Building the Menger Sponge, a Mathematical Marvel
The Menger Sponge created by Wentworth faculty and students contains old university-branded business cards
What do you get when you combine outdated business cards, origami, and a shared love for mathematics? At Wentworth Institute of Technology, the answer is a stunning Menger Sponge – a captivating fractal object brought to life through the collaborative efforts of Applied Mathematics faculty and students.
The Menger Sponge, a three-dimensional fractal, is known for its infinite surface area and zero volume, a concept that seems to defy the laws of traditional geometry. The structure is built by recursively removing the center cube and the centers of the 26 surrounding cubes of a larger cube, creating a mesmerizing pattern that repeats at increasingly smaller scales.
Wentworth's project was inspired by the Institute for Figuring's Menger Sponge initiative, which provides instructions and resources for constructing these fascinating objects. However, the Wentworth team took the project further, turning it into a campus-wide endeavor.
"We just put a few level-0 cubes, some business cards, and the plans for the Menger Sponge out in our common area one afternoon," said Associate Professor Rachel Maitra, "and people began to take notice, contributing to the project in different ways."
What began as a simple curiosity quickly evolved into a collective passion among a team including Professors Maitra, Mark Mixer, Lauren Melfi, and Kevin Mackie, and students Jacob Yoon, Master of Data Science ’24; Jadon Watson, Cybersecurity ’24; and Owen Parker, Computer Science ’26. Some folded and assembled the intricate origami modules, while others collected outdated business cards from across campus. The project became a testament to the unifying power of mathematics.
"It was truly everyone's project," Maitra added, "and for me, it underscored how math belongs to everyone and everything in different ways."
The team followed the methods for a level-2 Menger Sponge, a significant undertaking that involved constructing many individual cubes from business cards, assembling them into larger units, and finally combining those units into the final, impressive structure.
Professor Mixer, who also participated with Maitra in a global Menger Sponge build in 2014, highlighted the unique blend of art, math, and teamwork that the project embodied.
"The Menger Sponge is both an interesting mathematical object and an aesthetically pleasing sculpture," he said. "The process of building it as part of a team with other faculty, staff, and students allowed me to engage in a hands-on experience that was both stress-free and intellectually stimulating."