I didn’t know this! From a recent XKCD comic:
This is correct! The value of epi - pi is 19.999099979 (plus a trailing infinite list of numbers). I strongly suspect this is just a coincidence — after all, why not pie - pi (19.317565) or pie - e (19.740875)? If you pick enough numbers, one of them is bound to come out near an integer coincidentally. Hoagland bases his whole "Face on Mars" nonsense on this numerology fallacy.
It’s funny how coincidences seem like more than they are. Our brains are wired for that sort of thing.
January 31st, 2007 at 1:50 pm
Um…I like the thoughts and I find interest in them…but….am I missing part of this….is ACM par tof the joke? Sorry….perhaps a rediculously unintelligent way to start a post link but, oh well. I gatz ta no
January 31st, 2007 at 1:51 pm
And to make the post even more simplistic, I made a spelling mistake. Sorry.
should be ‘part of the joke’.
regards,
M
January 31st, 2007 at 2:00 pm
This is just the first frame of the joke (: There are two more frames. Click the link (:
January 31st, 2007 at 2:02 pm
Left-handed smilies making brain hurt!
January 31st, 2007 at 2:25 pm
You may not have heard of the ‘Feynman point’ in PI- which has its own Wikipedia article:
http://en.wikipedia.org/wiki/Feynman_point
January 31st, 2007 at 2:26 pm
I just ran it thru Mathematica and here is the result to 100 figures:
19.99909997918947576726644298466904449606893684322510617247010181721652594440424378488893717172543215 …
Sometime in the 1970s, Martin Gardner presented a similar expression in an April issue of Scientific American – and the joke was that the result was an integer ( =x.99999999 ….). In those days it was difficult to find the solution to an arbitrary degree of precision. Actually the result of the expression diverged from a series of 9s after only a few digits.
I have to go find that article!
January 31st, 2007 at 2:42 pm
Hey, I’m 17, nearly 18, and I live near US 17, and there are approximately 17 donuts in a box of 17 donuts.
Coincidence?
I think not.
January 31st, 2007 at 2:43 pm
Yet another coincidence - I saw this just yesterday on Wikipedia under Gelfond’s constant. It’s even given the heading “Numerical coincidences”
January 31st, 2007 at 2:52 pm
This is a wierd coincidence: The Riemann Hypothesis predicts a regular pattern primes might display in their distribution,which turns out to correspond with quantum properties of atoms. If you compare a strip of zeros from Riemann’s critical line, they seem to correspond to energy levels predicted by quantum physicists in the nucleus of heavy atoms.
http://www.seedmagazine.com/news/2006/03/prime_numbers_get_hitched.php?utm_source=seedmag-main=rss&page=1
January 31st, 2007 at 2:56 pm
God, I am so stupid. This is why I am not a scientist. I have no idea what you guys are talking about. And I think life is better that way. lol
January 31st, 2007 at 2:57 pm
Some coincidences are even weirder, and maybe even hint at something going on underneath: try e^(pi * sqrt(163)), for instance. I’m not a number theorist, but apparently they can tell you why it turns out the way it does. (Kuwaiti Demon — is this expression what you were referring to?)
Also, there’s http://www.math.harvard.edu/~elkies/Misc/pi10.pdf.
January 31st, 2007 at 3:03 pm
Looks like the above link included the period at the end of my sentence. It should be http://www.math.harvard.edu/~elkies/Misc/pi10.pdf
January 31st, 2007 at 3:04 pm
Not purely mathematical, but astronomy related:
light-year / astronomical unit = 63239.67
mile / inch = 63360
Now you can visualize vastly different astronomical distances
Also, knowing this will save three keystrokes on your calculator and still allow greater precision:
mile / km = 1.609344
ln(5) = 1.609437912
January 31st, 2007 at 3:23 pm
I wondered where you were going with it and I like where you went.
Is there a numerical version of pareidolia, say pireidolia?
January 31st, 2007 at 4:30 pm
My favorite is this one
January 31st, 2007 at 4:37 pm
OK Phil & Co. Please spell it out so a business major like myself can understand…
What, exactly, is special about 19.999099979?
January 31st, 2007 at 4:44 pm
\!\(\[ExponentialE]\^π - \(1 + π\^2 + π\^4 +
π\^7 + π\^8 - π\^10 + π\^17\)\/π\^16\) = 20
(to 9 decimal places). Hope it comes out ok -
January 31st, 2007 at 4:45 pm
it didn’t so here it is
exp(pi) - (1 + pi^2+pi^2+pi^7+pi^8-pi^10+pi^17)/pi^16
January 31st, 2007 at 4:46 pm
and i made an error -
exp(pi) - (1 + pi^2+pi^4+pi^7+pi^8-pi^10+pi^17)/pi^16
January 31st, 2007 at 4:51 pm
Can you prove epi > pie? Is it a coincidence?
January 31st, 2007 at 4:52 pm
I meant. e^pi > pi^e.
January 31st, 2007 at 5:12 pm
Proof: This is why mathematicians do not succeed in comedy.
January 31st, 2007 at 5:26 pm
“Proof: This is why mathematicians do not succeed in comedy.”
TomPaine gets my vote for comment of the week
January 31st, 2007 at 6:32 pm
ACM = Association for Computing Machinery
e^pi > pi ^e - Just do the math! 23.14069… > 22.45915…
Now, that this near integer diverges as quickly as the 1/10,000s place is unimpressive
I work in an industry where we measure availability of ourt systems at the 1/1000000 place (that’d be .99999x - or 99.999x % available) and worry when that 6th digit isn’t also close to 9.
jbs
January 31st, 2007 at 6:46 pm
ourt? I don’t remember that T being there…. :0
Obviously, ourt = our.
January 31st, 2007 at 6:51 pm
Cruel jokes are the best!
