Course Idea
Mathematics in Architecture is a course for students who want to see mathematics not only as a set of techniques, but as a way of noticing, describing, and understanding the built world.
The course studies significant buildings and architectural traditions through the mathematical ideas that help explain their beauty, structure, and design. Students encounter geometry, proportion, symmetry, forces, equilibrium, coordinates, and modeling in conversation with architecture from the ancient world to the modern era.
The goal is not simply to use buildings as examples of mathematics. Rather, the course asks how architecture can make mathematical ideas visible, and how mathematics can deepen our appreciation for architecture.
Why Architecture?
Architecture is one of the places where abstract mathematics becomes concrete. A curve becomes an arch. A symmetry becomes a pattern. A proportion becomes a room that feels ordered. A force diagram becomes a building that stands.
In this course, mathematics is approached as a human activity: something connected to history, culture, beauty, experiment, intuition, and design.
Geometry and Proportion
Students study how geometric ideas shape architectural design, from classical constructions and proportion to perspective and spatial reasoning.
Structure and Forces
Buildings must not only look beautiful; they must stand. The course uses mathematical models to understand arches, domes, trusses, and equilibrium.
Pattern and Symmetry
Symmetry offers a bridge between mathematical structure and visual design, especially in architectural traditions that use repetition, transformation, and ornament.
Historical Arc
The course follows a broad historical path, using major architectural examples to introduce mathematical ideas in context.
- Greek geometry and the Parthenon
- Roman arches, forces, and the Pantheon
- Symmetry and Islamic architecture
- Romanesque and Gothic structures, trusses, and cathedrals
- Coordinates, three-dimensional thinking, and the Duomo of Florence
- Renaissance proportion, perspective, Palladio’s villas, and St. Peter’s
- Modern arches and domes, including Hooke’s principle and structural models
How Students Learn
Students work through mathematical ideas by solving problems, discussing buildings, reflecting on their learning, and connecting abstract ideas to physical spaces.
Projects and Reflection
The course includes opportunities for students to investigate buildings, communicate mathematical ideas clearly, and reflect on how their understanding develops over time.
A Different Kind of Mathematics Course
Mathematics in Architecture is designed especially for students who may not initially see themselves as “math people.” The course emphasizes curiosity, careful observation, communication, and the ability to connect mathematical thinking with human creativity.
Students are invited to take intellectual risks, revise their thinking, and focus on understanding rather than simply chasing points. The aim is for students to leave the course with a deeper appreciation for both mathematics and the built world.