1. Standard memberPBE6
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    07 Nov '07 19:45
    What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?
  2. Standard membersven1000
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    08 Nov '07 07:14
    Is that a theoretical or practical question?
  3. Joined
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    08 Nov '07 07:17
    Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

    Since 1+1/2+1/3.... is infinity, then the length is infinite.
  4. Standard membersven1000
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    08 Nov '07 07:23
    http://www.fincher.org/CoinStacking/HowTo.shtml
  5. Standard membersven1000
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    08 Nov '07 07:26
    Originally posted by Dejection
    Idk. I know it's infinite for cards. You can experiment with cards if you like. Get a stack of cards, with length unit 2. Then push the top card out 1 unit, the next 1/2, the next 1/3. ect.

    Since 1+1/2+1/3.... is infinity, then the length is infinite.
    Well, ok, that is a theoretical result. I'd like to see someone try to successfully use that to bridge even 5 units of length (2.5 units from each side).

    The website above shows a practical success of a three penny distance, using some counterbalance techniques. Counterbalance with your cards would probably make bridge building much easier.
  6. Joined
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    08 Nov '07 07:48
    1+1/2+1/3+1/4... never reaches 9.
  7. Joined
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    08 Nov '07 08:55
    Originally posted by doodinthemood
    1+1/2+1/3+1/4... never reaches 9.
    Yes, it does. The series 1/1+1/2+1/3+...1/n is asymptotic to ln(n); ln(n) reaches 9 for n=8103-and-a-bit.

    Richard
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    08 Nov '07 09:441 edit
    Originally posted by doodinthemood
    1+1/2+1/3+1/4... never reaches 9.
    It does. The easy way to look at it is this:

    1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

    > 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

    = 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...
  9. Standard memberPBE6
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    08 Nov '07 16:50
    I got a different result. My series ended up being the inverse factorial series, not the harmonic series. Have to double check the calculations... 😕
  10. Subscriberjoe shmo
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    08 Nov '07 18:34
    Originally posted by mtthw
    It does. The easy way to look at it is this:

    1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + ...

    > 1 + 1/2 + (1/4 + 1/4) + (1/8 + 1/8 + 1/8 + 1/8) + (1/16 + ...) + ...

    = 1 + 1/2 + 1/2 + 1/2 + 1/2 + ...
    Is this like exponential decay?
  11. Standard memberuzless
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    08 Nov '07 19:431 edit
    Originally posted by PBE6
    What is the longest single-penny width bridge you can make by stacking pennies on top of each other on the edge of a table?
    So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.😉
  12. Standard memberwolfgang59
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    08 Nov '07 20:45
    Originally posted by uzless
    So far i've made it up to 5 but I've got the shakes after too many beers last night. I might be able to get to 7 when my hands settle down.😉
    thats a minimum of 226 coins (I think)

    7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

    🙄
  13. Standard memberPBE6
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    08 Nov '07 21:031 edit
    Originally posted by wolfgang59
    thats a minimum of 226 coins (I think)

    7 will take ... a MINIMUM of 1655 coins (I think) and a steady hand!

    🙄
    Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins... 🙄

    OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

    L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

    This series is divergent, so the theoretical length of the bridge is infinite.
  14. Standard memberwolfgang59
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    08 Nov '07 21:31
    Originally posted by PBE6
    Easy there, Frank Lloyd Right...I'm pretty sure he meant 7 coins... 🙄

    OK! Found the glitch in my calculations. I get the harmonic series now, too. More specifically, the position "L" of the furthest edge of the top coin is given by:

    L = sum(i=1...n) 1/(2i) = (1/2) * sum(i=1...n) 1/n

    This series is divergent, so the theoretical length of the bridge is infinite.
    😲

    5 COINS is not worth posting about!!! I assumed a 5 coin width!
  15. Standard memberuzless
    The So Fist
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    08 Nov '07 21:49
    Originally posted by wolfgang59
    😲

    5 COINS is not worth posting about!!! I assumed a 5 coin width!
    Far be it for anyone to post a bit of humour. I got up to 10 before they crashed onto the carpet and rolled down the office hallway
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