A simple question today:
Which do you prefer, e or π?
They're both irrational, they're both "about three," and of course they're related by Euler's formula, but they're very different. One is the ratio of the circumference of a circle to its diameter, the other is the base for the exponential function.
You can only pick one: which one is it?
I think I'll go with e. Nothing against π, but I've spent a lot of time working with differential equations, and you just have to love a function that is its own derivative.
And nobody has ever been dorky enough to attempt to show off by memorizing the first hundred digits of e.
What's your favorite irrational constant?
Comments
# 1 | Index Guy | August 13, 2007 10:19 AM
I own shirts with decimal expansions of both pi and e. Pi will be my choice, since it appears in some of the most important equations in physics.
# 2 | Brian | August 13, 2007 10:36 AM
Pi is my vote, since it has a nerdy symbol :)
# 3 | John Novak | August 13, 2007 11:02 AM
The Deathstar.
# 4 | Johan Larson | August 13, 2007 11:25 AM
e. Pi is for the middlebrows.
# 5 | Melissa | August 13, 2007 11:28 AM
My family.
# 6 | marciepooh | August 13, 2007 11:32 AM
I'll pick e. Snail shells are pretty.
Index Guy - I can go you one better I have a t-shirt with the Periodic Table and chairs (the lanthanide and actinide families have to sit separately).
# 7 | Guru | August 13, 2007 11:36 AM
Pi
# 8 | dr. dave | August 13, 2007 11:39 AM
π for sure, for two reasons...
1) the awesome film of the same name
2) all the secret messages from God encoded inside!!
# 9 | TomS | August 13, 2007 11:51 AM
e
But there are some other famous numbers, deserving of votes - φ, the Golden Ratio, is the first that comes to mind.
# 10 | Pam | August 13, 2007 12:16 PM
Pi, because it is homonymous with a delicious dessert.
# 11 | Andrew | August 13, 2007 12:22 PM
e is much more fun to shout.
# 12 | Manny | August 13, 2007 12:41 PM
Colin Adams and Tom Garrity, two math profs from Williams College, debate this issue in a very entertaining video available from the Mathematical Association of America.
# 13 | jk | August 13, 2007 12:41 PM
They aint got nothin' on i.
# 14 | KeithB | August 13, 2007 12:47 PM
e.
Because it is easy to memorize to 10 sig. figures.
# 15 | Dennis | August 13, 2007 1:15 PM
E vs. Pi deathmatch:
http://www.everything2.com/index.pl?node_id=1284084
# 16 | Aditya | August 13, 2007 1:43 PM
e, as it has made life with complex numbers so easy!
# 17 | Torbjörn Larsson, OM | August 13, 2007 2:36 PM
I dunno. Both are natural in DE's, but pi is more often a constant. So, pi I guess.
(The derivative invariance is nice, but modulo signs sin/cos are their own 2nd derivatives so you get stationarity again and pi pops up there.)
# 18 | Paul | August 13, 2007 3:09 PM
I prefer e. There's a certain arbitrariness about Pi ... for instance, arctan 1 is not Pi, but rather Pi/4, and the ratio of the circumference of a circle to its radius is not Pi, but 2 Pi. No such problems with e. But Pi is a fine constant too.
# 19 | cisko | August 13, 2007 3:18 PM
e. Not sure why, though it's probably because I was continually surprised by all the different places where it cropped up.
If we were permitted to expand the field, I'd vote for ℵ1. Everybody groks ℵ0, but understanding the difference between the two -- and the proof of the difference -- was by far my favorite "a-ha" moment of school.
# 20 | Sean | August 13, 2007 3:20 PM
What, no phi love here?
# 21 | Thony C. | August 13, 2007 3:26 PM
eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee...
# 22 | m | August 13, 2007 3:30 PM
Given that I loathe, hate and despise logarithms...I'm definitely going to have to say 'pi'.
# 23 | Doug | August 13, 2007 3:35 PM
How can e relate to PI without "i" [or "j"]?
Don't you need all three.
Then there is -1 [or both 1 and 0].
# 24 | Kea | August 13, 2007 4:00 PM
I choose e. Euclidean circles are overrated, and pi is easily expressed in terms of zeta(n) values anyway.
# 25 | Rajesh | August 13, 2007 4:18 PM
My wife.
Oh, you meant irrational _numbers_. Then, it's e (pi is too easy to explain to grandma.)
# 26 | Mr. Upright | August 13, 2007 4:20 PM
I like e because everyone knows pi, at least kind of. Knowing about e makes you part of a more elite club and what's the point of learning math if not to be in a clique?
# 27 | Luke | August 13, 2007 4:31 PM
e. The universe e-folds. It doesn't π-fold.
