Habits of Mind

  • Synthesize

Transformational Geometry

Discussion through works of art encourage how to approach ambiguous and complex ideas, thoughts, and feelings. The MFAH offers a democratic space where students and teachers can develop, practice and articulate these habits of mind. Remember that the quality of the conversation is what is important, not finding the artist’s “answer.” Slow down and take the time to make careful observations. Talk about what you notice, and try to avoid jumping to conclusions and interpretations. Be sure to give enough time for silent looking and thinking.

This Curriculum Connection also includes Crown, Nias Island, Indonesia.

Curriculum Objectives

  • The student will be able to use the art to identify and apply mathematics to everyday experiences, to activities in and outside of school, with other disciplines and with other mathematical topics.
  • The student uses transformational geometry to develop spatial sense. The student will generate similar figures by graphing rotations, reflections, and translations on a coordinate planes
GRADE LEVELS


SUBJECT AREA


HABIT OF MINDS

After teaching and discussing symmetry and its applications in math, you can use this necklace as a warm-up to explore transformational geometry, and discuss the value of symmetry in the real world.

First, look closely at the work of art together, as a class. Then, do the following activity to test students’ knowledge and explore transformational geometry.

  1. Hand out or project images of the artwork. Guide students to draw and label a coordinate plane on the necklace, where the x axis crosses the hinge and the y axis runs through the center line.
     
  2. Look closely at the many gems set into the necklace. Using individual gems as vertex points, draw a shape on the necklace.
     
  3. Explore transformations of that shape, drawing each new reflection on the grid. Use the following prompts as a starting point, or explore your own ideas:
    1. Reflect the shape across the X axis
    2. Reflect the shape across the Y axis
    3. Reflect the shape over the line x= -1
    4. Reflect the shape over the line y=-2
    5. Choose a line to reflect the shape over; label that reflection with the line you reflected it over.
    6. Rotate the shape 90 degrees clockwise about the origin
    7. Rotate the shape 180 degrees counter-clockwise about the origin
    8. Translate the shape 5 left and 3 down
    9. Translate the shape 4 to the right.
       
  4. Analyze the results of your transformations.
    1. Are there lines of symmetry in this necklace? Where are they?
    2. Did your transformed shapes help you locate any lines of symmetry? How?
    3. What type of symmetry does this necklace exhibit?
    4. Imagine that the necklace had no symmetry. How might it look or feel different? Why might the artist have chosen a symmetrical design?

  • Describe the shape of this piece. Does it look like a necklace you could wear today? Why or why not?
  • Consider how it might feel to wear this necklace. Do you think it would be light or heavy?
  • Describe the placement of the gems. How does the artist create balance?
  • How do the colors of the stones give balance to the piece? Do you think the colors are soft or strong?

  • Considering the materials and ornate nature, what type of occasion do you think this item would have been worn to?
  • What can you infer from this necklace about the important of ritual within the Balinese culture?
  • Can you tell if the individual wearing this piece would be wealthy or a regular person? Why
  • Do you think this is an object meant for decoration or as a functional object? Explain your answer.
  • From the earliest times people in Indonesia believed that gold and gems were empowered with supernatural force: How does this add to your interpretation of the necklace


               Use these questions in a discussion as a warm-up to a unit or lesson.

  • Describe the shape of this piece.
  • Describe the placement of gems. How does the artist create balance?
  • Did you know: From the earliest times people in Indonesia believed that gold and gems where empowered with supernatural force: What does that tell us about this piece?
  • This is a 22-karat gold necklace set with rubies, sapphires and diamonds. A king wore it. There is a central alignment of the gemstones that run along the middle of the necklace. They are balanced in terms of color, size and shape (round, oval and rectangular).
  • What does this show about the necklace? [It is symmetrical]


This elaborately worked neck ornament in 22 karat repoussé gold (shaped by pressing the designs from the reverse side) is lavishly set with rubies, sapphires, and diamonds. This extraordinary piece was worn by the king, with the larger part on his chest and the smaller on his back. While exact dates are difficult to ascertain, it would seem that the necklace was created circa 1890. Commissioned by the palace of Singaraja, it and a second necklace were fashioned for an important wedding ceremony—a pair for the bride and groom. The necklace was likely used only once, due to its preciousness and value, and then preserved by the family. Made from heavy pure gold, rare for Balinese jewelry, the necklace indicates that this royal family was particularly affluent.

 

Scattered over the equator like a string of pearls, the Indonesian archipelago ranks as the largest in the world. A country composed of more than 17,000 islands located north of Australia and south of Malaysia, it is a crossroads of trade, allowing contact with merchants from China, India, Arabic lands, and Europe. Many islands developed individual artistic styles that were also influenced by these foreign cultures. No other country offers such variety of people, culture, and landscape. It is home to the world’s major religions—including Islam, Hinduism, Christianity, Buddhism—and indigenous beliefs and traditions. The terrain ranges from lush tropical rain forests to snow-covered mountains, pristine beaches with coral reefs, and shrub lands.

 

Indonesia ranks as one of the largest gold-producing countries in the world. An ancient name for Indonesia was Svarnadvipa, a Sanskrit word meaning "Island of Gold." From earliest times, its peoples believed that gold and gems were empowered with supernatural force. Gold is deeply symbolic in many Indonesian cultures and signifies public representation of political power and kinship, rituals and myth. It is a sign of aristocratic standing and nobility of character. A portable form of wealth, it is easily displayed and carried on the body as a public assertion of high social position. Jewelry is placed in two main categories: heirloom pieces retained by the family as house treasures and kept in sacred areas to be worn only during special rituals; and jewelry exchanged during marriage. Gold is considered “masculine” and is gifted by the groom’s family to the bride.

 

Thanks to Mr. Alfred Glassell Jr., our collection of Indonesian gold ranks as one of the largest outside the archipelago.


The Learning Through Art program is endowed by Melvyn and Cyvia Wolff.

The Learning Through Art curriculum website is made possible in part by a grant from the Institute of Museum and Library Services.

All Learning and Interpretation programs at the Museum of Fine Arts, Houston, receive endowment income from funds provided by the Louise Jarrett Moran Bequest; Caroline Wiess Law; the William Randolph Hearst Foundation; The National Endowment for the Humanities; the Fondren Foundation; BMC Software, Inc.; the Wallace Foundation; the Neal Myers and Ken Black Children’s Art Fund; the Favrot Fund; and Gifts in honor of Beth Schneider