Building Harmonographs: Bridging Maths and Art at Waterloo, Canada

Bridges Lecture Series

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.

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.

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).

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.

 

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.

 

 

 

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

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.

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.