# 28 | Epistaxis | August 13, 2007 5:27 PM
e, because statistics (including the normal distribution) can be applied to everything, but pi only comes up in geometry and freaky calculus. Also, pi is too obviously useful because you can just measure the circumference of a circle; e works in subtler ways.
# 29 | Xanthir, FCD | August 13, 2007 5:42 PM
Pi. E shows up everywhere, to be sure, but you pretty much expect it. It's the growth constant, for gosh sakes, so of course it'll show up wherever there's growth.
Pi, on the other hand, shows up for no apparent reason pretty much everywhere. I have absolutely no idea why it appears in the equation for the normal curve, for example.
When I have the disposable income to do it without feeling bad, I'm getting pi tattooed on my upper arm. Spiraled around so that it finishes just below where it starts, so that I can continue it as long as I have arm left. ^_^
(However, I also have a soft spot in my heart for phi.)
# 30 | Jonathan Vos Post | August 13, 2007 6:08 PM
I like them together.
A114605 Sum of first n digits of e to digit-wise power of first n digits of pi.
8, 15, 16, 24, 56, 134217784, 134217785, 134479929, 134479961, 134480473, 134481497, 134872122, 522292611, 522292611, 522554755, 522554880, 522554884, 522554911, 522945536, 522945617, ...
e^(pi i) = -1. Decimal expansion of e^pi = A039661. Here we are taking digit-by-digit e^pi and summing the partial terms. a(10) = 134480473 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5 + 8^9 + 1^2 + 8^6 + 2^5 + 8^3 is the first prime in this sequence. a(20) = 522945617 is the second prime in this sequence.
Example:
Since e = 2.71828182845904523536028747135266249775724709369995957496696762772407663...
and pi =
3.1415926535897932384626433832795028841971693993751058209749445923078164062...
a(1) = 8 = 2^3.
a(2) = 15 = 2^3 + 7^1.
a(3) = 16 = 2^3 + 7^1 + 1^4.
a(4) = 24 = 2^3 + 7^1 + 1^4 + 8^1.
a(5) = 56 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5.
a(6) = 134217784 = 2^3 + 7^1 + 1^4 + 8^1 + 2^5 + 8^9.
# 31 | bigTom | August 13, 2007 6:25 PM
For reasons others have stated, e is a bit more mysterious, and PI is usually a multiple of the "natural" number for many problems (usually 2PI or PI/2 or sqrt(PI).... Also as stated above everyone learns about Pi in grade school, I bet only about 5-10% of the population knows e. E of course has a psuedo inversion LOG(2) as well!
# 32 | Lab Rat | August 13, 2007 6:28 PM
e, hands down. You can always define 2*pi = h = c = 1, like a lecturer of mine used to say, but without e, spectral analysis would be a major nightmare.
# 33 | Tyler DiPietro | August 13, 2007 7:36 PM
I'll go with e, if only because it takes a wee bit more mathematical geek-dom to fully understand it's significance.
# 34 | Stu | August 13, 2007 9:09 PM
Oh come on jk (#13), get real!
I'm going to sit on the fence on this one, so I guess I'll take (e+pi)/2
# 35 | Agnostic | August 13, 2007 9:16 PM
Well then, I pick pi -- choosing e is clearly already very fashionable, so I'll appropriate prole values just to show that I'm sooo above the e-choosers. I mean, Donald Trump can wear jeans, or Denis Rodman can dress in drag, and no one'll be confused.
Picking e is for nouveau riche mathematicians who are in danger of being mistaken for prole dolts. Picking pi says that you're such a singular genius that you can afford to pick pi.
[i hate to say this, but with geeks, you can never rely on a sense of humor, so -- I'm obviously being facetious.]
# 36 | Kea | August 13, 2007 9:51 PM
To the sexist pig ... how to explain e to your grandma: it's the cardinality of the category of finite sets and bijections - duh.
# 37 | wildcardjack | August 13, 2007 9:58 PM
For the longest time, the signature in my emails read
This universe brought to you by the number e
I thought it was properly deep an a little confusing, which was what I wanted. Now I'm a book dealer and I don't want the christians I sell so much to catching that one.
# 38 | Tyler DiPietro | August 13, 2007 10:05 PM
One more thing that makes e way cooler than pi: ex is it's own derivative, no matter what order you derive to. Awesome.
# 39 | Zuska | August 13, 2007 10:37 PM
My wife. Oh, you meant irrational _numbers_. Then, it's e (pi is too easy to explain to grandma.)
Nice. Turn a perfectly beautiful dorky poll into a sexist bashing of both your wife AND your grandma. Jerk.
