Object Lessons: Calculus in the KAM

How is art relevant to calculus and calculus relevant to art? Every semester for the past two years, Dr. Stephanie Edwards, professor of mathematics and chairperson of the department, has been bringing her Calculus I and II classes to the Kruizenga Art Museum to consider exactly these questions.

To answer the first question — how art is relevant to calculus — the students begin by learning about the art-making process in which artists break down an envisioned artwork into smaller constituent components and then work out the logistical steps that are needed to transform each component into reality. Students are helped to understand the often experimental nature of art making by looking at a group of preparatory drawings, trial prints and sculptural models that show how artists figure out certain aspects of their artworks, including forms, compositions, and color schemes.

Students begin by learning about the art-making process in which artists break down an envisioned artwork into smaller constituent components and then work out the logistical steps that are needed to transform each component into reality.

Next, the students look at a group of finished artworks that reveal how artists sometimes make mistakes when putting together the different components of their artwork, resulting in passages that are flawed or show obvious signs of correction. In many cases the class is able to reverse engineer the creative process and speculate about how and why the mistakes likely occurred.

Finally, the students are asked to compare the processes of art-making to the processes of mathematical problem-solving. Different students see different parallels between art and math, but most end up agreeing that the processes of both disciplines are similarly creative and dynamic.

Now, the second question: how is calculus relevant to art? Dr. Edward’s students are asked to step into the shoes of a Ming-dynasty Chinese bell maker.

Temple Bell. Chinese, 17th century. Bronze. Gift of David Kamansky and Gerald Wheaton, 2014.23.160.

Now, the second question: how is calculus relevant to art? Dr. Edward’s students are asked to step into the shoes of a Ming-dynasty Chinese bell maker. The students learn that in 17th-century China, bronze bells were made using full-size wax models that were encased in clay molds and heated to melt the wax, leaving a hollow space in which to pour the molten bronze. Because bronze was expensive, bell makers did not want to buy and melt too much of the semi-precious metal, so they calculated the volume of bronze they would need using the dimensions of the wax model.

Hope calculus students do the same thing, but instead of using a wax model, they use a Ming Chinese bell that was cast around 400 years ago. By measuring the bell’s circumference, its thickness, and the length from its crown to its rim, the students are able to use the math skills they learned in class to figure out the bell’s volume, allowing some variation for the bell’s irregular decorative features. Admittedly, there is usually no pressing need to know the volume of an already cast bell, but this class exercise provides an opportunity to apply practical math skills while at the same time learning about an interesting historical artifact.

One last lesson: The bell above would have been used in a Chinese Buddhist temple to call monks to prayer and to meals. It is not like a Western-style bell that is swung and rung with a clapper inside the bell. Rather, bells like this were hung in a stationary position and struck on the side with a padded mallet. It was cast in clay molds using the lost-wax technique. The body of the bell was cast first and then the double-headed dragon loop was cast directly onto the top of the bell later. The Chinese have been using bronze to make both sacred and secular objects since the 3rd millennium BCE.

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