WMass. Professor uses origami to teach, win prize
SPRINGFIELD, Mass.—For Thomas C. Hull, mathematics is about more than numbers and functions: It's about origami -- or is the inverse correct?
Nonetheless, the associate professor of mathematics at Western New England University uses the art of paper folding in geometry, calculus, graph theory and combinatorics, but he also uses it -- quite successfully -- outside of the classroom.
Hull was honored recently at the 2012 Mathematical Art Exhibition Awards in Boston where he received second place for "Pleated Multi-sliced Cone," a work created in collaboration with Robert Lang, of California, and Ray Schamp, of New York.
The concept and crease pattern for this work were devised and modeled in Mathematica, a computational software program used in scientific, engineering and mathematical fields, by origami artist Lang; the crease pattern was printed onto elephant hide paper by artist Schamp; and the paper was folded along the crease pattern by mathematician and origami artist Hull.
The traditional Japanese art of paper folding, which started in the 17th century, was popularized outside Japan in the mid--1900s. It has evolved into a modern art form.
The goal of this art is to transform a flat sheet of paper into a finished sculpture through folding and sculpting techniques; cutting and gluing are not used in origami.
"Part of the charm of paper folding is its capacity for simple, elegant beauty as well as stunning complexity, all within the same set of constraints," he said. "This mirrors the appeal of mathematics quite well."
Geometric origami, which encompasses most of his artwork, strives to express in physical form the inherent beauty of mathematical concepts in geometry, algebra and combinatorics -- the science of counting. "The constraints that origami provides challenge the artist in a way similar to being challenged by a mathematical problem."
Hull, a 42-year-old Hadley resident, spent about 20 hours folding "Pleated Multi-sliced Cone" over a two-week period. He began with a star-shaped piece of ocean blue paper, about two feet wide from point to point. His product was about a foot wide and 5 inches tall.
It was recognized with The Mathematical Art Exhibition Award "for aesthetically pleasing works that combine mathematics and art" which was established in 2008 through an endowment provided to the American Mathematical Society by an anonymous donor who wanted to acknowledge those whose works demonstrate the beauty and elegance of mathematics expressed in a visual art form.
The awards are $500 for first place, $300 for second place and $200 for third place.
Hull's uncle, Paul Chapman, introduced him to origami when Hull was an 8-year-old living in Richmond, R.I. "I saw his work and liked it, so he gave me a book" about origami, recalled Hull who has co-authored two origami books: "Origami Plain and Simple" and "Russian Origami."
"I really love its simplicity," he said of the art form. "Paper is everywhere. Just by folding it you can transform it into something."
He has made all kinds of origami from whimsical flapping bats to functional CD cases.
But his masterpieces are two pieces he invented: the "Five Intersecting Tetrahedra" and "The Phizz (Pentagon Hexagon Zigzag) Units. The former he described as "a rather complicated geometric model" that uses more than one piece of paper and locks them together without glue. "It has been very popular on the Internet," he said.
The Phizz Units are simple origami units that can be joined like Legos to make shapes of buckyballs, soccer balls, inner tubes and jack-o-lanterns. "They're fun to look at," Hull said.
When he uses origami in a math class, students "love it," he said. "They can appreciate that it is mathematical but it's also pretty. You end up with something pretty."
Hull explained that folding paper involves mathematics. "The paper has to follow certain rules without ripping or tearing," he said. "You make creases in nice, straight lines so geometry is going on. You have to pay attention to angles and make sure parts of the paper come together properly. All that is geometry."
Besides its use in class and its "pretty" results, Hull likes origami because it's relaxing and satisfying. He likes to work out the math to realize his vision for a piece, and to "have an art object at the end, to me, that's the real spark," he said.
Once he creates or invents something with his origami, he likes to share it with other people interested in origami. "You immediately want to teach other people," he said.
Though he has sold a few pieces, he has never sought to be a professional artist. Paper is fragile, and people who are interested in sculpture usually want something permanent, he said, noting that his office is littered with origami; he gives some away and stores some.
And for those who want to learn -- no matter what age -- Hull says it's helpful to have good three-dimensional spacial skills but most important are the ability to pay attention to direction and persistence.