What is Pick's Theorem, please give a example to support your explaination.
2007-06-11 22:03:50 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
It's simple geometry theorem that allows us to find the area of any polygon that is embedded on a lattice or grid. It is especially useful for concave polygons, for which the usual textbook area formulas do not work.
Given such a shape, the apparently "easy" way to calculate its area is to split it into rectangles and triangles and sum their areas. Pick's beautiful result shows that even this is doing too much work: one need only count the number of lattice points (a "lattice point" is a point where two grid lines cross, that is, a corner of some square in the grid) lying within the shape and count the number lying on its boundary. If the number of interior points is I and boundary points B, then the area of the polygon is given by I+B/2-1 units squared (each square in the grid is assumed to have side length of one unit).
2007-06-11 22:12:38 · answer #1 · answered by Anonymous · 1⤊ 0⤋
See this web page. I'll be honest here. I'm only in Class X in Inida. They do not teach us this until we're 2 years older. But I did a search on the net for you, and found an excellent web page I'm sure you'll like
http://en.wikipedia.org/wiki/Pick%27s_theorem
2007-06-11 22:21:27 · answer #2 · answered by Akilesh - Internet Undertaker 7 · 1⤊ 0⤋