The Mathematics of Sculpture

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.

Work of Art

Hercules Upholding the Heavens depicts a moment in the mythological story of Hercules, a fabled hero of Ancient Greece, the son of the Greek god Zeus and a mortal woman, Alcmene. As a punishment for killing his children in a fit of madness, Hercules was forced to perform twelve tasks assigned by the gods. For one task, Hercules asked Atlas to retrieve the golden apples that were guarded by Ladon, a multi-headed dragon. Atlas entrusted the weight of the heavens to Hercules, which Atlas had been forced by the gods to support on his shoulders. When Atlas returned with the apples, he decided to leave Hercules with the eternal responsibility of upholding the heavens. Hercules asked Atlas if he would take his place just long enough for him to fetch a cushion for his shoulders. Atlas obliged, and Hercules fled, never to return.

Manship’s sculpture depicts a specific moment from this myth—when Hercules is holding the heavens upon his shoulders. In choosing to portray Hercules at this specific moment, the sculptor was able to convey a contradictory sense of energy and action in contrast to stillness. Although his tense, toned muscles suggest that Hercules is in a moment of action, his kneeling position is one of still, motionless contemplation. He grasps a club in his left hand and is cloaked in the protective skin of the Nemean lion—. Both items are Classical attributes and identify the figure as Hercules. Here, man and beast (represented by the lionskin) meld together into one symbol of power.

Despite its imposing size, Manship’s bronze sculpture is sleek and streamlined. The negative space of the sphere is treated with as much importance as the sculpture itself, providing a sense of balance and modern elegance to the massive sculpture. The linear stylization of Hercules’s hair and drapery—as well as his realistic, anatomically correct musculature and proper weight distribution—indicate Manship’s traditional knowledge and technical skill, as well as the influence of ancient Greek art.

Commissioned by Charles M. Schwab in 1918 for display in his outdoor garden, the sculpture functions as a sundial of heroic size. The finely modeled bronze bands of the open sphere have the names and symbols of the zodiac, representing the heavens, inscribed in relief. Additionally, Roman numerals are etched in the center of the sphere to indicate the hours of the day. The juxtaposition of the classical, realistic elements with the sleek and streamlined further contributes to the modern tone of this sculpture.

While in Europe, Manship was greatly influenced by classical works and subjects that became recurrent motifs in his works. The influence of the Art Deco movement inspired him to use bold lines, geometric shapes, and streamlined forms—making the artist and his works of art intensely modern for his time.

Conversation

• What do you first notice about this sculpture? Describe the figure and the various objects that he holds.
• What clues reveal that this work of art is part of a larger narrative?
• Consider the posture of the figure. What does his strained pose reveal about the narrative?
• This sculpture depicts a specific scene from the mythological story of Hercules holding the world on his shoulders. Why do you think the artist would choose this specific moment within the narrative?
• Describe how the sculpture depicts both a sense of action and stillness.
• What elements does the artist incorporate to achieve a sleek and streamlined effect despite its monumental size?
• What does the inclusion of negative space within the sphere add to the sculpture? How does the sphere balance with the figure of the man?
• Compare this work to sculptures from ancient Greece that emphasizes the beauty of anatomically correct bodies. How is this sculpture similar to its archaic predecessors?
• On the other hand, how does the artist modernize the work so that it feels fresh compared to ancient Greek works of art?

• What does the monumental size of the figure add to this work? How would the tone of the work change if the sculpture were table-top size? What if it were placed on the ground instead of on a pedestal?
• Even though the figure struggles to hold the world on his shoulders, how is his strength and heroism revealed?
• How would the message of this work be different if Hercules was depicted standing upright and without any signs of struggle? Do you think the sculpture would be as powerful?
• Consider the culture of America at the turn of the century. Why do you think the artist would chose to create a sculpture that uses both classical and industrial references to honor the past, as well as the present?
• Explain how this work can be viewed as a celebration of modernity.
• This sculpture was originally intended to be displayed in an outdoor garden. Does that change the meaning of the sculpture? Why or why not?
• What associations do we hold for works of art that are placed in gardens or public spaces? How does this work carry the same monumental and grandiose tones of public sculptures that honor heroes?
• Explain how this work can be viewed as a celebration of modernity.

Hercules Upholding the Heavens portrays the ancient Greek hero performing the eleventh of his twelve labors. Hercules asked the Titan, Atlas, to retrieve golden apples that were guarded by a dragon. Hercules assumed Atlas´s burden, upholding the heavens, while Atlas captured the apples. When Atlas returned he attempted to leave Hercules with the responsibility of this enormous weight. Hercules outsmarted him, however, by asking if he could fetch a cushion for his shoulders, before fleeing the scene forever.

The artist, Paul Manship, was one of the most important American sculptors in the 1920s and 1930s. What clues has he given that you are looking at a great hero? Describe how Hercules feels at this moment.

Subject Matter

When creating a large sculpture, artists must often consider both the function and the stability of the final piece. This lesson explores those considerations, using mathematical skills and geometric formulas needed to build a working sundial.

Assessment

1.  Study the sculpture, Hercules Upholding the Heavens.

View Explore the Art in the Learn about the Art section with your students and ask the following question:

• This work of art was originally commissioned as a garden sundial.  Why do you think the artist chose this particular subject matter for a sundial?

 

 

2.  Create a working sundial.

Following the steps below, students will create a sundial and examine the ways in which accuracy is needed to create the device (see Handouts section for diagram).

• On paper, draw an 18 centimeter line segment and put a point on the line at the 9 centimeter mark.  Set the compass for a radius of 9 cm and put it on the center point and draw a semicircle.
• Line up the protractor at the 9 cm mark and start marking off every 15 degrees.
• Draw line segments through your degree marks.  The perpendicular line segment will be 12:00 noon.  The other markings go from 6:00 a.m. to 6:00 p.m.
• Glue the sundial base to cardstock and cut out the semicircle.
• On paper, draw a right triangle with legs of 12 cm and 9 cm.
• Draw a tab at the bottom of the triangle.
• Glue the triangle (called a gnomon) to cardstock and cut it out.
• Mount the triangle to the base by either gluing the tab to the base or cutting a slit through the perpendicular line and putting the tab through and gluing it down.
• The sundial should be placed on a flat level surface.  The gnomon should be aimed due North.

3.  Investigate sundials using mathematical formulas. 

 Have students respond to the questions using the Sundial Diagram in the Handouts section.


4.  Consider the artist as mathematician.

• Why do you think a sundial would be an important feature of a garden?
• Reflecting on the process of creating a sundial, what skills did Manship need to possess in order to be able to create a working sundial?

Conclusion

Ask students to share their work. What strategies did they use to solve the problems? What obstacles did they encounter as they built their sundial?

Extensions to the lesson

Math: Armillary Spheres
Using Hercules Upholding the Heavens as a model, have students research and create armillary spheres. 

Science: Examining Sundials
Have students research the history of sundials, as well as identify patterns in shadows.  Discuss how shadows may be used to tell time and identify the seasons.

Language Arts: What´s in a Word?
Mythology´s influence is evident in art and language.  Have students research the history of words that come from Greek myths.  For example, what does it mean to have an "Achilles heel" or to make a "Herculean effort?"  Ask students to speculate on the meaning of some modern-day expressions and then research the definitions to compile a class mythological dictionary.

 

Resources

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