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Math things that blew your mind

  1. Nov 14, 2006 #1

    ShawnD

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    Let's share some stories about math things that are interesting enough to tell somebody about, even if it's just to sound smart at parties.

    My head exploded when I learned that dropping the compound period for growth to 0 increased growth by a factor of "e". Up until then I had no idea why anybody cared about e, e^x, or natural log.
     
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  3. Nov 14, 2006 #2

    siddharth

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    http://xkcd.com/c179.html

    Warning: this comic contains strong language (which may be unsuitable for children), unusual humor (which may be unsuitable for adults), and advanced mathematics (which may be unsuitable for liberal-arts majors).


    That was a wow moment when I first learnt it in school.
     
  4. Nov 14, 2006 #3
    Yeh, that screwed with me too.

    (XKCD is the best. I run around the forums a lot).
     
  5. Nov 14, 2006 #4
    Linear algebra. Seriously.
     
  6. Nov 14, 2006 #5
    e^2*pi*i=1 always gets people who haven't gone through the Taylor expansion to get Euler's relation. When you first look at it, 'e', 'pi' and 'i' have absolutely nothing to do with each other, and all come from different areas of math.

    My first reaction upon getting handed Euler's relation (having just spent a week just working with the theoretical underpinnings of the Taylor expansion in another class, so it was sort of inviolate) was, "That's just sick."

    Of course, it was also over two decades ago, so I may be misremembering the name of "Euler's relation". I mean by it the mapping of e^x*i onto the unit circle in the complex plane.

    After you work with it constantly for so many years (no way to avoid it in theoretical physics, for those who aren't or are just beginning), you forget just how twisted the relation actually is in terms of the underlying concepts. It's the rest of the world that looks weird in contrast.
     
  7. Nov 14, 2006 #6
    Was teaching my brother about exponential functions yesterday and he was pretty surprised to hear that if you fold a piece of paper 50 times it would be 50 million miles thick (assuming 0.1mm thickness).
     
  8. Nov 14, 2006 #7
    Actually what just screwed me over was that e^(pi*i) gives a negative answer, yet e is positive.
     
  9. Nov 14, 2006 #8

    Ivan Seeking

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    Cantor's Theorem.

    An infinity of infinities...:eek:
     
  10. Nov 14, 2006 #9

    BobG

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    More surprising to me was the natural log of a negative number always resulted in a complex number with pi as the imaginary part.

    (Maybe more surprising was that my math teacher said there was a reason for that, but he couldn't recall exactly what it was at the moment. Once a person recalled Euler's identity, the result was more of a 'Duh!' realization than a shocking result. The subject came up when a student asked why integrals used the natural log of the absolute value of some variable.)
     
  11. Nov 14, 2006 #10

    selfAdjoint

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    Dearly Missed

    I LOVED the Cantor Set. c points, totally disconnected, everywhere dense, what's not to like? Antoine's necklace is even better.
     
  12. Nov 14, 2006 #11

    BobG

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    You can't fold a piece of paper 50 times. You can only fold it twelve times.
     
  13. Nov 14, 2006 #12

    Office_Shredder

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    And that's the reason you can't
     
  14. Nov 14, 2006 #13

    Ivan Seeking

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    Also, not only did we have the greatest professor for that class, there were only about six of us in it. It was a real treat.
     
  15. Nov 14, 2006 #14

    Ivan Seeking

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    There is very simple brain teaser that caught me off gaurd.

    If you wrap a string around the earth at the equator and pull it tight, and then add one foot to the length of the string, what would be the resulting gap?

    What is the radius of a circle having a circumference of one foot?
     
  16. Nov 14, 2006 #15

    EL

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    Wow, that's a good one!
     
  17. Nov 14, 2006 #16

    chroot

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    I don't even get it... what gap? Gap in what?

    - Warren
     
  18. Nov 14, 2006 #17

    Ivan Seeking

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    ...the gap formed between the string and the earth by adding one foot to the length of the string.
     
  19. Nov 14, 2006 #18

    chroot

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    Oh, I see.. so the ends of the string are brought together and pulled off the surface of the earth.

    - Warren
     
  20. Nov 14, 2006 #19

    Ivan Seeking

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    Implicity we assume a uniform gap. :rolleyes:
     
  21. Nov 14, 2006 #20

    chroot

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    What does a "uniform gap" mean? You seem to have put all kinds of assumptions into this "brain teaser," to the point where it doesn't even make any sense to me what quantity I should try to find. Sorry.

    - Warren
     
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