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Math Help - Turn 64 square to 65, find Slope please help!

  1. #1
    dnd
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    Turn 64 square to 65, find Slope please help!

    Please help me with this question. I did attacth the question here
    Attached Thumbnails Attached Thumbnails Turn 64 square to 65, find Slope please help!-2.jpg  
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  2. #2
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    That is a classical riddle. Obviously something is wrong! It would be difficult to explain but what happens is that there is a thin long parrallelogram in the second diagram (65 squares) whose area is 1 unit (it is covered with thick black line thus it would be inconcievable by the human eye). Thus in the second diagram the number of squares is also 64 not 65!. Also, notice that the slope of the two lines do not match thus, it cannot be a straight line in the second diagram. This puzzle proves something important which many people reject when they first learn math. That just because two things look equal does not mean they are. For example just because it looks like the largest angle we have to prove that it is, just like here.
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  3. #3
    MHF Contributor
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    Quote Originally Posted by dnd
    Please help me with this question. I did attacth the question here
    In the title of your question you said about slopes. Umm, it was not done like you meant that as a hint or clue, (besides, this kind of thing is disproved by slopes anyway), so let me answer your question.

    Here is one way.

    Look at the second or bottom rectangle.
    ---slope of the line from upper left corner to bottom right corner is 5/13.

    ---slope of a "portion" of that same line that is supposed to be the incline of trapezoid A is 2/5. Uh-oh, not 5/13.

    ---slope of a "portion" of that same line that is supposed to be the incline of triangle C is 3/8. Uh-oh, not 5/13.

    That means the 3 lines are not really aligned. Meaning, no way the 64 squares of the 1st or top rectangle are really equal in area to the 65 squares of the 2nd rectangle.

    5/13 = 0.3846....
    2/5 = 0.4000
    3/8 = 0.3750
    If those 3 are the same, I'd go to school again and learn that kind of Math. Modern Math? Pure Math? Sets?

    ------------------------
    Er, ah, a square is a rectangle? The 1st figure is a square, an 8 by 8, not a rectangle.
    Yeah, but you'd learn later. Before you'd finished with all your schoolings.
    Last edited by ticbol; February 4th 2006 at 05:21 PM. Reason: rectangle? square?
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