One folded paper pyramid at a time, middle school students at Ravenscroft built a towering “tetrix” that has earned Guinness World Record certification.
The 9-foot-tall pyramid they built out of 1,024 smaller paper pyramids was based on the Sierpinski triangle fractal, a mathematical design in which each large piece is made of matching smaller pieces.
Melissa Spainhour, a middle school math teacher at the Raleigh private school, enjoyed learning about fractals in college and wanted to find a way to introduce the concept to younger students. So she started having the school’s math club build small Sierpinski models several years ago. The students enjoyed the hands-on approach, but they started thirsting for more. Why not make a bigger model, they asked her? Like, really big?
“I said, ‘Well, if we’re going to go to the trouble of doing a larger one, then we might as well go for a record, because it’s going to take us all year to make it,’” Spainhour said.
So the Math Club got started last October, enlisting help with measuring and cutting from several Ravenscroft math classes, and in May, they put the last piece on the top of the pyramid.
“Then when we all stepped back, and it actually stood up on its own,” Spainhour recalled. “That was when it was like, ‘Oh my God, we just did this.’”
Caroline Vande Berg , a seventh-grader last school year and member of the Math Club, had seen the previous, smaller versions of the shape and was eager to work on the bigger project – and she wasn’t alone.
“Everyone seemed really excited about it and we wanted to really work together and make something big,” she said.
As the school year went on, the tower of triangles started to take shape, and the students started to see the fruits of their efforts.
“They could see it coming together, and they could see the bigger pieces getting bigger and bigger and bigger, and that’s when their excitement was really high,” Spainhour said.
All along the way, the students were learning about scale, proportion, volume and other mathematical concepts, but that’s not all.
“I recognize patterns afterward, with how precise everything had to be,” said Justin Mauzy , now in eighth grade. “And it also helped with teamwork because there was so much going on at once, we had to really work together.”
Caroline, too, learned that just as each little pyramid was an important part of the great big one, each person had an important role to play in achieving the bigger goal.
“When we were putting the final triangle together, if one person slipped or moved their hand, then the whole thing could fall apart,” she said. “So I learned a lot about teamwork and depending on each other.”
Reaching the top
There were definitely some bumps along the way. The structure, with just as much space as substance, was delicate, held together only by tiny dots of hot glue. Sometimes the paper pyramids weren’t cut exactly to spec and had to be redone. But Caroline and Justin and many other students (the Math Club swelled in size during the project, Spainhour said) stuck it out until the very end.
“My favorite part was putting the final top on,” Caroline said. “It was right after school one day and the whole Math Club was there and we all put it on together.”
Then it was time for Spainhour to file a mountain of paperwork and other documentation, and two witnesses visited the school to take measurements and fulfill the Guinness requirements.
After a long wait over summer break, word arrived: the project, which Guinness dubbed a “tetrix,” was a world record.
“It was a big relief to know that it all turned out,” said Justin.
Now, the school has the certification in hand, but, sadly, the tetrix itself is no more.
Paper and glue will only last so long amid air conditioning and humidity changes, and Spainhour put it out of its misery over the summer, a task she called “a little heartbreaking.”
But, as mathematicians will appreciate, she also made this calculation: “It took a lot less time to tear it down than it did to work it up.”