Calculating the Earth's Radius

Around 240 B.C., Greek mathematician, astronomer, and geographer Eratosthenes became the first person to accurately calculate the Earth’s circumference. Over two thousand years later, WT student Yijia ‘Eric’ Chen, Class of 2018, successfully modeled his Advanced Topics in Mathematics STEM project after the ancient scholar’s achievement.

“I wanted to to do something geometry-related, and Mr. Nassar suggested the idea of astronomical geometry,” explains Chen. “At the same time, I was reading Euclid’s Elements, and combining ancient Greece with astronomical geometry was appealing. I was amazed by how early humans were able to calculate the size of the earth. Eratosthenes made his discovery almost 2,000 years before Ferdinand Magellan’s expedition!”

Eratosthenes was inspired by a famous well in the Egyptian city of Syene where, each year at noon on the summer solstice, the sun was positioned directly overhead, its rays shining straight down into the water. On that same day, also at noon—500 miles away in his home city of Alexandria—Eratosthenes measured the length of the shadow of a vertical gnomon, the triangular blade in a sundial. As Chen researched and wrote for his STEM presentation: “… the height of the stick and the length of the shadow allowed him to calculate the angle between the vertical at Alexandria (as indicated by the gnomon) and the direction of the Sun's rays at noon, which is also the angular difference between Alexandria and Syene. He then used his angular difference to estimate the circumference of the earth.”

For his project, Chen didn’t travel to Alexandria or Syene, but he did enlist students on WT’s City and North Hills Campuses, and—4,000 miles away—a classmate’s friend in Malmö, Sweden. Students measured the length and directions of shadows at the same time of day—10:00 a.m. in Pittsburgh, 4:00 p.m. in Malmö—using meter sticks, a right triangle, and a piece of paper to obtain the necessary data for Chen’s calculations.

When first test resulted in an error percent exceeding 40, Chen realized two things: the distance between WT’s two campuses was “…too short to yield an accurate result for the earth radius,” and his assumption about the directions of the shadows was incorrect, which implied a structural mistake in the calculation procedure. For his second test, Chen used measurements obtained only from City Campus and Malmö, and adjusted the method of measuring and calculating shadows. This slashed the error percent to 1.06 — much closer to the error of 0.16% achieved by Eratosthenes.

“It was like hope appeared again,” recalls Chen. “I was wracking my brain to see where the error was, and I was very excited when I found it.”

It’s classes like these that drew the Wuxi, China native to Winchester Thurston in 2014. “My classmates in China are doing a lot of memorization and homework assigned by teachers, not a lot of developing their own interests. That’s one of the reasons I came here. For example, when Mr. Nassar suggested the idea of earth, I started to wonder: when was the first time that people were able to visualize the shape, or even the size, of the earth they lived on? That pushed me to do the research.”

Chen’s favorite subject is geography — the discipline invented by Eratosthenes —and he intends to seek a career that blends both STEM and the humanities.