I just finished teaching another Light, Math, and Color minicourse. Twenty students researched a math topic and illustrated it with a stained glass window. Their projects this time around are really spectacular, especially considering these are first tries. (Note: If you hover over a picture, the math topic it illustrates will show up.)
In a earlier post, I explained the steps involved in making an artglass window using lead came. In this one. I’ll show you how to make a window using the copper foil technique. This technique is good for smaller pieces, and designs that have a lot of detail.
I’ve been using Desmos to brainstorm window designs. It’s so easy to plot polar graphs with it, and they usually have a lot of symmetry. For this particular design, I played around with a tangent plot. In Desmos, I entered r = a*tan(b*theta) + c, and created sliders for a, b, and c. Then I adjusted them until I found a promising design; in this case a = 1.8, b = 1.6, and c = 5.3:
Next, I printed out the design and traced it onto a large sheet of paper. This will be my working pattern, called a cartoon:
Now comes the most time-consuming step: cut all the pieces of glass to fit into the cartoon. I decided to go with green in the center, then alternate clear, blue, and yellow pieces as you work out from the center. Here are the pieces of glass as I cut them in stages:
Once all the pieces are cut (make sure there are no pieces overlapping their boundaries), I wrapped them in copper foil tape. It’s exactly like it sounds: copper with a sticky backing.
Now the window is ready for soldering. I brush all the copper with flux (a chemical that enables the lead/tin solder to adhere to the copper tape), and then use a soldering iron to melt the solder onto the tape. I do this on both sides. On the front side, I add more solder to “raise a bead” and make it look finished. Here’s the result:
The ease with which Desmos plots complicated polar equations makes it an ideal tool to design symmetric artglass windows. I think this is the beginning of a beautiful relationship!
Update: I’ve made three more windows using Desmos.
This one uses the polar plot of r = 1.9tan(0.3θ) – 5.1:
r = 0.3sec(1.6θ) – 3.65:
r = sqrt(10sin(3.3θ)) – 6:
And two more:
r = -2.8³√(csc(0.6θ) + 0.8):
r = tan(0.5θ) + sin(0.8θ):
Every year, for three weeks between semesters, Harpeth Hall offers an alternative curriculum for its freshmen and sophomores (Juniors and Seniors do off-campus internships and travel). I have taught a course on designing and making stained-glass windows that incorporates mathematical topics. My students always rise to the challenge, and this year was no exception.
The girls’ projects included a series of small windows representing the Platonic Solids, the Four-Color Theorem, Ptolemy’s Theorem, the Butterfly Theorem, Napoleon’s Theorem, Morley’s Trisector Theorem, and an Ulam Spiral, among many others.
I’d also like to recommend to my readers an excellent publication and blog devoted to fostering girls’ interest in mathematics: Girls’ Angle. Their latest blog post and print issue feature some pictures of previous Math, Light, & Color students’ work. If you are looking for an engaging and beautifully laid out resource for your math students, I highly recommend Girls Angle!
Without further ado, here are this year’s projects. Enjoy!
For several years now I’ve taught a three-week course on making artglass windows. After learning the basic technique, I ask each student to research a math-related topic and illustrate it with an artglass window. This year’s group did exceptionally good work! The projects ranged from perennial favorites like the Pythagorean Theorem and tessellations to some new topics – tesseracts, Borromean Rings, and Johnson’s Circle Theorem.
Pictures of their projects are below: