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    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:


      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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    Last updated: June 2013
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