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Academy logo Patterns: Mathematics Is Everywhere

Kathy Nicolaus, Instructor

I.  Games of Strategy and Game Theory

    A.  Learn games

    B.  Determine and discuss strategies

    C. Analyze games and  define strategies

    D.  Play GOPS

       1. discuss reactions

       2. apply to politics, business and war

    E. Create a strategy game and determine strategy

    F. Tower of Hanoi

       1. learn strategy

       2. discuss recursive pattern and write equation

II.  Fibonacci Sequence

    A. Rabbit problem

    B.  Fibonnacci Sequence

       1.  Geometric Fallacy

    C.  Golden Ratio (T)

       1.  Construct Golden Rectangles

       2.  Golden Spiral

       3.  Golden section

       4.  Pascal’s Triangle

       5.  Serpinski Triangle

       6.  Penrose Tillings

III.  Tessellations

    A. Regular/irregular polygons of one sort

    B. Semi-regular tessellations

       1. overlaying tessellations

    C. Types of symmetry

    D. Escher Tessellations

    E. Use of symmetry in tessellations

    F. Tessellations on the rectangle, triangle, and hexagon

    G. Final Project

MSA Major/Minor Course: Patterns; Mathematics Is Everywhere

References:

1. Briggs, J., Fractals The Patterns of Chaos, Simon and Schuster, 1992

2. Britton, Jill, Introduction to Tessellations, Dale Seymour Publications, 1989

3. Devlin, Keith, Mathematics The Science of Patterns,  Scientific American Library, 1994

4. Farmer, David W., Groups and Symmetry: A Guide to Discovering Mathematics, American Mathematical Society, 1996

5. Gardner, Martin, Mathematical Puzzles and Diversions, Simon and Schuster, 1959

6. Luce, R. Duncan, Raiffa, Howard, Games and Decisions Introduction and Critical Survey, 

IV.  Fractals

    A.  Chaos Theory

    B. Feedback

       1. Video Feedback Experiment

    C. Chaos Game

    D. Self-Similaritiy Activities

    E. Box Self-Similarity and the Limit

    F. Fractal Construction

    G. Fractal Dimension

    H. Function Iteration

    I.   The Mandelbrot Set

       1. Movie:  The Geometry of the Mandelbrot SetÓ

       2.  Fractal microscope:  www.shodor.com

    J.  Creating a recursive design using Geometer’s Sketchpad