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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
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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ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3sorry i think the polygon needs to be convex, try this dw:1435488165543:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435488883158:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1my intention was to divide any polygon to triangles idk if i make sense but i might have something to do with it

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

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435492530592:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435492795920:dw

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1well we need to show its correct for right triangle first xD

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1dw:1435493122358:dw the area of the triangle DEF=1/2 (area of the rectangle)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3dw:1435493472081:dw

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3select and delete it

ikram002p
 one year ago
Best ResponseYou've already chosen the best response.1so 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