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Folding Forays

Cheng Herng Yi, Class of 2011

For many, the visceral act of doodling provides an addictive sense of satisfaction. For Cherng Herng Yi, it lies in the art of paper folding.

Origami Artwork by Herng Yi

Child's Play

Herng Yi’s journey in investigating the maths behind origami began when he learned how to fold a model of the Eiffel Tower with an interesting technique: through repeatedly folding cuboid blocks from the same sheet of paper. From there, he began experimenting with this technique to create other buildings like pyramids and castles of his own design. In the process of taking this technique further, he began to question the math underlying it and created variations of his own that allowed him to form other complex shapes and structures, such as a house with a sloped roof. 

Rather than any single event, Herng Yi attributes his passion for mathematics to a culmination of various experiences. Since young, he had enjoyed the ‘Murderous Maths’ series of math books greatly, and his mother, a math teacher, was also an important influence. Besides stocking his bookshelves with the aforementioned series, she introduced him to new areas of mathematics such as calculus at his request. These epiphanic moments gradually moulded his interest in Mathematics.

Exploring the Maths of Paper Folding

Herng Yi’s continued experimentation with origami pushed him further and further into the waiting arms of mathematics. Based on previous experiences, he knew that he could fold many different kinds of blocks and combine them. But to fold blocks that resembled prisms, he would require the application of mathematics. In 2008, Mr Tan Boon Keong, the former Head of the Mathematics Department, suggested that he carry out a research project on the problem and submit it to the Singapore Mathematics Project Festival. Thus, began the start of the synergistic relationship between origami and maths. 

Over the course of three years, Herng Yi completed three projects describing the wide range of geometric blocks that could be folded and combined together. His first project, in 2008, was on folding blocks with horizontal tops and slanted sides. In 2009, he wrote a computer programme to automatically generate creases on a sheet to fold into a block with a slanted top. The results were presented at the 5th International Conference on Origami in Science, Mathematics and Education. While there, a lecture by Japanese researcher, Jun Mitani, inspired his third project that was completed in 2010: the use of a novel procedure to stack multiple blocks together in order to fold more complex shapes. 

In similar vein, he also attempted to further explore the connection between origami and abstract algebra, as well as attacking various open (i.e. unsolved) problems in computational origami. The origami-algebra connection occurred to him while he was working on his various projects, stemming from a recurring observation he had made: certain similarities existed between arithmetic and the combinations of folded blocks, and this might yield a mathematical model for origami.

Credit goes to his mentors, former teachers from NUS High, for contributing to his forays into research and for teaching him important and necessary skills. Mr Samuel Lee, his project mentor in 2008, coached him in his presentation skills, as did Dr Cheong Kang Hao when he took on the role in 2009 and 2010. Dr Cheong also introduced him to academic publishing and taught him how to distil and refine his results so that they could be presented in a paper for submission to international peer-reviewed journals.

Herng Yi’s project, Composing Frusta to Fold Polyhedral Origami, snagged the First Award in the category of Computer Science at Intel ISEF 2011. He received a cash prize of US$3,000. He also won two Special Awards; a 2nd Award of cash prize US$500 from the Association for Computing Machinery, and a 2nd Award of cash prize US$150 from the U.S. Patent and Trademark Office Society. Apart from these wins, Herng Yi also has the honour of having an asteroid named after him. At the moment, he quips that his namesake could be an excellent conversation starter at parties.

Into the Future
Now in his first year at the Massachusetts Institute of Technology (MIT), Herng Yi says that studying at MIT has helped him to stretch himself. The freedom to choose courses in any subject has allowed him to pursue interests in algebra, popular science writing, theoretical computer science and information theory. These courses have allowed him to form a more concrete understanding of any vague interests he might have. In the coming semesters, he hopes to do the same for art history, music and physics.