Dorky Poll: e or π?

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. #1 Index Guy
    August 13, 2007

    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. #2 Brian
    August 13, 2007

    Pi is my vote, since it has a nerdy symbol :)

  3. #3 John Novak
    August 13, 2007

    The Deathstar.

  4. #4 Johan Larson
    August 13, 2007

    e. Pi is for the middlebrows.

  5. #5 Melissa
    August 13, 2007

    My family.

  6. #6 marciepooh
    August 13, 2007

    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. #7 Guru
    August 13, 2007

    Pi

  8. #8 dr. dave
    August 13, 2007

    π for sure, for two reasons…

    1) the awesome film of the same name
    2) all the secret messages from God encoded inside!!

  9. #9 TomS
    August 13, 2007

    e

    But there are some other famous numbers, deserving of votes – φ, the Golden Ratio, is the first that comes to mind.

  10. #10 Pam
    August 13, 2007

    Pi, because it is homonymous with a delicious dessert.

  11. #11 Andrew
    August 13, 2007

    e is much more fun to shout.

  12. #12 Manny
    August 13, 2007

    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. #13 jk
    August 13, 2007

    They aint got nothin’ on i.

  14. #14 KeithB
    August 13, 2007

    e.

    Because it is easy to memorize to 10 sig. figures.

  15. #15 Dennis
    August 13, 2007
  16. #16 Aditya
    August 13, 2007

    e, as it has made life with complex numbers so easy!

  17. #17 Torbjörn Larsson, OM
    August 13, 2007

    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. #18 Paul
    August 13, 2007

    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. #19 cisko
    August 13, 2007

    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. #20 Sean
    August 13, 2007

    What, no phi love here?

  21. #21 Thony C.
    August 13, 2007

    eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee…

  22. #22 m
    August 13, 2007

    Given that I loathe, hate and despise logarithms…I’m definitely going to have to say ‘pi’.

  23. #23 Doug
    August 13, 2007

    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. #24 Kea
    August 13, 2007

    I choose e. Euclidean circles are overrated, and pi is easily expressed in terms of zeta(n) values anyway.

  25. #25 Rajesh
    August 13, 2007

    My wife.

    Oh, you meant irrational _numbers_. Then, it’s e (pi is too easy to explain to grandma.)

  26. #26 Mr. Upright
    August 13, 2007

    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. #27 Luke
    August 13, 2007

    e. The universe e-folds. It doesn’t π-fold.

  28. #28 Epistaxis
    August 13, 2007

    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. #29 Xanthir, FCD
    August 13, 2007

    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. #30 Jonathan Vos Post
    August 13, 2007

    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. #31 bigTom
    August 13, 2007

    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. #32 Lab Rat
    August 13, 2007

    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. #33 Tyler DiPietro
    August 13, 2007

    I’ll go with e, if only because it takes a wee bit more mathematical geek-dom to fully understand it’s significance.

  34. #34 Stu
    August 13, 2007

    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. #35 Agnostic
    August 13, 2007

    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. #36 Kea
    August 13, 2007

    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. #37 wildcardjack
    August 13, 2007

    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. #38 Tyler DiPietro
    August 13, 2007

    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. #39 Zuska
    August 13, 2007

    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. #40 Tyler DiPietro
    August 13, 2007

    Whoops, forget that was actually mentioned in the OP. Sorry all.

  41. #41 Coin
    August 14, 2007

    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. #42 Stephan
    August 14, 2007

    e. Transform Hamiltonians to Unitary operations and give me complex phases.

  43. #43 Jonathan Vos Post
    August 14, 2007

    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
    e+pi=5.859874482048838473822930854…
    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. #44 CCPhysicist
    August 14, 2007

    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. #45 Squiddhartha
    August 14, 2007

    I’ll go with pi, which one can celebrate on Pi Day (3/14)… by eating pie.

    mmmm, pie

  46. #46 goffredo
    August 14, 2007

    I like e soooo much, in particular it role in Euler’s theorem whereby I re-appreciate pi.

  47. #47 Torbjörn Larsson, OM
    August 14, 2007

    pi also arises from simple harmonic oscillators, etc. But e has always seemed more fundamental to me.

    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. #48 Peter M
    August 17, 2007

    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.

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