Joseph Rosenfeld didn’t understand the fuss.
He said there were three mistakes in the formula for the Golden Ratio at Boston’s Museum of Science — minuses where there should be pluses. They have been there, part of the Mathematica exhibit developed by designers Charles and Ray Eames, since 1981. No one seemed to notice.
Until June 4, when 15-year-old Rosenfeld noticed.
The story of how he caught the supposed errors has gone viral, and initially the Museum of Science let him know they’d be correcting the mathematical display. Reporters have reached out to the teen about his numerical wizardry.
Rosenfeld, a Winchester, Va., resident, said it was simple logic.
“I immediately thought it was incorrect, but I still double-checked myself on my cellphone, going to Wikipedia and other websites,” Rosenfeld said. He even took a picture.
After a follow-up e-mail to the museum, the rising sophomore at John Handley High School received a letter from the Museum of Science. It seemed Rosenfeld’s attention to detail had paid off.
“You are right that the formula for the Golden Ratio is incorrect,” wrote Alana Parkes, the exhibit content developer at the Museum of Science. “We will be changing the – sign to a + sign on the three places it appears if we can manage to do it without damaging the original.”
But now it seems the museum has had a change of heart.
On Tuesday afternoon, Museum of Science spokeswoman Erin Shannon released a statement saying that the Golden Ratio display in the Mathematica exhibit is correct after all.
“It’s not at all surprising that this enterprising student noticed the minus signs because the way the Museum presents the Golden Ratio in its exhibit is in fact the less common — but no less accurate — way to present it,” the statement read. “It’s exciting that people around the country are talking about math and science and that, in the process, we learned something too.”
So . . . can they both be right?
Arthur Mattuck, an emeritus professor of mathematics at MIT, said yes. The two formulas are equal. It’s just that the Golden Ratio is normally presented the way the museum did.
“There’s no logical reason it can’t be presented the other way,” Mattuck said. “The two numbers are the same even if they look different . . . the student is just presenting the fraction upside down, in other words using the reciprocal number.”
To recognize Rosenfeld’s achievement, the Eames Office is putting together a small package of Eames materials for the young mathematician.
“We figure Charles and Ray would have gotten a kick out of a student so engaged with the ideas of Mathematica that he helped make the exhibition even stronger,” said Eames Demetrios, one of the famous designers’ five grandchildren, in an e-mail.
Many believe the golden ratio appears again and again throughout art, geometry, nature, and architecture.
Some have debated whether Da Vinci used the ratio in some of his works to make them more aesthetically appealing. It can be seen in the spiral of a nautilus shell and, some say, in the measurements of the Great Pyramids. Rosenfeld did a project on the Golden Ratio at Daniel Morgan Middle School with his class. It was there that he met his favorite teacher.
“Probably Ms. Carpenter, she taught sixth grade science,” Rosenfeld said. “A lot of times I ask questions and teachers put me down or don’t answer them, but she would take time out of class to answer any questions. She was a good teacher and inspired curiosity.”
Sheila Goddess, a real estate agent and one of Rosenfeld’s aunts, described her nephew as remarkably well-rounded. He plays soccer, occasionally asks her to explain mortgages, and spends time on YouTube watching science and math videos. He is one of three children, and all his siblings like math and have played the piano since they were young.
Rosenfeld wants to go to MIT and become an engineer like his grandfather.
“He is a beautiful soul and a beautiful mind,” said Rosenfeld’s father, Scott Rosenfeld, 56, a developer, who grew up in Lawrence with his sisters and twin brother, Steve. “I knew I couldn’t help him with his homework at an early age.”
Cristela Guerra can be reached at firstname.lastname@example.org.