Comments on: epi - pi http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/ I am an astronomer, writer, and skeptic. I likes reality the way it is, and I aims to keep it that way. My real name is Phil Plait, and I run the Bad Astronomy blog. Sun, 05 Jul 2009 05:51:25 +0000 http://wordpress.org/?v=2.3.1 By: Steven http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-159806 Steven Tue, 03 Mar 2009 08:07:09 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-159806 http://mathworld.wolfram.com/AlmostInteger.html http://mathworld.wolfram.com/AlmostInteger.html

]]> By: Action Lyrics http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-157201 Action Lyrics Wed, 18 Feb 2009 05:43:36 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-157201 I agree with you, I think it's just a coincidence. There are plenty of them if u look for them. Eg sqrt(10) approx = 22/7 approx = pi. Even though none of those are integers. I agree with you, I think it’s just a coincidence.

There are plenty of them if u look for them.

Eg sqrt(10) approx = 22/7 approx = pi.

Even though none of those are integers.

]]> By: Patrick http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-128134 Patrick Fri, 24 Oct 2008 18:31:50 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-128134 The most explicit definition of e is e = 1 + 1/1! + 1/2! + 1/3! + ... This is a rapidly converging sum (remember n! = n times (n-1) times ... times 1). The most explicit definition of e is e = 1 + 1/1! + 1/2! + 1/3! + …

This is a rapidly converging sum (remember n! = n times (n-1) times … times 1).

]]> By: Sephiroth http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28889 Sephiroth Mon, 17 Dec 2007 16:03:25 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28889 e=the tangent line of f(x)=e^x where x=0 e=the tangent line of f(x)=e^x where x=0

]]> By: Some other guy http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28888 Some other guy Wed, 12 Sep 2007 03:24:34 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28888 Does anyone know the official definition of "e"? I know one fact, that if you tetrate (see http://en.wikipedia.org/wiki/Tetration) e-rt(e) (The base-e root of e) to infinity, the result is e, but if you tetrate anything higher than that to infinity, be it just 10^-1000000000 higher, it goes to infinity. (Well, I actually found this out from experimentation.) Does anyone know the official definition of “e”?

I know one fact, that if you tetrate (see http://en.wikipedia.org/wiki/Tetration) e-rt(e) (The base-e root of e) to infinity, the result is e, but if you tetrate anything higher than that to infinity, be it just 10^-1000000000 higher, it goes to infinity. (Well, I actually found this out from experimentation.)

]]> By: Brian http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28887 Brian Tue, 13 Feb 2007 22:09:53 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28887 e[sup]pi>pi[sup]e e[sup]pi>pi[sup]e

]]> By: Brian http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28886 Brian Sun, 11 Feb 2007 20:22:09 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28886 Thanx all for some very interesting posts. In response to Samuel's hint of a deeper reason that e^pi > pi^e, let f(x) = ln(x)/x. Then f'(x)=(1-ln(x))/(x^2). f'(x)=0 if and only if x=e, which yields a maximum at x=e for all positive values of x. So if A>0 and A not equal to e, f(e)>f(A) ln(e)/e>ln(A)/A Aln(e)>eln(A) ln(e^A)>ln(A^e) e^A>A^e e^pi>pi^e is a special case. Thanx all for some very interesting posts. In response to Samuel’s hint of a deeper reason that e^pi > pi^e, let f(x) = ln(x)/x. Then f’(x)=(1-ln(x))/(x^2).
f’(x)=0 if and only if x=e, which yields a maximum at x=e for all positive values of x. So if A>0 and A not equal to e, f(e)>f(A)
ln(e)/e>ln(A)/A
Aln(e)>eln(A)
ln(e^A)>ln(A^e)
e^A>A^e
e^pi>pi^e is a special case.

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