I pick e. Because, even though pi makes an appearance, e is featured prominently in the famous MIT cheer:
e to the x dy dx
e to the x dy
cosine secant tangent sine
3.14159!
# 40 | Tyler DiPietro | August 13, 2007 10:50 PM
Whoops, forget that was actually mentioned in the OP. Sorry all.
# 41 | Coin | August 14, 2007 4:33 AM
e.
Pi is much less meaningful if you don't happen to have something like a flat plane lying around.
Yes, yes, I know, pi also arises from simple harmonic oscillators, etc. But e has always seemed more fundamental to me. I can imagine a world without euclidean geometries more easily than I can imagine a world without logarithms.
# 42 | Stephan | August 14, 2007 5:00 AM
e. Transform Hamiltonians to Unitary operations and give me complex phases.
# 43 | Jonathan Vos Post | August 14, 2007 5:11 AM
Other ways to have your pi and e it too:
A092033 Decimal expansion of e/pi.
e/pi =
.865255979... to a hundred places:
8, 6, 5, 2, 5, 5, 9, 7, 9, 4, 3, 2, 2, 6, 5, 0, 8, 7, 2, 1, 7, 7, 7, 4, 7, 8, 9, 6, 4, 6, 0, 8, 9, 6, 1, 7, 4, 2, 8, 7, 4, 4, 6, 2, 3, 9, 0, 8, 5, 1, 5, 5, 3, 9, 4, 5, 4, 3, 3, 0, 2, 8, 8, 9, 4, 8, 0, 4, 5, 0, 4, 4, 5, 7, 0, 6, 7, 7, 0, 5, 8, 6, 3, 1, 9, 2, 4, 6, 6, 2, 5, 1, 6, 1, 8, 4, 5, 1, 7,
A059742 Decimal expansion of e+pi.
COMMENT
It is not presently known if this number is rational or irrational.
EXAMPLE
to a hundred places:
5, 8, 5, 9, 8, 7, 4, 4, 8, 2, 0, 4, 8, 8, 3, 8, 4, 7, 3, 8, 2, 2, 9, 3, 0, 8, 5, 4, 6, 3, 2, 1, 6, 5, 3, 8, 1, 9, 5, 4, 4, 1, 6, 4, 9, 3, 0, 7, 5, 0, 6, 5, 3, 9, 5, 9, 4, 1, 9, 1, 2, 2, 2, 0, 0, 3, 1, 8, 9, 3, 0, 3, 6, 6, 3, 9, 7, 5, 6, 5, 9, 3, 1, 9, 9, 4, 1, 7, 0, 0, 3, 8, 6, 7, 2, 8, 3, 4, 9, 5, 4, 0, 9, 6, 1
There are many more where that comes from. We typically don't even know if these are irrational, let alone transcendental.
# 44 | CCPhysicist | August 14, 2007 9:09 AM
Oh ye of little faith in geekdom. One of my math colleagues can recite e to hundreds of places. He uses this "skill" to amuse and befuddle his business calc students (where e rather than trig is crucial).
I'll take e, for pretty much the same reasons listed above, plus one only alluded to by others: You can get pi (actually pi/2) from the zeroes of e^x in the complex plane. Another is that you need the gaussian function for lots of things in physics, not to mention the normal distribution in statistics.
As for grandma, a lot depends on whether grandma is an electrical engineer or is married to one.
# 45 | Squiddhartha | August 14, 2007 9:25 AM
I'll go with pi, which one can celebrate on Pi Day (3/14)... by eating pie.
mmmm, pie
# 46 | goffredo | August 14, 2007 10:16 AM
I like e soooo much, in particular it role in Euler's theorem whereby I re-appreciate pi.
# 47 | Torbjörn Larsson, OM | August 14, 2007 6:23 PM
If we are allowed to express these constants by each other (as others suggest here) instead of having to reject one of them, e wins hands down. But then you don't need to appeal to physics.
[We need clocks to measure time. Since time is more fundamental than spacetime geometry, by the above argument pi; wins I think.]
# 48 | Peter M | August 17, 2007 4:18 PM
Clearly e^x is the most important real function, since it is the solution of the most basic differential equation df/dx = f . Pi then appears in its period, e^(x + 2 Pi i) = e^x . Thus, a devotee of analysis would probably prefer e.
However, Pi is a more geometric quantity since it also appears in metric formulas for the circle, or more generally the n-dimensional sphere, and hence in many isoperimetric problems. This leads to Pi's appearance in Riemannian geometry, such as in the Gauss-Bonnet formula stating that the total scalar curvature of a closed even-dimensional manifold is 2 Pi times its Euler characteristic. I can't think of any natural geometric problem whose solution involves e (for example a natural picture containing e as a length).
Since only total geeks like analysis, I vote for Pi.