Talk:Pi
The article says:
It was shown that the existence of the above mentioned Bailey-Borwein-Plouffe formula and similar formulas imply that the normality in base 2 of ð and various other constants can be reduced to a plausible conjecture of chaos theory.
What is the conjecture? Who showed this reduction? Can you give a reference for the papers involved? Or their websites? Even a few keywords suitable for web searching would be very much appreciated!
I see you've added "Bailey and Crandal in 2000". That's great. It would be good to add a link to their paper (or it's abstract) if it exists somewhere on the web. I've tried searching for it, and haven't had any luck.
But the article does give an URL, and you can find the paper there, in both PDF and PostScript. (The PDF is very badly done, however.) --Zundark, 2001-08-21
You're right. My mistake. I'd missed the URL in the earlier section.
Of particular interest to me is this: if we live in a non Euclidian universe, does that alter the value of pi? Is it possible that a non euclidian universe would render pi a distance dependedt function? Just musing, really.
I define Pi as a function of the distance metric in a metric space: Pi equals half the arc length of the curve created by the locus of points of distance 1 from a given point. In a hexagonal world such as that used in many turn-based video games, Pi == 3. In a geometry with distance metric d((x1, y1), (x2, y2)) == (abs(x2 - x1) + abs(y2 - y1)) such as city blocks, Pi == 4. Of course, the familiar Euclidean distance metric provides a value of Pi just a bit more than 355/113, and nearly all digital signal processing takes place in Euclidean geometry.
In geometries that don't preserve lengths of translated lines (such as the geometry of curved spacetime), "distance 1" is meaningless, and Pi depends on the location and the radius.
That is not the standard definition however: Pi is a well defined real number, and it has nothing to do with geometry. It is always 3.14.. no matter what. Mathematical constants don't depend on physical contingencies. If our world is not Euclidean, then there will be some circles of diameter one whose circumference is different from Pi. --AxelBoldt
I deleted the image at http://www.nersc.gov/~dhbailey/dhb-form.gif from the article. It might be OK to swipe the image and put it on the Wikipedia server, but it's not OK to link to the image itself on the government server. We don't own their bandwidth... --LMS