Art museums present outstanding opportunities for math connections for students of all ages. "The visual arts should be used to make mathematics visible to the body's eye, not to keep it confined to the mind's eye as they usually are," Piergiorgio Odifreddi, Professor of Mathematical Logics at the University of Turin. Recognizing mathematical properties in a work of art enhances the appreciation of the art object, regardless of whether the artist intended to incorporate mathematical ideas into his or her work.
Connections between mathematics and art are ubiquitous and the intricacies of art can be understood and described using mathematical concepts. The following examples from the Cooper Hewitt, Smithsonian Design Museum in NYC, provide a glimpse of the types of mathematical questions to discuss with your students to enrich their appreciation of art and reinforce their understanding of math.
1. Cabinet on Stand, 1665-1700, England. There are many repetitive patterns and types of symmetry applied in this design. Identify them. Explain why the patterns and symmetry, project a strong sense of harmony, despite the complexity of the design.
2. Platter, 1888-98, William Fend De Morgan, England. Although the shapes differ, there is still symmetry in the design. What is the name of the polygon formed by the 16 figures on the outer edge of the plate? What are the total degrees of the internal angles of this polygon? What is the name of the polygon formed by the inner 6 figures? What are the total degrees of the internal angles of this polygon? Using this information, derive the formula for the interior angle sum for any convex polygon.
3. Tazza, ca. 1720, manufactured by Clerissy Factory, France. What types of symmetry are evident in this design? How many times is the design on the edge of the plate rotated, without changing the object, in a full circle? What is the angle of rotation? Describe how the symmetry and angle of rotation changes from the outer edge towards the center of the well.
4. Poster, Stephen Frykholm, ca. 1978. In math, the four color map theorem states that no more than four colors are needed on a map so that no two adjacent regions have the same color. Using the following poster, explain why.
5. Tile (Iran) 1301-50. The geometric designs and calligraphy of Islamic art include many elements of symmetry, including combinations of repeated shapes that may have been overlapped or interlaced. Describe the tile in this geometric context.