January 31st, 2007 at 8:35 pm
John B. Sandlin: Aw, I preferred ourt systems. More exotic. Random ‘t’s from the Ourt. Or is that the definition of comets? Sorry, long day.
Being a mere BioBABlogee, I am impressed with the precision of your equipment. Here’s a bit of inanity this group may chuckle over.
I once worked with a small group of fellow biologists in a federal chemistry lab. One day the Lab Quality Assurance officer paid my boss (also a biologist) a visit to discuss data management issues and brought up the term “significant figures”. Without blinking, my boss replied, “Oh, ALL of our figures are significant.”
January 31st, 2007 at 9:43 pm
A fun almost integer involving pi, phi, and e is:
( 7 * pi ) / ( 5 * phi * e ) = 0.9999902974580796214743940244…
where phi is, of course, “the golden ratio.”
January 31st, 2007 at 11:13 pm
e^(pi*i)= -1. and it isn’t a coincidence. See http://www.math.utoronto.ca/mathnet/questionCorner/epii.html
February 1st, 2007 at 12:10 am
I don’t see anything special in the number derived except the digits all are 9s or 0s. Pi itself is much more interesting in the first 10 digits you get all 10 digits. Of course this is in the base 10 number system which only appeals to us because we have 10 fingers. In base 3 or hexadecimal or octal you’d get a different pattern. e and pi are sort of opposite sides of the same coin so the fact you get a non random pattern isn’t all that stunning to me. As for Hoagland maybe we should take up a collection so he can get some meds, I mean he’s either a flake or insane or some combination of the two! I can’t believe anyone actually pays to buy stuff he wrote! I’m surprised my little joke of the ‘face’ being a ‘butte’ hasn’t caught on. Of course I always thought the Great Lakes Huron and Erie were funny because one sounds like ‘hear’ and the other like ‘ear’.
February 1st, 2007 at 12:55 am
Some numerical coincidences are useful!
When I took geophysics, we would cancel out the pi that results from the earth’s orbit in various geophysical calculations by approximating a year as pi x 10^7 seconds. Obviously you don’t want the guys who do spacecraft trajectories using this trick, but it’s close enough for the order-of-magnitude type calculations that we did in undergrad planetary.
February 1st, 2007 at 2:13 am
My favorite is
e^(i * pi) + 1 = 0
Three basic arithmetic functions (+, *, ^), five fundamental constants (0, 1, pi, e, i [= imaginary unit, i^2 = -1]), one equation.
And it is not a coincidence.
Ah, Dr. Goulu already mentioned it.
February 1st, 2007 at 6:25 am
I (physics student) caught out a few of the Comp Sci majors with this today. Not really significant but funny to see them struggle with thier program.
Oh and TomPaine, check out Tom Lehrer before you say mathematicians aren’t funny. Especially “That’s mathematics” (and “Werner von Braun” for the Phil’s interest…).
February 1st, 2007 at 6:26 am
I was gonna make some pithy comment about those stupid emails that have you go through some silly math gymnastics and arrive at some result that sounds impressive or surprising. But then you all start throwing around imaginary numbers, natural logarithms, etc., makes my comment seem kinda sophomoric, so I’m gonna just keep my mouth shut…
February 1st, 2007 at 10:12 am
Pi itself is much more interesting in the first 10 digits you get all 10 digits. Of course this is in the base 10 number system which only appeals to us because we have 10 fingers.
Huh?
3.141592653…
Two 1’s, two 3’s, two 5’s, no 0’s, 7’s, or 8’s.
February 1st, 2007 at 11:13 am
It’s a coincidence.
Kind of like the coincidence that
10! (=10*9*8*…*3*2*1) is exactly equal to the number of seconds in 6 weeks.
Given that there are an infinite number of numbers, coincidences can always be found.
February 1st, 2007 at 11:42 am
Sweet Lord Christ, could someone please explain what the $%*k this means to those of us who don’t get it?
Maybe we should just accept that we’re out of our league and leave you Matharians to enjoy yourselves, but I feel I’m smart enough to play with you guys if you’ll help me understand.
Thanks
Rob
February 1st, 2007 at 11:47 am
I used to like math humor until my uncle was killed in a tragic long division accident.
February 1st, 2007 at 12:33 pm
Physics has interesting numerical coincidences which suggest that our standard measurements need tweaking:
The number of seconds in a tropical year is about 3.1557 x 10^7 seconds, remarkably close to pi x 10^7. If the second was just a little “longer”, then they would match, as long as the earth doesn’t slow down.
In SI units, the acceleration of gravity near the surface of the earth is very close to the SQRT(pi). Hmmmm…
Finally, we know where Ol’ McDonalds Farm is: on the Argand Plain [sic] about 0.6517 units from the origin (wherever THAT is), 38.22 degress east of south. Check out e^(i^(e^(i^0))). Oh, and the imaginary component of the farm has a magnitude close to (slightly larger than) the mass-energy of the electron in MeV. Ooooo…
February 1st, 2007 at 12:35 pm
Correction:
In Si units, the acceleration of gravity near the surface of the earth is very close to pi^2. Hmmmm. [I SQRT’d the wrong thing…that can be dangerous]
February 1st, 2007 at 1:39 pm
Phil is commenting on the fact that the result is near 20, but that’s not the end of joke. Read the rest of the comic!
February 2nd, 2007 at 2:51 am
Phill you B*$*£”% 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)
February 11th, 2007 at 12:22 pm
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.
February 13th, 2007 at 2:09 pm
e[sup]pi>pi[sup]e
September 11th, 2007 at 9:24 pm
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.)
December 17th, 2007 at 9:03 am
e=the tangent line of f(x)=e^x where x=0
October 24th, 2008 at 12:31 pm
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).