A Mathematical Look at our World: “Geometry in Art”

At Lawrence Technological University, mathematics is in the core curriculum. That means that all students at LTU must complete seven credit hours of math, unless your degree program is a Bachelor of Arts.

Why? The goal of the Core Curriculum is to ensure that all Lawrence Tech graduates have the:

• Capacity to evaluate conflicting ideas
• Savvy to seek alternative solutions to problems
• Perseverance to succeed in difficult projects
• Ability to read and analyze challenging works
• Poise to articulate ideas orally and in writing
• Competency to simplify complex problems through the manipulation of symbols
• Discipline to apply scientific principles to improve understanding
• Confidence to be creative
• Knowledge of the past that informs the role of citizens in a free society

For students coming from engineering, architecture and design, media communication and other disciplines where traditional mathematics classes might not work into their educational or career goals, there’s Geometry in Art.

Patrick Nelson, Ph.D., dean of the College of Arts and Sciences, explains, “Geometry in Art is a nontraditional math course, specially designed for the non-traditional student who does not need pre-calculus or calculus.”

The course utilizes things from nature. The ancient Greeks and Roman demonstrated how nature has all these patterns and how math underlies the creation of it all. As a matter of fact, said Nelson, “All these features have a very specific mathematical foundation.”

This course exposes students to many mathematical principles in how buildings are designed and built, in how products are engineered. Nelson invited us to look around: “Everything has a mathematical pattern to it, trees, buildings, the length of the fingers of your hand has a pattern to it, seashells, people’s ears.

“What your eyes perceive as beautiful is because of its geometrical features.”
Yelena Vaynberg

“What your eyes perceive as beautiful is because of its geometrical features. If you look at the features of models’ faces, their eye location fits into a mathematical ratio of approximately 1.6 called the Golden Ratio. In architecture, for example, students look at two things: aesthetics and structure. Is it beautiful and how does it work structurally?”

Geometry in Art has been offered for the last ten years at LTU, originally designed by the late Professor Ruth Favro and now taught by Senior Lecturer in the Math & Computer Science Department Yelena Vaynberg, She says, “I want students to see how math, especially geometry, is deeply connected to art and design. I hope they can apply what they learn not only in their other classes, like architecture or digital design, but also in their future careers. I want them to recognize patterns, proportions, and shapes in everything they do and use these ideas to improve their creativity and problem-solving skills.”

The title of the textbook hints strongly at her wish for her students: The Heart of Mathematics: An Invitation to Effective Thinking.

“Geometry teaches students to think logically and approach problems step by step, which will help them in many areas, not just in art. They also learn technical skills, like using GeoGebra, an interactive geometry, algebra, statistics, and calculus application; Blender, a 3D computer graphics software tool set for creating animated films, visual effects, art, 3D-printed models, motion graphics, interactive 3D applications, and virtual reality; MATLAB, software that allows matrix manipulations, data plotting, and implementing algorithms; and 3D printers. These are skills they can use in both creative and technical fields.”

“I also hope that by the end of the class students develop a deeper appreciation for the beauty and order in the world around them.”
Yelena Vaynberg

In this 15-week course, Vaynberg covers a lot of ground:

• Symmetry & Tiling (rigid motions; rosette, frieze, and wall pattern groups; tilings of the plane). [Tilings are all around us. A tiling is just a way of decomposing some space into lots of little pieces (tiles) that fit together without gaps or overlaps.]
• Solids & Golden Ratio (platonic and archimedean solids; fibonacci numbers and the golden ratio).
• Perspective; Surfaces & Motion (perspective; further study of limits: area under curves, slope of tangent line).

In each part, students learn the underlying mathematical principles, relating them to different aspects of art and architecture.

“I also hope that by the end of the class,” Vaynberg said, “students develop a deeper appreciation for the beauty and order in the world around them. Whether they’re working on a project, solving a problem, or simply observing nature, I want them to recognize how geometry shapes everything in ways both subtle and profound.

“Most importantly, I want students to appreciate the connection between different disciplines, like math and art. This will help them be more innovative and adaptable in the future. I also hope they leave with a better understanding of the history of geometry in art, and how it influences design and engineering today. This can inspire them to bring something unique to their own work, whether it’s rooted in the past or pushing forward into the future.”