WEST ORANGE, New JerseyOne day in the third century BC, a librarian named Eratosthenes in Alexandria, Egypt, read something in a papyrus book that captivated his attention. The book noted that at noon on June 21, a stick placed in the earth at Syene would cast no shadow. Yet, Eratosthenes knew that a stick placed in the earth at the very same time at Alexandria, far to the north, would cast a pronounced shadow. The reason, he surmised, was that the earth was not flat as most people of the time believed, but a sphere, and that the difference in shadow length was created by the curvature of the earth's surface. Further, Eratosthenes surmised that he could calculate the circumference of the earth by comparing measurements of these shadows and by performing a series of calculations. Using only primitive tools including a couple of sticks and his own feet, he accurately calculated the north-south circumference of the earth to be approximately 40,000 kilometers.
Today, using a similar approach and a bit of technology, eighth-grade students at Edison Middle School are testing their wits against those of the ancients to see if they can beat Eratosthenes' degree of accuracy. The Noon Day Project, developed by the Center for Improved Engineering and Science Education, allows students around the globe to collaborate on the experiment. At local noon on the vernal equinox, students around the globe measure the length of a shadow cast by a meter-long stick and then share this data electronically. Students then use scale drawings and a spreadsheet to make comparisons and use this information to calculate the circumference of the earth.
Teacher Susan Zaccaro says students finalize the project by creating a Web page to share their experience of the project with other students around the world. The interdisciplinary project melds math and science and gives students an opportunity to see how subject matter they have studied in school can be applied in the real world.
Zaccaro's students first used data collected by a school in Puerto Rico because it was located at a similar longitude. "We held longitude standard," Zaccaro says, explaining that it makes the calculations easier and thus more likely to be accurate, "and we didn't consider latitude." By measuring their local noontime shadow, students could calculate the angle of sunlight in New Jersey, factor in the data from their sister site in Puerto Rico, consider the distance between the two sites and, with a few more calculations, determine the angle formed if lines were drawn from both sites to the center of the earth. This angle, in turn, could be factored into 360 degrees to determine how many like-sized "slices" of earth it would take to complete the earth's sphere. By multiplying the distance between sites by this factor, students were able to calculate the circumference of the earth.
The students were hoping that with their trigonometry tables and more sophisticated equipment, they could beat Eratosthenes' margin of error. "But each time, they found they didn't beat his error," says Zacarro. "They came close, but couldn't beat it." In the end, she says, "they decided that considering his primitive equipment, he must have been a pretty smart guy."
Once students had the process down, Zaccaro says, they continued to practice with the data from other sites in the US, as well as sites in South America and Australia. They would frequently visit the library to go online and check their results.
"The students were very excited when they received an e-mail from Antilles High School in Guaynabo, Puerto Rico," Zaccaro says, "telling them that they had used our sun angle data to estimate the earth's circumference."
Edison Middle School (named after West Orange's most famous citizen, Thomas Edison) serves a diverse student body of 629. The school contains a large media center in its library as well as additional computers in some classrooms. Zaccaro has four computers in her room and says she takes her class to the library when they need more work-stations.
Zaccaro reports that her district has provided opportunities for teachers to receive training in integrating technology into the curriculum. "I began training staff members at our school this year," she says, "and many are beginning to use the Internet to deliver their curricula."
Of the Noon Day Project, Zaccaro says, "This project gave students the opportunity to collaborate with students all over the world and to see firsthand how math and science are related."
Center for Improved Engineering and Science Education (www.k12science.org*)