Talk:Pi (mathematical constant)

[Image:http://commons.wikimedia.org/wiki/Image:Pi-symbol.svg]

what's the policy on using wikimedia images/media?

--Chief Mike 04:24, 25 January 2007 (CST)

Algebraically independent?

It says "lthough π itself is transcendental, it is an open problem whether many other transcendental numbers are algebraically independent from π. " in "Relation to other constants". If this means that it's not known whether there exist many transcendental numbers which are algebraically independent from π, then it sounds wrong to me. Maybe it means that for many other known transcendental numbers, it is an open problem whether those numbers are algebraically independent from π. If so, it should be reworded to clarify. --Catherine Woodgold 17:32, 2 May 2007 (CDT)

It can't be the first, by a simple countability argument. Greg Woodhouse 17:35, 2 May 2007 (CDT)

That's what I thought. Thanks for rewording it. --Catherine Woodgold 20:27, 2 May 2007 (CDT)

zeta(n) for n odd

It's remarked in the current version that it "may seem probable" that zeta(n) is a rational multiple of pi^n when n>1 is odd; I don't feel this is correct.

First off "may" should be "might". But more importantly, if zeta(3) were a rational multiple of pi^3 for example, then presumably the rational multiple wouldn't involve a ridiculously large numerator and denominator. I just did a quick computation (by computer) that verified, however, that zeta(3)/pi^3 doesn't equal any rational number whose numerator or denominator has less than 500 digits. I'm sure this sort of computation has been done before and to more precision. So I doubt many number theorists believe zeta(n)/pi^n is rational for n odd. - Greg Martin 02:02, 3 May 2007 (CDT)

Indeed, that's why many number theorists believe; the point is that it might come as a surprise given the pattern of the even-indexed zeta numbers. Anyway, I'd rather see this section deleted (if not the entire article). Fredrik Johansson 02:27, 3 May 2007 (CDT)

Possibly "might have seemed probable" but that makes it sound as if we're sure it isn't. I like this article but maybe it goes on just a little too long about calculation records. --Catherine Woodgold 07:31, 3 May 2007 (CDT)

Misnamed section?

Areas of mathematics where $\pi$ appears This section right now looks like a nearly complete list of areas of math where pi doesn't appear. Anthony Argyriou 15:38, 22 May 2007 (CDT)

Indeed! Greg Woodhouse 17:35, 22 May 2007 (CDT)

More digits!

I think an ambitious general reference work should have more than 50 digits of pi (somewhere--maybe a subpage). Or am I full of it? --Larry Sanger 12:45, 28 July 2007 (CDT)

Perhaps. I wouldn't give really high priority to that. As the beginning of a program for future development of this and related articles, here's Wikipedia's "List of topics related to π":

(begin list)

• Arithmetic-geometric mean
• Bailey-Borwein-Plouffe formula
• Basel problem
• Borwein's algorithm
• Borwein's algorithm (others)
• Buffon's needle
• Cadaeic Cadenza
• Circle
• Computing π
• Euler's identity
• Feynman point
• Gauss-Legendre algorithm
• Gaussian function
• History of π
  • History of numerical approximations of π
  • Chronology of computation of π
• Indiana Pi Bill
• Lindemann-Weierstrass theorem
• List of circle topics
• List of formulae involving π
• Mathematical constant (sorted by continued fraction representation)
• Rhind Mathematical Papyrus
• π
• Pi (letter)
• Pi approximation
• Pi Day
• PiFast
• PiHex
• Pimania (computer game)
• Piphilology
• Proof of Leibniz formula
• Proof that π is transcendental
• Proof that 22 over 7 exceeds π
• Milü
• Proof of Viète formula
• Proof of Wallis product
• Radian
• Salamin-Brent algorithm
• Software for calculating π
• Squaring the circle

See also

• List of formulae involving π

(end list)

Pi definition

Shouldn't the definition of Pi make some mention of "the ratio of a circles' circumference to radius or diagonal"? David E. Volk 16:02, 16 May 2008 (CDT)