Brain Teaser number pi/2

Discussion in 'Science' started by HereWeGoAgain, Jan 17, 2018.

  1. HereWeGoAgain

    HereWeGoAgain Banned

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    If you wrapped a string around the earth at the equator and pulled it tight, and then added one foot to the length of the string, what would be the uniform gap formed between the string and the surface of the earth?

    Surprising answer!
     
  2. waltky

    waltky Well-Known Member

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    I dunno...

    ... one foot?
     
  3. tecoyah

    tecoyah Well-Known Member Past Donor

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    There would be no gap....the string would stretch when pulled tight.
     
  4. Diablo

    Diablo Well-Known Member

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    2 inches.
     
  5. HonestJoe

    HonestJoe Well-Known Member Past Donor

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    I put my string around a soccer ball to get the answer. It was much easier. ;)
     
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  6. HereWeGoAgain

    HereWeGoAgain Banned

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    Your avatar reminded me of this:
    Kekulé had another dream, in which he saw atoms dance around, then form themselves into strings, moving about in a snake-like fashion. This vision continued until the snake of atoms formed itself into an image of a snake eating its own tail. This dream gave Kekulé the idea of the cyclic structure of benzene.
     
  7. WillReadmore

    WillReadmore Well-Known Member

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    I'd say the circumference =2 * pi * r

    So, r = c/(2*pi)

    The new radius is r' = (c+1 foot)/(2*pi)

    So, the difference in radius (the height above earth) is the difference in r which is r'-r, which is (c+1 foot)/(2*pi) -c/(2*pi)

    = ((c+1) - c) / (2*pi)

    =1/(2pi)

    True?
     
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  8. Diablo

    Diablo Well-Known Member

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    1 foot divided by 2*pi equals 12 inches divided by 6.28 which rounds up to 2 inches, which is what I said above, so well done.
     
  9. HereWeGoAgain

    HereWeGoAgain Banned

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    Everyone knows that math answers are meaningless if you don't show your work. ;)
     
  10. Diablo

    Diablo Well-Known Member

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    It's so obvious, there's no need..... and then you need people to be able to understand it...... that makes 2 of us.....
     
  11. HereWeGoAgain

    HereWeGoAgain Banned

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    Yes. So it doesn't matter how long the string is or how large the object. By adding one foot, the gap will always be 1/2pi, be it a soccer ball or a planet.

    That is sooooooooooo counter intuitive!
     
  12. HereWeGoAgain

    HereWeGoAgain Banned

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    Sorry, the answer is 1/2pi. not 2.
     
    Last edited: Jan 17, 2018
  13. HereWeGoAgain

    HereWeGoAgain Banned

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    And if you have a string one foot long, you can form a circle having a radius of 1/(2pi) feet
     
    Last edited: Jan 17, 2018
  14. Diablo

    Diablo Well-Known Member

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    1/2pi is a number, the question referred to a foot which is a measurement.
     
  15. squidward

    squidward Well-Known Member

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    you forgot the units
     
    Last edited: Jan 17, 2018
  16. WillReadmore

    WillReadmore Well-Known Member

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    True, but we have the luxury of knowing stuff like pi, which I think came from wrapping strings around stuff and making more and more accurate measurements.

    I'm always blown away by how much progress has been made through thought experiments like Einstein's and measurement of results like the scatter patterns from collisions in particle accelerators.
     
  17. HereWeGoAgain

    HereWeGoAgain Banned

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    Pi is a value we discovered, not derived. Likewise, all physical constants can only be determined using measurements.

    You don't do physics without math. In fact you really can't even start a physics problem [real physics] without knowing Calculus.

    The Greeks taught us that philosophy [no math] has limited value. The world cannot be understood through thought experiments. If Einstein couldn't do the math, he would just be another nameless dreamer long forgotten, who never accomplished anything.
     
    Last edited: Jan 17, 2018
  18. WillReadmore

    WillReadmore Well-Known Member

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    True. Not good.

    I was going to make it clearer that for every foot of string added the radius increases by 1 foot /2pi.

    But, it was starting to look like I was already overly pedantic.
     
  19. WillReadmore

    WillReadmore Well-Known Member

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    Well, I certainly agree that if someone plans on a college degree in physics they better start cranking on math. In fact, those with physics degrees tend to be very good at applied math. They often get jobs in fields that have everything to do with advanced applied math methods and little to do with physics!

    On the other hand, there are lots of cool methods for allowing middle school or high school students to derive equations related to gravity, mass, elasticity, etc., without knowing what calculus is. Typically speaking, relationships in physics are understood through measurement. And, Einstein trashed a major percent of physics based on his thought experiments.
     

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