Pick’s Theorem in Two-Dimensional Subspace ofR3
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In the Euclidean spaceR3, denote the set of all points with integer coordinate byZ3. For any two-dimensional simple lattice polygonP, we establish the following analogy version of Pick’s Theorem,kIP+1/2BP-1, whereBPis the number of lattice points on the boundary ofPinZ3,IPis the number of lattice points in the interior ofPinZ3, andkis a constant only related to the two-dimensional subspace includingP.
2005 ◽
Vol 71
(1)
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pp. 107-111
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1969 ◽
Vol 10
(1-2)
◽
pp. 177-181
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1976 ◽
Vol 34
(2)
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pp. 200-202
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