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Incommensurable Proof

  1. Sep 8, 2008 #1
    Does anyone know a theorm in number theory or mathematics that could be used to prove the following problem: Given a function f(x) = x sq. Graph the function and with two vertical lines, divide the area under the graph such that the two areas are equal. Denote the point on the x-axis where the first vertical line intersects as point a. Denote the point on the x-axis where the second vertical line intersects as point b. Denote point c on the x-axis as the maximum number in the domain of the function. Thus, the area above the line segment from 0 to a is equal to the area above the line segment from b to c. Prove that the line segment from 0 to a is always incommensurable with the line segment from b to c.
     
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  3. Sep 9, 2008 #2

    HallsofIvy

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    What do you mean by 'x sq." ? x^2?

    What "area under the graph". If you meant y= x^2, that graph does not a have an upper bound. Do you you mean the area of the regions having y= x^2 as upper edge, for x> 0 and x< 0? I am going to assume you mean to find two numbers, a and b, such that the area of the region bounded by y= x^2, y= 0, and x= a is the same as the area of the region bounded by y= x^2, y= 0, x= a, and x= b.

    There is no such maximum for y= x^2. And is c a point or a number?

    ??Didn't you just say that that was true for y= 0?

     
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