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Pick's Theorem Resources
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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]
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