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Students attempt to replicate ancient measurements

Re-2 NewsTheresa HamiltonGlenwood Springs, CO Colorado

There is a saying from an unknown author that reads, “Many great ideas have been lost because the people who had them, couldn’t handle being laughed at.”More than 2,200 years ago, Greek astronomer and mathematician Aristarchus of Samos was the first to measure the distances to the moon and sun and theorized that the earth actually rotated around the sun, a concept that generated little support at the time, and indeed Aristarchus was scorned. Today, 2,200 years later, the students in Charlie Yates’ math classes attempted to replicate Aristarchus’ measurements, using his formulas and theories, lending additional validity to the man who was laughed at so many years ago.

Yates’ students worked in teams of three to five students, and had to be at Coal Ridge High School at 7 a.m. to take their first set of measurements. To make the exercise even more authentic, Yates had to teach himself and then teach his students to use a sextant, an astronomical instrument that is used to determine latitude for navigation by measuring angular distances, like the altitude of the sun, moon and stars.

“That was an interesting experience,” said Yates with a smile. “That was several hours of self-learning.”Aristarchus argued that the sun, moon, and earth form a near-right triangle at the moment of first or last quarter moon. He estimated that the angle was 87 degrees. Using correct geometry, but inaccurate observational data, Aristarchus concluded that the sun was 20 times farther away than the moon. Yates’ students were challenged to determine the diameter of the sun, and the approximate velocity of earth as it orbits the sun using the calculations gathered during the waning and waxing moons in February. The final project, a stand-alone report, had to include not only the calculations, but also the scientific method they used to reach their conclusions, relevant diagrams, a discussion of the results, and the student’s impression of the techniques employed by the Greeks.This is just one of several projects Yates requires of his students during the school year. In just his second year of teaching, Yates is focused upon providing engaging lessons that are differentiated for his students and that show them the true relevance of math.”It is important to me that my students not only learn the formulas, but that they see how math is incorporated into what they do every day,” he explained.



At the same time his advanced students were decoding Aristarchus’ equations, Yates’ Math III students were commemorating the 100th anniversary of a New Jersey math teacher’s two-year horseback excursion to Buenos Aires, Argentina. In this case, however, the students were allowed to complete the trip on paper via bicycle. Students were asked to calculate longitude and latitude for a variety of cities and they had to determine how many sets of bearings, bike tubes and tires they would need through the course of their trip as well.All of these projects, of course, take many hours of extra preparation time, but Yates is committed to providing these kinds of lessons for his students.”It does take quite a bit of time,” he said, “but the payoff is worth it!”


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