Connecting Art and Mathematics

Possibly for students the most surprising connection to math is art. The resources below are proof of that connection through fractals, architecture, tessellations and 3-D geometric figures. Some sites are like art galleries—just for visiting, but others involve students in creating their own artistic designs. All involve significant mathematics!

Cynthia Lanius’ Fractal Unit
A former mathematics teacher created this unit for middle school students. The lessons begin with a discussion of why we study fractals and then provide step-by-step explanations of how to make fractals, first by hand and then using Java applets. But the unit goes further; it actually explains the properties of fractals in terms that make sense to students and teachers alike. Excellent material!

The Fractal Science Kit allows users to generate their own fractals. As stated on the site, “a fractal image is created by evaluating a complex equation or by performing a sequence of instructions, and feeding the results back into the equation over and over again.” But without writing a line of computer code, students can use built-in programs to create beautiful images such as swirling spirals, geometric objects arranged in infinitely complex patterns, geologic designs, and more.

Math-Kitecture, a site on “using Architecture to do Math (and vice versa),” involves students in creating a floor plan of their classroom—not a novel idea, perhaps, but here each step is explained and illustrated, from sketching the classroom to making an exact scale model. In another area, Geometry in Architecture, students are led to recognize the geometric shapes in buildings and other structures.

Classroom Polyhedral Activities
In these lesson ideas for teachers, George W. Hart, polyhedral master, gives ideas and instructions on how to construct polyhedral models from paper, soda straws, wood, and the Zometool kit. Although Hart does not give step-by-step directions here, he does make his ideas clear and shows a picture of each model.

Fibonacci Numbers and the Golden Section in Art, Architecture, and Music
If you are looking for examples of the golden section in the arts, you will enjoy this collection of historical information on its use in the works of Da Vinci, the design of Stradivari’s violins, and even modern architecture. Links to illustrations show the golden section at work.

The Mathematical Art of M.C. Escher
Tessellations and Escher have become practically synonymous! This web site examines the mathematics behind his complex drawings. You will find many examples of Escher’s work, each illustrating mathematical principles such as the tessellations and polyhedra that are common building blocks of his drawings. You may feel the mathematics is beyond your students’ interest, but seeing how Escher transformed basic designs into intricate artworks is worthwhile for students at every level.

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