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Math Help - Really amazing Theorem.

  1. #1
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    Really amazing Theorem.

    Let XYZ be a triangle. Then the area of XYZ is given by  A=\frac{1}{2}B+I-1 , where B is the number of boundry lattice points; I is the number of interior lattice points.
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  2. #2
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    Both B and I are the number of interior lattice points? I know virtually nothing about this theorem, but that does strike me as a bit odd.
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    Sorry, I meant that B is the number of boundry lattice points
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    Ok. Are you asking for help proving this theorem, or are you just posting it for our edification?
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    I just posted it because I thought people might find it interesting.
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  6. #6
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    That's cool. I think it would be even more interesting if you were to outline the construction of the lattice. I've seen a result or two similar to this, I think, in number theory. If it's what I'm thinking of.
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  7. #7
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    This is the special case (for triangles) of Pick's Theorem. See

    Pick's theorem - Wikipedia, the free encyclopedia

    However, you left out a condition: The vertices of the triangle (or polygon, in the general case) must lie on grid points.

    I agree with you, it's a fascinating theorem.
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