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A new pick-type theorem on the hexagonal lattice

✍ Scribed by Ren Ding; Krzysztof KoŁodziejczyk; John Reay

Publisher
Elsevier Science
Year
1988
Tongue
English
Weight
688 KB
Volume
68
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Let L be the lattice of all vertex points in a tiling of the plane by regular hexagons of unit area. Suppose the vertices of a planar polygon P are points of the lattice L, and points of L occur frequently along the edges of P. Then the area of P is A(P) = ;b + ii + &c -1, where b is the number of lattice points on the boundary of P, i is the number of lattice points in the inter;-* .Vm of P, and c is the boundary characteristic of P.

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