Geometry and Art

By Megan Hancock

Imagine you are a student in a high school Geometry class.  Which scenario sounds more appealing?

1. Your teacher gives notes about different geometric concepts and sometimes shows examples of how to use these concepts outside of the classroom. 
2. You go on a field trip to a geometric art museum and learn about different geometric concepts through studying art.

Most students would choose scenario 2. As teachers, we want our students to see the importance of their high school mathematics courses.  By stepping out of the classroom, students experience the richness of mathematics in the real world, and this allows them to begin to understand the value of mathematics.   

I recently visited The Museum of Geometric and MADI Art in Dallas.  MADI stands for movement, abstraction, dimension, and invention. This museum is filled with bright colored art that is made solely out of geometric shapes.  Much of the artwork in this museum spills off the traditional canvas.  Artwork comes from around the world, and students can also display their own geometric art.  

 

In high school Geometry, students learn about geometric transformations, tessellations, and three-dimensional shapes.  All of these topics are present in most of the artwork found in this museum.  The museum offers workshops and classes for students of all ages to learn about the relationship between geometry and art.  They can create their own three-dimensional artwork inspired by the artwork in the museum.   By incorporating artwork in a Geometry class, I believe students will have a deeper understanding of geometric concepts.  

For centuries, different cultures have been integrating different aspects of Geometry into their artwork.  This artwork could consist of quilts, designs on clothing, sculptures, paintings, or photography.  In the American colonies, women used quilting as a social gathering.  They would use these quits as their artistic expression.  African American women were even able to purchase their freedom from slavery with their beautiful, handmade quilts (Zaslavsky, 1996, p. 145).  Shapes, symmetry, rotation, measurement, tessellations, and reflections are all geometric concepts that are present in quilts.   

When studying tessellations in high school Geometry, students can discover which shapes will tessellate and which will not. The National Council of Teachers of Mathematics (NCTM) created the lesson, “What’s Regular About Tessellations?”, that guides students through the discovery of why certain shapes will not tessellate.  This lesson is geared towards a middle school mathematics classroom, but it could easily be tweaked to fit in a geometry course.  After students understand what makes shapes tessellate, they can create their own pieces of artwork using tessellations.  If the students have already visited The Museum of Geometric and MADI Art, they can use the artwork to inspire their own pieces. 

 Students can also use tangrams in a high school Geometry classroom.  Students probably played with tangrams when they were little, so they would be familiar with them.  Tangrams are interesting because the area will always be the same, but the perimeter will change depending on what shape is created.  Students might assume that the area and perimeter will always be the same if the same shapes are being utilized, but they can discover this is not the case.  A larger unit or lesson could be created around this concept in a high school classrooms, and tangrams could be one of the tools that is provided.  

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By incorporating art in a high school geometry classroom, students are able to understand how the concepts they learn in class are used outside of the classroom.  Students who are interested in art but not mathematics are given an opportunity to use their talents when creating their own pieces of art. As a math teacher, I am always on the lookout for examples of mathematics in the real world.  High school students struggle to see how mathematics relates to their lives outside of the classroom, so by taking students to museums such as The Museum of Geometric and MADI Art, they are able to make connections between mathematics and art.   

Blasjo, V. (2009).  Two applications of art to geometry.  The Montana Mathematics Enthusiast, 6(3), 297 – 304. 

Zaslavsky, C. (1996).  Multicultural math classroom: Bringing in the world.  Portsmouth, N.H.: Heinemann.