Art Projects Using Geometry

Introduce students to applications of geometry through different art projects

Geometry plays an important role in many aspects of art. From perspective to the proportions of the human body, artists regularly use principles of geometry to create visually appealing, realistic artwork. The following projects for high school-level art classrooms can both improve students' abilities in art and increase their understanding of how theories of mathematics apply to many different disciplines, including drawing and painting.

The Grid Method

Artists have used the grid method for centuries as a way of resizing a smaller drawing or photograph onto a large canvas. Begin by introducing students to the grid method by showing examples of Old Master drawings with the grid lines evident, and the final artworks that were the end products of these designs. Have students choose a photograph or an art print they wish to reproduce. They will measure the dimensions of the image and carefully draw a grid of 1/2-inch squares over it until covered completely. Then they will determine the paper size needed to enlarge their reproduction two or three times, and draw a corresponding 1-inch or 1.5-inch grid on paper for it. Students finish by using the grid to draw their chosen image, using the grid squares to help with accurate angles, lines and placement of objects.

The Golden Ratio

Since ancient Greek times, the golden ratio has been studied and used in many forms of art, including architecture, painting and music. It is an irrational mathematical constant, approximately equal to 1.618, where the ratio of a + b is to a as a is to b, if a is the larger of the two quantities. The simplest form by which to explain the ratio is in the golden rectangle. Golden rectangles are found throughout Renaissance art compositions, where the sides of the rectangle are in the ratio of 1:1.618. Introduce students to the golden rectangle and how they can find it in paintings such as the "Mona Lisa" by Leonardo Da Vinci. Then provide instructions on how to draw a golden rectangle using a ruler and a compass. Explain how a square drawn within the rectangle, to the size of its shorter side, forms another golden rectangle in the remaining section. Students can then create an abstract drawing similar to the work of Piet Mondrian, designing an image utilizing squares and rectangles all following the golden ratio.

One-Point Perspective

Understanding and use of perspective would become a key turning point in the evolution of Renaissance artwork. Present students with an overview of the work of Filippo Brunelleschi and Leon Battista Alberti in the 15th century and their experiments in discovering linear perspective. Show students examples of Renaissance paintings that used these ideas to create depth in their compositions, such as Raphael's "School of Athens." Students can then practice by creating a drawing of one-point perspective, with a vanishing point and parallel lines. The drawing can include geometric shapes such as squares and rectangles, drawn using proper perspective.

Tessellations

M.C. Escher popularized the use of mathematical tessellations in art with his fantastical repeating designs and optical illusions. Introduce students to the basic ideas of geometric tessellations, first regular and then semi-regular. In both cases, the illustration must consist of repeating geometric forms where every vertex has the same configuration, no forms overlap and there are no gaps. Students can then progress to more complex tessellations, using a computer graphics program to create and propagate images that follow the same rules of construction.

References

• University of Georgia; Constructing the Golden Rectangle; Leanne May
• University of Georgia; Golden Ratio in Art and Architecture; Samuel Obara
• Houston Teachers Institute: Geometry and Art, What a Concept!
• Cool Math Lessons: What Are Tessellations?
• "Classical Drawing Atelier: A Contemporary Guide to Traditional Studio Practice"; Juliette Aristides; 2006
• "Drawing School"; Ian Simpson; 1993

Resources

• Tesselations - Escher and How to Make Your Own
• Piet Mondrian