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ganeshie8

  • one year ago

show that \[A=i+\frac{b}{2}-1\] for a polygon with integer coordinates. \(A\) : Area of polygon \(b\) : number of lattice points on the boundary \(i\) : number of lattice points in the interior of polygon

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  1. ganeshie8
    • one year ago
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    sorry i think the polygon needs to be convex, try this |dw:1435488165543:dw|

  2. ikram002p
    • one year ago
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    |dw:1435488883158:dw|

  3. ganeshie8
    • one year ago
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    what are g and r ?

  4. ikram002p
    • one year ago
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    green and red

  5. ganeshie8
    • one year ago
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    okay

  6. ikram002p
    • one year ago
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    my intention was to divide any polygon to triangles idk if i make sense but i might have something to do with it

  7. geerky42
    • one year ago
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    *

  8. ikram002p
    • one year ago
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    i have this crazy idea, 1-i'll assume any polygon could be divided into triangles 2-i'll prove that a triangle can have area of this formula 3-lets generate this for several joined triangles 4-generate to any polygon "this should end up neat"

  9. ikram002p
    • one year ago
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    |dw:1435492530592:dw|

  10. ikram002p
    • one year ago
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    |dw:1435492795920:dw|

  11. ikram002p
    • one year ago
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    Area=1/2(x1)*y2

  12. ikram002p
    • one year ago
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    -.-

  13. ikram002p
    • one year ago
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    well we need to show its correct for right triangle first xD

  14. ikram002p
    • one year ago
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    |dw:1435493122358:dw| the area of the triangle DEF=1/2 (area of the rectangle)

  15. ganeshie8
    • one year ago
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    |dw:1435493472081:dw|

  16. ikram002p
    • one year ago
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    without coordinate

  17. ganeshie8
    • one year ago
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    select and delete it

  18. ikram002p
    • one year ago
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    so to find the area we divide them into squares and each square being denoted by number of lattice points in the interior |dw:1435493745391:dw|