The intersections of math and art are varied and abundant. Music is counted out in measured beats that define sixteenth, eighth, quarter, half and whole notes, and their infinite combinations produce varied styles: jazz, rock, pop, country. Concepts such as proportion, symmetry, and the golden ratio are key in visual arts.
While those overlaps are common, what is not so common are opportunities for students to dig a little deeper into how math and the arts connect.
High school digital arts teacher Blanca Schnobrich and high school math teacher Michelle Bergman recently conducted a cross-curriculum project to give math and art students a chance to learn from one another and explore the convergence of their disciplines.
Known to be an art enthusiast, Bergman has a lot to say about how art can be seen in math. Together, with Schnobrich, they decided to create a lesson for Graphic Design I students about tessellations, a special type of tiling, a repeating pattern of geometric shapes with no gaps or overlaps.
Maurits Cornelis Escher (1898-1972) is one of the world’s most famous graphic artists who widely used math concepts, including tessellations, in his art. His work, and that of mathematician Sir Roger Penrose, brought attention to the math/art connection.
"I have always been fascinated by the artistic, orderly beauty of mathematics and the interconnectedness between math, creativity, and Creation. I am inspired by the visual and graphic art in our hallways and have a kinship with art teachers, so I was thrilled to collaborate with Mrs. Schnobrich in designing a lesson intertwining math and art," Bergman shared.
Bergman presented the history of tessellations, and how they can also be seen throughout God’s beautiful and creative nature; beehives, snake skins, pineapples, turtle shells, sunflowers, and fish scales, to name a few places. The Devil’s Postpile National Monument near Mammoth Lakes, California is one of the most recognizable geological, hexagonal tessellations in the natural world. Man-made tessellations also abound: a chain link fence or a tiled floor, for example.
Students created a tessellation shape using paper, scissors, and tape. Then, they traced their shape, translated it, reflected it, and created a tessellation pattern on a piece of paper. The kinesthetic exercise helped them gain a better understanding of what a tessellation was and how it was created.
From there, Schnobrich had the students create a digital tessellation shape in Adobe Illustrator, then take the shape into Adobe Photoshop to create their pattern and add Photoshop layer styles and effects.
The results were colorful and mesmerizing. Students had the choice of applying their tessellation art to an iPhone cover if they wanted to take their art a step further.
"In graphic design, I teach students that visual communication is all around them and utilized in every facet of their lives. I teach the tools to create digital imagery for self-expression, to communicate ideas, or to persuade others," said Schnobrich. "But often students come into class and put their graphic design hats on, complete assignments, and then take off their hats and head to the next class. I wanted to help them see that what they are learning here transcends into other classes. That their new found skills could be used creatively for an assignment for another class, such as a poster or a brochure, or that they see creativity and design in some aspect of the curriculum in their other classes. Math seemed like a great place to start, and Mrs. Bergman confirmed that. There is math in everything we do and everywhere we look in the world around us and in God’s creation."
Freshman Georgia Scott wants to be an architect, so the collaborative project gave her insight into the math behind architecture, and the beauty behind its design.
"Architecture is a mixture of art and engineering and a lot of it is technical, so I am learning about that. This type of collaboration is helping me come up with my own ideas and learning how to put them digitally into the computer, so this is great for my future goals," she said.
Opening Black and Red Tessellation by Freshman Anthony Grischenko. Blue and Red Tessellation by Freshman Jack Isola. Blue and Gold Tessellation by Freshman Michael Fischbach.