Geometry Meets Architecture

The Upper School hallways have undergone an architectural transformation this term, with freestanding arches now gracing windows and adorning locker tops. Joe Buteau’s students have been applying the principles of geometry as they design and construct carefully measured and hand-cut cardboard arches. The Roman Arch Project concludes the class’ study of quadrilaterals and special quadrilaterals and links math, history, and design in an immersive, hands-on task. 

Before starting the project, students learned about the history and application of the arch in architecture and why its uniquely strong design made it a game-changing innovation. They learned vocabulary specific to arch construction, such as keystone, voussoirs, rise, and span. Working in small groups, students began by selecting a location in the Root Building for their arch. Some groups decided to work on a small scale, designing an arch for a classroom window. While others chose to build arches that spanned a row of lockers. Students took measurements and set to work designing their arches on paper, ensuring that the span and rise of their arch would fit in the space they had chosen. 

Instead of moving directly from design to build, each group transferred their design to Adobe Illustrator, which many students had already used in Fay’s design curriculum. The program allowed them to virtually build their arches to scale and test them to ensure their calculations were correct, the arch would sit flat, the voussoirs would fit, and the finished arch would be the right size for the chosen space. Testing their designs in Illustrator first gave each group confidence in their design, says Joe, because they could make any adjustments before cutting the cardboard. During the week it took to build each arch, students still had to work through some frustrations. “Time Management was a challenge because we needed to make sure everything was right, and when we realized that some of the pieces were wrong, we had to go back and remeasure and recalculate everything,” says Charlie G. ‘25.

Throughout the project, students tracked their progress in their math journals, documenting their plan, progress, and any challenges they encountered. After completing the arch, each student also reflected on the experience with a project report paper where they summarized the experience, evaluated the success of the arch, and discussed the geometry concepts that were essential to the design.