A formal proof of Pick's Theorem
نویسنده
چکیده
We start by establishing the result for an elementary triangle: one whose vertices are lattice points and which contains no other lattice points either in its interior or boundary. Pick’s theorem for such a triangle simply asserts that it has area 1/2, or 0 in the degenerate cases where it is flat. Given two vectors A and B, we can consider them as defining the linear transformation of the plane f : (x, y) → Ax+By. It is not hard to show that if the image under f of the set of integer lattice points is exactly this same set of integer lattice points, then the determinant of the matrix of f is ±1:
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عنوان ژورنال:
- Mathematical Structures in Computer Science
دوره 21 شماره
صفحات -
تاریخ انتشار 2011