A many-sided or polygonal shape
Pick’s theorem gives a means for computing the area enclosed by a many-
sided (or polygonal) shape formed by joining up points whose coordinates are
whole numbers. This is pinball mathematics.
To find the area of the shape we shall have to count the number of points •
on the boundary and the number of interior points o. In our example, the
number of points on the boundary is b = 22 and the number of interior points is
c = 7. This is all we need to use Pick’s theorem:
area = b/ 2 + c – 1
From this formula, the area is 22/2 + 7 – 1 = 17. The area is 17 square units.
It is as simple as that. Pick’s theorem can be applied to any shape which joins
discrete points with whole number coordinates, the only condition being that the
boundary does not cross itself.
marcin
(Marcin)
#1