1. Standard memberPBE6
    Bananarama
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    15 Oct '07 18:10
    This is an old one that I posted a few years ago, but I don't remember it being answered analytically (not sure if it's possible or not). So here we go again!

    A farmer owns a circular field, and wants to put his goat in it. However, he only wants to allow the goat to graze over half the field (i.e. he's a sadist). If the goat is tied to the edge of the circular field, how long should the rope be to allow the goat to graze over half the field? Give your answer as a fraction of the diameter.

    PS - This is easily solvable numerically, but can anyone come up with an analytical solution?
  2. Los Angeles
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    15 Oct '07 18:19
    It all depends upon the strength and determination of the goat.
    If we're talking about an extremely hungry goat then he'll strain
    and pull and reach further than the rope.
    It's nearly impossible to tell with a live creature, rather than if you're using --- let's say a
    blade tied to the rope. You can't tell how much the goat is going to eat, how far it will crane it's neck and other variables that I can't even begin to fathom.
    I'm not just trying to sound smart here... I think I have a valid point.

    Goats are funny.
  3. Standard memberPalynka
    Upward Spiral
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    15 Oct '07 18:211 edit
    Originally posted by inthegreenroom
    It all depends upon the strength and determination of the goat.
    If we're talking about an extremely hungry goat then he'll strain
    and pull and reach further than the rope.
    It's nearly impossible to tell with a live creature, rather than if you're using --- let's say a
    blade tied to the rope. You can't tell how much the goat is going to eat, how f ot just trying to sound smart here... I think I have a valid point.

    Goats are funny.
    YouTube

    Edit: And you ARE trying too hard to be smart.
  4. Standard memberPBE6
    Bananarama
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    15 Oct '07 18:29
    Originally posted by inthegreenroom
    It all depends upon the strength and determination of the goat.
    If we're talking about an extremely hungry goat then he'll strain
    and pull and reach further than the rope.
    It's nearly impossible to tell with a live creature, rather than if you're using --- let's say a
    blade tied to the rope. You can't tell how much the goat is going to eat, how f ...[text shortened]... ot just trying to sound smart here... I think I have a valid point.

    Goats are funny.
    You'll get your coat? Right then. 😞
  5. Standard memberPalynka
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    15 Oct '07 18:30
    Originally posted by PBE6
    You'll get your goat? Right then. 😞
    Fedxi!
  6. Los Angeles
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    15 Oct '07 18:37
    I'm just saying... it's impossible to tell.

    It ceases to be an exact science when you're using an animal.

    You should join Mensa. I mean, if you can.

    Good times!
  7. Los Angeles
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    15 Oct '07 18:41
    Originally posted by Palynka
    http://www.youtube.com/watch?v=we9_CdNPuJg

    Edit: And you ARE trying too hard to be smart.
    That video was hilarious!

    🙂
  8. Standard memberuzless
    The So Fist
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    15 Oct '07 19:16
    Originally posted by PBE6
    This is an old one that I posted a few years ago, but I don't remember it being answered analytically (not sure if it's possible or not). So here we go again!

    A farmer owns a circular field, and wants to put his goat in it. However, he only wants to allow the goat to graze over half the field (i.e. he's a sadist). If the goat is tied to the edge of the ci ...[text shortened]... PS - This is easily solvable numerically, but can anyone come up with an analytical solution?
    (radius of farm - X)2 + (radius of farm - X )2 = (radius of farm)2
  9. Standard memberPBE6
    Bananarama
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    15 Oct '07 19:31
    Originally posted by inthegreenroom
    I'm just saying... it's impossible to tell.

    It ceases to be an exact science when you're using an animal.

    You should join Mensa. I mean, if you can.

    Good times!
    Ahh, right! I forgot, one always ends up with fractions when counting sheep. 🙄
  10. Standard memberuzless
    The So Fist
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    15 Oct '07 20:54
    Originally posted by uzless
    (radius of farm - X)2 + (radius of farm - X )2 = (radius of farm)2
    that's a ridiculous equation.

    You end up with a radius + 0.3 units as your approximate answer for any given radius.

    Hmm...
  11. SubscriberAThousandYoung
    All My Soldiers...
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    16 Oct '07 05:01
    How dare you treat my people in this fashion!
  12. Standard memberPBE6
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    16 Oct '07 16:20
    Originally posted by AThousandYoung
    How dare you treat my people in this fashion!
    How did you get off your rope? 😕
  13. Subscribersonhouse
    Fast and Curious
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    16 Oct '07 16:412 edits
    Originally posted by uzless
    that's a ridiculous equation.

    You end up with a radius + 0.3 units as your approximate answer for any given radius.

    Hmm...
    Its actually about 0.7. Where do you get 0.3? did you check your work? that comes out to more like one tenth the area. Suppose a radius of ten units, squared, 100, times PI, 314 square units and change. So do 3, squared, 9 times PI, 28 square units, less than one tenth. Now try 0.7
    7 units squared, 49, times PI, is 153 square units. Divided by 314, about half. Wait, I think I see what you are talking about, starting at 0.7 units, you add 0.3 and end up with 1 which would double I think. That is the opposite though, that gives the radius to double the area, we want the radius to half the area. I guess we are talking about the inverse of the same problem, just semantics.
  14. Standard memberwolfgang59
    howling mad
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    16 Oct '07 16:50
    This is a very good problem. Even with a Maths degree I'm not sure I can do it! (Didnt take the Geometry units!!!)

    However I will attempt it from basic principles
    (... it is half term next week!)
  15. Standard membersmw6869
    Granny
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    16 Oct '07 22:32
    Originally posted by PBE6
    This is an old one that I posted a few years ago, but I don't remember it being answered analytically (not sure if it's possible or not). So here we go again!

    A farmer owns a circular field, and wants to put his goat in it. However, he only wants to allow the goat to graze over half the field (i.e. he's a sadist). If the goat is tied to the edge of the ci ...[text shortened]... PS - This is easily solvable numerically, but can anyone come up with an analytical solution?
    The definitive answer:

    YouTube

    Granny.
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