|In this section of the Graded Gazette, we celebrate extraordinary students and their outstanding accomplishments in academics, athletics, the arts, service learning, and other extracurricular activities.
You’ve probably seen it before without realizing its complexity. You’re walking down the street and notice a distorted image on the ground or the side of a building that doesn’t quite make sense. Suddenly, as you reach its intended vantage point, it crystallizes. This concept is called anamorphosis, a distorted projection of an image that appears correct only when viewed from a specific perspective or reflected on a surface. What may appear to be a magical illusion to some is just mathematics.
Each year, only a small number of Graded seniors choose to complete their IB extended essay in mathematics. Still, senior Minjae K. was up for the challenge, asserting that he “wanted to push the boundaries of the IB extended essay to demonstrate the potential that it can hold for creativity and innovation.”
Minjae has been at Graded for four years and previously lived in Korea and the US. From an early age, he exhibited a special interest and talent in mathematics. When he returned to Korea from the US at age 10, he enrolled in a math-focused hagwon (a private academy that students attend in addition to their day school). Initially, he was placed in entry-level courses but quickly climbed to the highest level and completed calculus during his first year of middle school. In this hagwon, he was first introduced to the area of mathematics he would explore for his extended essay.
He was intrigued by the practical applications of projective geometry. It’s a specialty field of mathematics students don’t generally study in high school, or even university. But if you pay attention, you can see projective geometry all around you in art and architecture. Minjae’s extended essay advisor, High School Mathematics Teacher Tim Trotter, remarks that “creative application of concepts is at the core of a successful math extended essay. The main trick is: How do you apply or extend these ideas in a novel way? And Minjae really excelled at that with his project.”
Specifically, Minjae wanted to investigate the mathematics behind cylindrical catoptric anamorphosis, which uses a curved mirror to reflect a distorted image correctly. Minjae derived an equation, which he used to create a computer program that transformed each coordinate (x, y) of an original (undistorted) image into the coordinates of its anamorphic counterpart. This process allowed him to create the distorted image that was painted as a mural. Initially, Minjae did not intend to create a physical art installation. However, Mr. Trotter encouraged him to bring his extended essay to life in a truly interdisciplinary and collaborative process. A friend and member of Graded's High School Art Club, Jeongseo C., designed the original image, and other club members, Thais S., Tommy C., and Lia T., volunteered to paint the mural. High School Visual Arts Teacher and Art Club Advisor Amanda York oversaw the process.
With the final distorted image generated, it was time to get everything in place for the moment of truth. The Facilities team generously lent their assistance to ensure everyone’s safety and temporarily cordoned off the student work area. Facilities staff had also constructed the reflective cylinder according to Minjae’s specifications and were ready to install it. Minjae was nervous at the time, saying, “We didn’t know how it would turn out until we placed the mirror at the end. If any step of the process had a mistake, it wouldn’t reflect correctly. When we installed the last piece, and everything came together, we celebrated—it was a gratifying moment.”
The outcome encapsulates what Minjae loves about math—how practical it is and how it can be applied to any subject. “The interdisciplinary nature of math is what draws me to it,” he reveals. “Using math to better understand the world around us.”
Minjae is still thinking about what his path of study might look like in the future—he is a natural mathematician, but he also loves physics and computer science. He does know that he would like to continue to pursue large-scale projects at university.
Mr. Trotter is confident that Minjae will succeed in whatever field he chooses. “Minjae is driven to learn by pleasure and interest. He is an extraordinarily talented, bright, and humble student.”
Community members are invited to view the art installation outside the Athletic Center next to the Graded Greens. Thank you to Minjae, the Art Club, Mr. Trotter, Ms. York, and the Facilities Department for adding vibrant student work to our campus!