Pick s theorem history books

Let p be a lattice polygon, and let bp be the numbe of lattice points. This theorem is used to find the area of the polygon in terms of square units. At first the theorem wasnt recognized as very important. Picks theorem is a useful method for determining the area of any polygon whose vertices are points on a lattice, a regularly spaced array of points. The theorem as stated above is only valid for simple polygons, i. For a general polygon, picks formula generalizes to where is the number of vertices both in and on the boundary of the polygon. If we add the interior angles at all the vertices, we get. Search the worlds most comprehensive index of fulltext books. Maors book is a concise history of the pythagorean theorem, including the mathematicians, cultures, and people influenced by it. Pick s theorem was first illustrated by georg alexander pick in 1899. According to pick s theorem, which is the correct area of the polygon. The work is well written and supported by several proofs and exampled from chinese, arabic, and european sources the document how these unique cultures came to understand and apply the pythagorean theorem. Block pounds national council of teachers of mathematics.

Log in above or click join now to enjoy these exclusive benefits. If you count all of the points on the boundary or purple line, there are 16. You may use the software geogebra in your research. Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Pic k tells us that there is a nice, b eautiful, easy form ula that tells us the area of p olygon if w e kno w. Pick s theorem let us divide our polygon into n elementary triangles. Picks theorem 1 you will rediscover an interesting formula in the sequel expressing the area of a polygon with vertices in the knots of a square grid. Chapter 3 picks theorem not a great deal is known about georg alexander pick austrian mathematician. Pick s theorem expresses the area of a polygon, all of whose vertices are lattice points in a coordinate plane, in terms of the number of lattice points inside the polygon and the number of lattice points on the sides of the polygon. From its discovery in the 1700s to its being used to break the germans enigma code during world war 2. The sequence of five steps in this proof starts with adding polygons by glueing two polygons along an edge and showing that if the theorem is true for two polygons then it is true for their sum and difference the next step is to prove the theorem for a rectangle, then for the triangles formed when a rectangle is cut in half by a diagonal, then.