Of the many connections between mathematics and art, none is stronger than the shared concept of symmetry. Mathematicians find symmetry pleasing in geometry, physicists find it pleasing in the study of motion, poets appreciate it in the play of words, and artists employ it in the creation of beauty.

Thou shalt remain, in midst of other woe
Than ours, a friend to man, to whom thou say’st,
‘Beauty is truth, truth beauty,—that is all
Ye know on earth, and all ye need to know.’
—John Keats, from Ode on a Grecian Urn

Symmetry and Balance in Art and Math

This lesson, designed to accompany the teaching of geometry, examines mirror (line) symmetry and its effects on the viewer.

PA Academic Standards:

Mathematics: 2.9.3.F,G,H (Identifying and demonstrating symmetries)
Art: 9.4.A (Aesthetic interpretation)

New Jersey Academic Standards:

Mathematics: 4.2.A (Geometric Properties)
Art: 1.4 (Aesthetic Responses & Critique Methodologies)

Grade Level:

For grades 7–9, with modifications for elementary and high school

Art Images Required:

(A note about images: All images listed can be found by searching the collections at the Museum’s website. Images that are available from ARTstor are also indicated; typing this exact search phrase will direct you to the specific image from the ARTstor database.)

• Cushion Cover, artist/maker unknown, Turkish
  ARTstor: “1876-1523”
• Handkerchief, artist/maker unknown, Belgian
  ARTstor: “1889-34”
• Yaqui Church, by Edna Andrade
  ARTstor: “2003-56-1”
• Point on Point, by Sophie Taeuber-Arp
  ARTstor: “1952-61-120”
• Painting No. 4 (A Black Horse), by Marsden Hartley
  ARTstor: “41822000925501”

Background:

Students need to be introduced to the following terms (often used synonymously): mirror/line symmetry.

Lesson Process:

• Put both of your hands on your desktop, with thumbs touching. Imagine a straight line drawn vertically, dividing your two thumbs. Note how the image of your hand on one side of the line is a mirror image of the image of your hand on the other side of the line. This “mirror image” is called mirror symmetry, or line symmetry (referring to the vertical line between your thumbs).
• Look at the Cushion Cover. Made in Turkey in the early seventeenth century, this textile shows line symmetry. Draw the line which shows this symmetry. If you draw a line horizontally through the middle of the cover, would that also be symmetrical? Explain.
• Now look at the Handkerchief from Belgium during the mid-1800s. Does this show line symmetry? How many lines could you draw that would reveal two symmetrical sides? This handkerchief shows four-line symmetry. (NOTE: Students typically see two lines, the vertical and the horizontal. Actually, there are four, since the two diagonal lines also create symmetrical sides.)
• Artists can use symmetry to provide a pleasing image, without necessarily making everything in the painting symmetrical. Compare the following two paintings and discuss how the artist uses (or decides not to use) symmetry, and the effect it has on the viewer of the work. View Edna Andrade’s Yaqui Church and Sohie Taeuber-Arp’s Point on Point. Notice how the purposeful break from symmetry draws your attention.
• Summarize the effects of symmetry with an examination of Painting No. 4 (A Black Horse), by Marsden Hartley. Be sure to discuss both symmetry and non-symmetry.

Assessment:

• Discussion: How does the concept of symmetry appear in music, architecture, poetry, and nature? Usually, we find symmetry appealing; can the lack of symmetry also be appealing?
• Formative assessment through ongoing discussion and/or written response to discussion questions.
• Summative assessments:
  • Find images of two or three objects selected to show mirror symmetry. Describe these forms of symmetry in the objects selected.
  • What is the effect of the artist’s use of symmetry? Use two of the images discussed earlier to examine the effect of symmetry on an audience.
  • Design the package for a product (cell phone, candy bar, etc.) where the design is basically symmetrical, but uses a break from symmetry to draw attention.

Extension and Remediation:

• Use any of the images listed below to continue your discussion of symmetry:
  • Face Vessel, attributed to Thomas J. Davies Pottery
    ARTstor: “1904-36”
  • Kimono, artist/maker unknown, Japanese
    ARTstor: “1985-79-1”
  • The Ascension of Saint Mary Magdalene, by Master of the Johnson Ascension of Saint Mary Magdalene
    ARTstor: “PMA.cat.75”
• Find examples of symmetry and the purposeful break from symmetry in other disciplines
  • poetry
  • music
  • architecture

For more information, please contact Education: School & Teacher Programs by phone at (215) 684-7580, by fax at (215) 236-4063, or by e-mail at .