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Math Help - Which diagram represents possible sets of points ?

  1. #1
    Junior Member mathbuoy's Avatar
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    Lightbulb Which diagram represents possible sets of points ?

    A person starts at his hut, travels 2km south, then 2km east,
    then 2km north and is then back at his hut. The expected answer is that the hut is at the North
    Pole. However, the hut could also be in the southern hemisphere.
    Which diagram represents possible sets of points near the South Pole?

    (The correct answer has three circles in a square)
    edits: in a square there's a circle, in the circle there's a circle with another circle in it.

    Please explain to me. Thank you!
    Last edited by mathbuoy; May 7th 2011 at 06:08 AM.
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  2. #2
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    Hello, mathbuoy!

    This is a classic puzzle.


    A person starts at his hut, travels 2km south, then 2km east,
    then 2km north and is then back at his hut. .Where is his hut?

    The expected answer is that the hut is at the North Pole.
    However, the hut could also be in the southern hemisphere.
    Which diagram represents possible sets of points near the South Pole?

    (The correct answer has three circles in a square) . I don't understand

    There is a point \,A near the South Pole.
    He walk 2 km south to point \,B.
    When he walks 2 km east, he walks around the earth and returns to \,B.
    . . (The circumference of the circle of latitude is exactly 2 km.)
    Then he walks 2 km north and arrives at \,A.

    Actually point \,A can be any point on its circle of latitude.
    . . Hence, there are brizillians of possible starting points.


    We can also locate point \,A so that he walks 2 km south to point \,B.
    Then when he walks 2 km east, he walks around the earth twice.

    Get it?

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  3. #3
    Junior Member mathbuoy's Avatar
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    hi soroban!

    edits: in a square there's a circle, in the circle there's a circle with another circle in it.
    Last edited by mathbuoy; May 7th 2011 at 06:08 AM.
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  4. #4
    Member HappyJoe's Avatar
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    What do you mean by "three circles in a square"?

    By the way, is it defined to go east, when you are exactly at the south pole? I suppose that either it is not defined, or otherwise it is defined as standing still.

    Anyway, after the guy has travelled 2 km south, what if he finds himself at the exact distance from the south pole with the property that if he travels east for 2 km, then he is back at where he started (so the lenght of the latitude is 2 km). Then he can travel back north for 2 km to his hut.
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  5. #5
    Junior Member mathbuoy's Avatar
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    Quote Originally Posted by Soroban View Post
    Hello, mathbuoy!

    This is a classic puzzle.



    There is a point \,A near the South Pole.
    He walk 2 km south to point \,B.
    When he walks 2 km east, he walks around the earth and returns to \,B.
    . . (The circumference of the circle of latitude is exactly 2 km.)
    Then he walks 2 km north and arrives at \,A.

    Actually point \,A can be any point on its circle of latitude.
    . . Hence, there are brizillians of possible starting points.


    We can also locate point \,A so that he walks 2 km south to point \,B.
    Then when he walks 2 km east, he walks around the earth twice.

    Get it?

    Quote Originally Posted by HappyJoe View Post
    What do you mean by "three circles in a square"?

    By the way, is it defined to go east, when you are exactly at the south pole? I suppose that either it is not defined, or otherwise it is defined as standing still.

    Anyway, after the guy has travelled 2 km south, what if he finds himself at the exact distance from the south pole with the property that if he travels east for 2 km, then he is back at where he started (so the lenght of the latitude is 2 km). Then he can travel back north for 2 km to his hut.
    I think the answer given means this:

    the biggest circle is the circumference of earth and the two smaller circles are the possible route taken by the hunter.
    thanks guys !
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