## 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.

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.

## Before a Turtle Can Perform…

…we must prepare. Many people experienced an outstanding performance by the Turtle Island Quartet, winners of two Grammy awards and leaders in crossing the jazz and classical lines. They returned to Hope College with jazz pianist Cyrus Chestnut on Nov. 9 and the Concert Hall at the Jack H. Miller Center was alive with creativity. But that 7:30 p.m. performance is actually the last part of a very busy day of preparing for the artists and the artists preparing for the performance.

9:00-11:00 a.m. Piano tuning.

Long-time Hope piano tuner Kelly Bakker knows the instruments well and has tuned thousands of pianos, including many for the legendary artists that have crossed Hope’s stages over the years.

11:00 a.m. – 2:30 p.m. Technical Setup.
Technical Director Erik Alberg and Asst. Technical Director David Johnson work on meeting the needs of the technical rider. Although a string quartet, the Turtle Island Quartet is wired for sound. The rider tells Erik everything from what types of chairs they require (piano benches are often favored by cellists), where the chairs should go, and how the technical equipment should be arranged. Erik makes a call on pulling out the back wall to create a sound shell and will adjust the drapes along the walls to either enliven or deaden the sound. The rider gives details, but creating the right balance is an art. Erik has been doing this for a long time with all levels of artists and he has the art part down. In the midst of all this, Drew Elliott, sound engineer for the Music Dept. hops in to make sure all the sound is connected to his software since the quartet has requested a recording of the performance.

2:30 – 3:30 p.m. Masterclass.
Before they take the stage, all of our artists connect with the community in different ways. This time, it was a masterclass with two Hope College student ensembles under the direction of faculty member Mihai Craiovneau. A music masterclass typically consists of students performing a prepared piece before an artist and then receiving feedback on their work. There is usually some give and take and the piece always sounds different by the end. Of course, leave it to the Turtles (as they often refer to themselves) to throw a wrench in the normal. Two members of quartet, including founder David Balakrishnan, listened to both a quartet and octet perform. They gave some feedback. And then they went all jazz on them having them work on a piece Balakrishnan wrote and teaching the students how to improvise. String players are not always encouraged to go off the printed page, but in this masterclass, it was a requirement. And the students were clearly enjoying the challenge. At the end, Balakrishnan dubbed them “honorary Turtles.”

“You can tell this is a strong department because the strings are strong. Usually the toughest area,” Balakrishnan commented later.

3:30 – 5:45 p.m. Soundcheck and rehearsal.
With the masterclass done the remaining quartet members arrive with Chestnut for soundcheck and rehearsal. Without fail, our artists are always impressed with how prepared Erik and David are with their requests. As a result, they just have to fine tune the equipment hookups and then quickly get to hearing how it sounds. Again, with our technical staff skills, what could be a two hour process is done quickly, leaving the quartet and Chestnut time to simply rehearse. And they rehearse hard. Some pieces go straight through, but there is a lot of starting and stopping and repeating until they get to where they want.

5:45 – 7:00 p.m. Eat and Change.

Like most artists, the groups goes past their scheduled rehearsal time, but they leave it to find a catered meal in the Music Dept. conference room. Well-fed artists are happy artists, and they eat well. A couple change in the Green Room and others run back and change at the Haworth Inn. While they are doing that the ticket office is opening in the lobby and the ushers are getting last minute directions on what they need to do. CDs are set in the lobby and everything is in place for the doors to open. Members of the group also seek out last minute places to warm up.

7:30 p.m. The Performance.
Finally. As a presenter (my role), this is the best part of the day. The group is introduced and I can sit back and simply enjoy another incredible performance along with 700 friends. And what a performance. The quartet opens with two pieces by themselves and then introduce Chestnut, whose light touch on the keyboard works very well with the quartet. The second half starts with two solo pieces by Chestnut before the quartet joins him. A lot of creativity ensues as the quartet and Chestnut are trying this full length collaboration for the first time. They premiered two pieces, including one they had rehearsed for the first time that afternoon! All members of the ensemble take turns introducing the pieces, which include spiritual works from a variety of backgrounds and provide a personal side to the evening. After a full performance, standing ovation, an encore, and then to the lobby to sign CDs and meet the audience, the quartet and Chestnut headed back for the hotel close to 10:30 p.m.

## A Professor-Mother And Student-Son’s Journey “Into The Woods”

*Editor’s note: The Department of Theatre at Hope College will present “Into the Woods” on Wednesday-Saturday, Nov. 14-17, at 7:30 p.m. Tickets are available at the Events and Conferences Office and at the door on performance nights.

My life has always been marked by the productions that I have designed. I know exactly what I was working on when I learned my best friend was getting married, when I learned my father had cancer, when I fell in love, and yes, when I was pregnant with both my children.

Hope College Theatre Department and Hope Summer Repertory Theatre have occasionally produced the same play over the years, but the Theatre Department has rarely repeated a title. In fact, it has only happened once in the 28 years that I have been at Hope.  “Into The Woods” was first produced at Hope in the fall of 1995. I don’t need to look this date up as this is one of those milestone productions for me. I was pregnant and about to give birth in January.  Anne de Velder, the costume shop manager at the time, made a baby quilt for my newborn made out of all of the fabrics I had selected for the costumes in the production.  It is a cherished possession.

I remember the production resonating with me about parenthood, the desire to have a child, and the fierce protection a mother feels about her offspring.

Time passes, dozens of productions grace the stage at Hope, and the baby that was born after the production of Into The Woods is now a senior majoring in theatre at Hope.  What goes around comes around.  The department decides that the time is right to once again produce Into The Woods.  Griffin, who will be 23 in January, is playing Cinderella’s Prince and the Wolf.

My husband and I took Griffin to see this production at Utah Shakespeare Festival the summer before his first year of college.  I remember sobbing through most of the musical because this time, what resonated with me is sending your child out into the woods…..it is scary and frightening, but necessary.

As I watch the dress rehearsals this week, I think about the years that have passed.  It is time for my son to take his next journey.  He is graduating in December and will be starting a contract with the Missoula Children’s Theatre. It is an exciting program and he will be touring the country in the spring connecting with hundreds of young people.  This will be Griffin’s last performance at Hope.

Every year at graduation, I am heartbroken when my students whom I have shared many hours of collaborative work and have become friends and colleagues must leave Hope. I am, of course, excited for their new adventures and am delighted that I stay in communication with most of them.   But the heart cracks a bit.   Just when I think I can’t do it again, the next fall an enthusiastic first year student appears in my office and I think, “Ok, here we go again.”

“Into the Woods” version 2018:  I will be the one crying in the audience when our beautiful Cinderella, Olivia Lehnertz, sings,  “You Are Not Alone.”

Mother cannot guide you
Only me beside you
Still, you’re not alone
No one is alone
Truly
No one is alone
I wish…
I know
Mother isn’t here now
Wrong things, right things
Who knows what she’d say?
Who can say what’s true?
Nothing’s quite so clear now
Do things, fight things
You decide, but
You are not alone
Believe me
No one is alone (No one is alone)
Believe me
Truly
People make mistakes
Fathers
Mothers
People make mistakes
Holding to their own
Thinking they’re alone
Honor their mistakes
Fight for their mistakes
Everybody makes
One another’s terrible mistakes
Witches can be right, giants can be good
You decide what’s right, you decide what’s good
Just remember
Just remember
Someone is on your side (Our side)
Our side
Someone else is not
While we’re seeing our side (Our side)
Our side
Maybe we forgot, they are not alone
No one is alone