St. Bonaventure University’s Quick Center for the Arts was invaded by a Sierpinski tetrahedron last week.
Frightening? No. More like breathtaking.
Mathematics professor Dr. Chris Hill couldn’t have been more thrilled.
With more than 80 middle school students, teachers, administrators and parents from Allegany-Limestone, Hinsdale, Olean and Portville taking part, four stage-5 Sierpinski tetrahedra were connected to create a stage-6 Sierpinski tetrahedron.
Built with 32,770 Zometool parts, the pyramid stood 13 feet tall, with a triangular base 16 feet on each side.
Zometool is a mathematically precise plastic construction set for building myriad geometric structures, from simple polygons to “shadows” of four-dimensional figures, from models of DNA molecules to works of art.
Zometool Chief Visionary Officer Paul Hildebrandt told Hill that he believes it’s the first time a stage-6 Sierpinski tetrahedron has ever been built using Zometool. Zometool President Carlos Neumann was so impressed, he featured the project on the company’s website.
“It was an incredible sight,” Hill said. “The structure was so large that adults could — and did — stand inside of it.”
To fully appreciate the students’ accomplishment, a bit of mathematical background is needed, Hill said.
“A triangular pyramid is also called a tetrahedron,” he said. “A Sierpinski tetrahedron is a beautiful geometric figure that has the shape of a tetrahedron, made from four half-scale tetrahedra, each of which is made from four quarter-scale tetrahedra, each of which is made from four eighth-scale tetrahedra, and so on, ad infinitum. A Sierpinski tetrahedron possesses ‘self-similarity,’ that is, parts of the whole have precisely the same shape as the whole.”
Hill said “a consequence of the geometry of a Sierpinski tetrahedron is that if you build four copies of a certain-stage Sierpinski tetrahedron,” they can be connected to make the next-stage Sierpinski tetrahedron.”
Teachers in each of the four school districts guided the students over the last several months to create stage-5 Sierpinski tetrahedra, each containing 8,194 parts and standing more than 6 feet tall. (The stage-5 tetrahedra were partially disassembled for transport to St. Bonaventure, then reassembled when they arrived for the May 7 event.)
Then, with the theme music from “2001: A Space Odyssey” playing as inspiration above the Rigas Family Theater stage, a group of teachers gently placed the fourth stage-5 tetrahedron atop the other three to complete the structure.
Hill said the collaborative effort was called the “Connect 4 Project” for two reasons.
“First, the four school districts involved are precisely those in the Connect 4 program, which facilitates the sharing of resources among the four districts,” Hill said. “Second, the four stage-5s were literally connected to form the stage-6.”
The event was two years in the making and was generously supported by Cattaraugus-Allegany BOCES, Hill said.
“Sadly, the stage was needed for another event later in the day, so we had to partially disassemble and remove the stage-6,” Hill said. “But it’s now on tour, visiting the Olean, Allegany-Limestone, Hinsdale, and Portville schools for several days each. Then, it will spend some time at the Olean Center Mall.”
The Connect 4 Project is one of many community outreach projects that Hill is involved with, including a Zometool workshop with a group of middle schoolers at the Dresser-Rand Challenger Center; and a Zometool Club at Southern Tier Catholic School.
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