make me marvel. On the one hand, it's amazing that such a nice, simple structure can be given to an otherwise seemingly random infinite number. On the other hand, this nice, simple structure can be used to model things in the real world (or at least, if we could draw perfect circles in the real world, it could be). The more higher mathematics I learn (I suppose most of the results all fall into the area of analysis, but I'm not sure), the more amazing it is that there is actually a connection between mathematical structures and the real world. There are all of these numbers, with all of these fascinating relationships and interrelationships, and yet somehow or other doing things with these numbers can actually lead to something being done in reality. How on earth did the world turn out to match up so well with mathematics? It's simply marvelous and awesome, in both the original and modern senses of the words.

Comments

[jpgsawyer.livejournal.com]

I think you just proved I am more of an engineer than mathematician. Whilst I can appreciate the beauty of this I just can't quite grasp any way to use it.

Still its good to know you do and perhaps one day this engineer will benefit from the mathematics it creates. :-D

[sharikkamur.livejournal.com]

I can't see how to use it either, but I do appreciate its elegance and simplicity. Chalk another one up for the engineer team. :)

[aryanhwy.livejournal.com]

I don't really know any way to use it either, I just think it's amazing that in principle it can be used. In fact, Joel knows some way to use it, because he was the one who found the website in the first place, and he found it while looking up information about rational approximations of pi for use in scaling graphics.

[pedropadrao.livejournal.com]

It never fails to amaze me, either. I'm in agreement with Einstein, I believe, who once quipped that he was lucky to understand any of it.

[smlibrarian.livejournal.com]

Thank you for making me realize that Liberal Arts and not Math or Sciences are indeed my true calling!! *grin*

[ursula]

Since when is math not a liberal art? :P

[jpgsawyer.livejournal.com]

Yep! See the comments from us Engineers above.

[smlibrarian.livejournal.com]

OK...I'll rephrase that...I'm REALLY glad to be a librarian...and an English geek. :) Long Live Jane Austen! Hehehe

[aryanhwy.livejournal.com]

I'll definitely second that comment about Jane Austen -- I remember absolutely dreading having to read Pride and Prejudice in my first semester freshman year English course, and then I did read it and loved it and read everything else, and last winter I checked out all her books from the university library here (they don't have much in terms of fiction in English, but they had the complete works of Jane Austen!) and re-read them all. Such fun!

[smlibrarian.livejournal.com]

Yes indeed! There's a newish movie out right now on her life - Becoming Jane. I was very entertained. :)

[thebronwen.livejournal.com]

Ummmm...

I make pretty stuff?

And I have one really smart daughter!!! :)

Annabelle says Hi. (Purple toothless thing)