Building Harmonographs: Bridging Maths and Art at Waterloo, Canada

Bridges Lecture Series

St. Jermoe's University, Waterloo, Canada

St. Jerome’s University, Waterloo, Canada

I spent the last week of February in the land of maple syrup, ice wine and snow. The Bridges Lecture Series is a collaborative project managed by Professor Benoit Charbonneau, Department of Pure Mathematics University of Waterloo, and Professor Alysia Kolentsis, Department of English St. Jerome’s University. Mathematicians and artists make joint presentations in a series of lectures hosted by St. Jerome’s University, on the same campus.

harmo image 8

A drawing made by a harmonograph

I was invited to collaborate with Professor John Baez, mathematical physicist and prolific blogger from U.C. Riverside. The subject of our collaboration was the harmonograph and pendulum frequencies. Harmonographs were invented in the 19th century as an outcome of scientific research into pendulum oscillations and sound frequencies. When two or more pendulums mounted perpendicular to one another are fitted with a pen and a paper, their movements cause them to draw fascinating patterns which are in fact visualizations of the combined frequencies of their swinging. You can see our Bridges presentation slides, along with an interactive digital harmonograph and other resources on John Baez’s web page The Harmonograph.

I was asked if my harmonograph Iron Genie could make the assignment with us, but alas, it is so heavy and large, we could not afford to transport it! We had a better idea – I would spend the week running up to the lecture with a select group of students, making new harmonographs to present at our lecture. And so I got to work in Waterloo University’s Department of Art & Design with art students, computer science students, and Adam Glover, the wonderful technician who worked with us to realize our project.

1 Adam and students

Adam Glover in the Art & Design workshop with students Stephanie and Laura

I brought a lot of resources and plans with me, and Adam had been busy sourcing materials prior to the workshop, so we were ready to go, first thing on a chilly Monday morning. So here is a photo journal of an intensely creative four days, in which we made two types of harmonograph: a three-pendulum Rotary Harmonograph (like the Iron Genie) and a two-pendulum Lateral Harmonograph (like the Newton model at the London Science Museum).

Sophia and Yomna measure out the table top for the rotary harmonograph

Sophia and Yomna measure out the table top for the rotary harmonograph

We began by marking out the measurements for the harmonographs’ table tops, their dimensions governed by the placement of the pendulums that drive the drawings. Once the trajectories of the pendulum movements are taken into account, one can get creative with the shapes of the table tops. The students tried out a variety of organic curved shapes, eventually coming up with an elegant kidney-shape for the lateral harmonograph, and a clever grand-piano design for the rotary harmonograph.

Elspeth, Reza and Sophia designing the shapes of the table-tops

Elspeth, Reza and Sophia designing the shapes of the table-tops

 

Ju Hyun cuts the curves on a band saw

Ju Hyun cuts the curves on a band saw

For some of the students this was the first (and exciting) time they had used power-tools in a workshop, expertly guided by Adam Glover.

Ju Hyun attaching the legs to the table-top

Ju Hyun and Elspeth attaching the legs to the table-top

 

Yomna, Reza and Sophia preparing laser-cut piano keys for the rotary harmonograph

Yomna, Reza and Sophia preparing laser-cut ‘piano keys’ for the rotary harmonograph

 

Sophia, Yomna and Reza attaching the laser-cut piano-keys

Sophia, Yomna and Reza attaching the decorative piano-keys

 

Trying out solutions for the drawing arm on the lateral harmonograph

Trying out solutions for the drawing arm on the lateral harmonograph

There were some problem-solving challenges. Minimising lateral movement on the drawing arm of the two-pendulum harmonograph was one of them.

18 John Baez

John Baez watches the lateral harmonograph in action

John Baez came along to see our creations, and to explain a bit about harmonic oscillators and phase space to us. If you want to know a bit more about the science of pendulum frequencies, take a look at John’s Harmonic Vibrations presentation slides.

The completed harmonographs

The completed harmonographs

We finished up with two handsome harmonographs, lovingly designed and crafted by a dream team under the technical supervision of Adam Glover. Set up to demonstrate our talks at St. Jerome’s lecture theatre, they attracted a lot of audience participation, supervised by our dedicated team of students.

For more information on the Bridges Lecture Series please visit https://www.sju.ca/public-events/bridges.

 

 

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