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. Sat, 10 Jan 2009 02:22:18 +0000 http://wordpress.org/?v=2.3.1 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.

]]> By: Steve http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28885 Steve Fri, 02 Feb 2007 10:51:57 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28885 Phill you B*$*£"% Hadn't been aware of that webcomic before, thanks for giving me another way to waste time at work (as if i didn't have enough already) :) Phill you B*$*£”% Hadn’t been aware of that webcomic before, thanks for giving me another way to waste time at work (as if i didn’t have enough already) :)

]]> By: Patrick http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28884 Patrick Thu, 01 Feb 2007 21:39:23 +0000 http://blogs.discovermagazine.com/badastronomy/2007/01/31/epi-pi/#comment-28884 Phil is commenting on the fact that the result is near 20, but that's not the end of joke. Read the rest of the comic! Phil is commenting on the fact that the result is near 20, but that’s not the end of joke. Read the rest of the comic!

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