
Pick's Theorem Resources

Pick's Theorem Definition
If a polygon is constructed on an equaldistanced lattice and all polygon's vertices are lattice points:
then Pick's theorem states:
where:
i is the number of interior lattice points located inside the polygon, and
b is the number of points placed on the polygon's perimeter
Background Information
 Pick's theorem  Wikipedia [View Resources]
 Pick's Theorem Proof [View Resources]
 Georg Alexander Pick life and work  St Andrews [View Resources]
 Archimedes Stomachion (Pick's theorem) [View Resources]
K12 Experiments, Labs, Lesson Plans and Science Fair Projects
 Pick's theorem Java applets [View Resources]
 Pick's Theorem Demonstration [View Resources]
 Investigating Pick's Theorem Lesoon Plans [View Resources]
 Proving Pick's Theorem for Lattice Polygons [View Resources]
 Prove Pick's Theorem and also see if this theorem works on alternately consistent spaced grids (science fair projects).[View Resources]
 Rediscovering the Patterns in Pick’s Theorem [View Resources]
 Area of lattice polygons [View Resources]
 Lab: Learn about the relationship between the numbers of boundary and interior points and the area of lattice polygons [View Resources]
 Extending perimeter, circumference and area [View Resources]
 Proof of Pick's theorem in three parts [View Resources]
 A Formal Proof of Pick’s Theorem [View Resources]
 Pick's Theorem Fun Fact [View Resources]
Advanced Studies and Articles
 Systematic approaches to experimentation: The case of Pick’s theorem [View Resources]
 Pick’s Theorem via Minkowski’s Theorem [View Resources]
 Lattice Point Geometry: Pick’s Theorem and Minkowski’s Theorem [View Resources]
 Triangulations and Pick's Theorem [View Resources]
 On Cantor's first uncountability proof, pick's theorem, and The irrationality of the golden ratio [View Resources]
Theses and Dissertations
 Classification of Ehrhart quasipolynomials of halfintegral polygons [View Resources]
 Optimal Polygon Placement on a Grid [View Resources]
 The Arithmetic of Rational Polytopes [View Resources]
 Planning and evaluating a mathematics camp for Grade Six students [View Resources]

