Explorations in the Fourth Dimension

As a seventh grader, Nicole Shigiltchoff, Class of 2020, was mesmerized by the animated movie Flatland, the tale of a square in a two-dimensional world who meets a sphere and discovers the existence of an alternate universe. As an eighth grader, Shigiltchoff turned her fascination with the fourth dimension into a full-on exploration in RAPID Lab—a Middle School STEM elective that empowers students to determine and direct their own investigations—and presented her findings at the fifth annual STEM Symposium.

“In our three-dimensional space, we have three dimensions: up-down, left-right, and forward-backward,” says Shigiltchoff. “If we were to live in a four-dimensional space, we would have (those dimensions) plus a new dimension, in-out. My project explains what the fourth dimension is, and how four-dimensional figures would look to us: like three-dimensional objects, except they would have the ability to grow, shrink, and disappear entirely.”

To design these 4D figures - known as tesseracts - Shigiltchoff utilized two CAD modeling programs, TinkerCad and the more advanced Fusion 360. A tesseract is a cube containing a smaller cube, with all of the corners connecting. Tesseracts appear to change shape as they rotate through the fourth dimension; Shigiltchoff’s 3D-printed models demonstrated how tesseracts look at specific moments of the process.

“A tesseract can fully rotate through all of the four dimensions without two edges crossing each other,” she explains. “It can rotate right and left, up and down, forward and backward, and turn itself inside out in two directions. The most complicated aspect of making all of my models was figuring out where the angles of my diagonal edges were supposed to be, and their length.”

Shigiltchoff trekked from Middle School to the Upper School regularly, sometimes twice a day, to learn Fusion 360 as she strove to create mathematically accurate models.

“I was able to more specifically measure angles and lengths of different shapes and create far more complex shapes and figures in Fusion 360, a rather difficult program requiring knowledge of many complex features. Once I mastered some basic skills, I could almost literally feel the doors of opportunity opening. This success made me realize that all of the struggles I encounter in learning will eventually pay off, and that I should never, ever abandon any of my endeavors.”

Shigiltchoff’s project not only introduced her to advanced CAD software not usually encountered in middle school; it expanded her knowledge of alternative geometries, and deepened her ability to understand and synthesize complex information.

“During the course of my research, I encountered many highly mathematical explanations and various complex equations. I was challenged as a thinker to not only digest all of my findings and explain everything in my own, simpler words, but to make sure that other people would still understand what I was telling them.”

Moreover, she says, the project allowed her to realize a cherished goal. “One of my biggest dreams throughout the entirety of Middle School came true,” she reveals. “I got to go over to the Upper School and do a cool and advanced project.”