Saturday Math Series April 12, 2003 Presented by Dr. Eddie Fuller Department of Mathematics...

Saturday Math Series

April 12, 2003Presented by Dr. Eddie Fuller

Department of MathematicsInstitute for Math Learning

West Virginia University

Mathematics in Art and the Art of Mathematics

Symmetry and Patterns in Our World and the World of Math

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.)

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."

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

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.

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) 0 1 2 3 4 5

Temp (deg)

120 110 100 90 80 70

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!

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

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

More MAA April 2003: Mathematics

Awareness Month http://mathforum.org/mam/03/

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)

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

Thanks for coming!

Eddie Fulleref@math.wvu.edu

http://www.math.wvu.edu/~ef/