1. Saturday Math Series April 12, 2003 Presented by Dr. Eddie Fuller Department of Mathematics Institute for Math Learning West Virginia University

2. Mathematics in Art and the Art of Mathematics Symmetry and Patterns in Our World and the World of Math

3. Mathematics Defn: (Websters) The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols. “Mathematics is often defined as the science of space and number … [but] a more apt definition [is that] mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns … Applications of mathematics use these patterns to ‘explain’ and predict natural phenomena …” (Steen, L.A. (1988), The Science of Patterns, Science, 240, 29, 616.)

4. Is There Art in Math? What is Art? Depends on who you ask. Defn: An object that has meaning or function that goes beyond any practical purpose. Defn: the conscious use of skill and creative imagination Bertrand Russell once said that "mathematics rightly viewed, possesses not only truth, but supreme beauty."

5. There Can Be! A part of math is learning how to do the basics: arithmetic, factoring, solving, functions… All of these things are used outside math in the real world to solve problems every day Once you master these math can become a tool for expression and exploration, just like learning to put paint on a canvas can become something beautiful

6. Math, Art and Patterns Really, math is about patterns and how to use them. Example: Suppose you notice that 2x1=2, 2x2=4, 2x3=6, 2x4=8, 2x5=10…You conclude that anytime you multiply an integer by two, you get an even number.

7. More Patterns: Data Analysis Math is sometimes about understanding data Example: Suppose someone gives you a chart of temperatures of a cup of hot water every minute for five minutes What can you conclude? Time (min)012345 Temp (deg)120110100908070

8. Graphing: Visualizing Patterns You can plot these points, thinking of time in the horizontal and temperature in the vertical directions What you see is then a straight line trough the points Conclude: change in temperature is constant Use this to predict temp in between readings!

9. The Theme Represent structure and pattern in ways that are informative Structure and pattern can also be appealing for other reasons The most informative patterns are often the most appealing

10. The Mathematical Association of America Math Awareness Month, April 2000 http://mam2000.mathforum.com/918/index.html

11. More MAA April 2003: Mathematics Awareness Month http://mathforum.org/mam/03/

12. More Artistic Displays Tom Banchoff's Artwork Home Page Math Art Gallery Math & Art John Robinson's Sculpture Sculpture and Mathematics Geometry and Art (Quilts, Pottery, Celtic Knots) Geometry and Art (Quilts, Pottery, Celtic Knots)

13. More Mathematical Stuff Bridges Conference Mathematics and Knots Mathematics and Pattern in Nature

14. Thanks for coming! Eddie Fuller ef@math.wvu.edu http://www.math.wvu.edu/~ef/