﻿ Pick's Theorem: Experiments, Labs, Articles, Studies and Background Information
Pick's Theorem
Experiments, Labs, Articles, Studies and Background Information
For Lesson Plans, Class Activities and Science Fair Projects

Pick's Theorem Resources

### Pick's Theorem Definition

If a polygon is constructed on an equal-distanced 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]

### K-12 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 quasi-polynomials of half-integral 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]      