Posers and Puzzles

Posers and Puzzles

  1. Joined
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    28 Jun '05 18:223 edits
    A (circular) coin is placed flat on a table so that it cannot slip.
    An identical coin is now placed flat on the table, touching the first coin, and rolled completely around its circumference without slipping,
    Relative to the first coin, how many complete revolutions does the second coin make?
  2. Standard memberPBE6
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    28 Jun '05 18:53
    I've got an answer, but I'll keep it to myself until a few more people post. I hate being a thread killer.
  3. Standard memberThe Plumber
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    28 Jun '05 18:53
    Originally posted by THUDandBLUNDER
    A (circular) coin is placed flat on a table so that it cannot slip.
    An identical coin is now placed flat on the table, touching the first coin, and rolled completely around its circumference without slipping,
    Relative to the first coin, how many complete revolutions does the second coin make?
    I'm not sure what "realtive to the first coin" means. Relative to the table, the coin makes two complete revolutions....
  4. Joined
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    28 Jun '05 18:59
    Originally posted by The Plumber
    I'm not sure what "realtive to the first coin" means. Relative to the table, the coin makes two complete revolutions....
    OK relative to the table, thread killer! 🙂
  5. SubscriberAThousandYoung
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    29 Jun '05 11:16
    Originally posted by THUDandBLUNDER
    A (circular) coin is placed flat on a table so that it cannot slip.
    An identical coin is now placed flat on the table, touching the first coin, and rolled completely around its circumference without slipping,
    Relative to the first coin, how many complete revolutions does the second coin make?
    One I think. I am not sure if I understood the question.
  6. Joined
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    29 Jun '05 13:40
    Originally posted by AThousandYoung
    One I think. I am not sure if I understood the question.
    What do you not understand?
    A coin is rolled round an identical coin.
    How many revolutions does it make relative to some fixed point?
  7. SubscriberAThousandYoung
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    29 Jun '05 13:541 edit
    Originally posted by THUDandBLUNDER
    What do you not understand?
    A coin is rolled round an identical coin.
    How many revolutions does it make relative to some fixed point?
    Am I right that the number of revolutions is one? As in, the center of the rolling coin went through one complete revolution around the center of the fixed coin?
  8. Joined
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    29 Jun '05 14:02
    Originally posted by AThousandYoung
    Am I right that the number of revolutions is one? As in, the center of the rolling coin went through one complete revolution around the center of the fixed coin?
    Nope. That's why I posted it.
    Anyway, thanks for making it worthwhile. 😵
  9. Standard memberXanthosNZ
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    29 Jun '05 14:11
    What if instead of one coin being rolled around you put 4 coins edge to edge so their centres form a square. How many rotations does it make now?
  10. Standard memberThe Plumber
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    29 Jun '05 15:281 edit
    Originally posted by XanthosNZ
    What if instead of one coin being rolled around you put 4 coins edge to edge so their centres form a square. How many rotations does it make now?
    If I understand correctly, you're saying you have four coins arranged in a square that are fixed in place, and a fifth coin that is "rolled" around these four, maintaining contact with at least one coin at all times, and contacting two coins at once on 4 occasions, when it transfers contact from one coin to the next.

    Then, assuming I've calculated correctly, that would be a total of three and a third revolutions.
  11. Standard memberXanthosNZ
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    29 Jun '05 15:35
    Originally posted by AThousandYoung
    Am I right that the number of revolutions is one? As in, the center of the rolling coin went through one complete revolution around the center of the fixed coin?
    Let the radius of the coins be r.
    Now look at what distance the center of the moving coin travels. It's 4*pi*r. That's twice the circumfrence of the coin so it makes two rotations.
  12. Joined
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    29 Jun '05 15:412 edits
    I agree with Plumber, 10/3 revolutions.
    How many with n touching coins?
  13. Standard memberXanthosNZ
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    29 Jun '05 15:43
    Originally posted by THUDandBLUNDER
    I agree with Plumber.
    I was responding to AThousandYoung's query earlier about the single coin and why it's two rotations.

    I think the Plumber is right as well.
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    29 Jun '05 21:41
    Surly the answer is 3 if you take into acount all dimentions
  15. Standard memberThe Plumber
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    30 Jun '05 01:05
    Originally posted by o0Ziggy0o
    Surly the answer is 3 if you take into acount all dimentions
    Well, if you go out to the 23rd dimension, I can see that, but if you limit it to 2, the answer is gonna' be pretty much three and a third....
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