Measuring the Surface of the Earth
Who was Eratosthenes?
Eratosthenes was a Greek geographer who lived between c.276 and 195 BC.He is best known for his accurate calculation of the Earth's circumference and he started a mathematical system, known as Eratosthenes' sieve, for determining prime numbers, and determined the inclination of the ecliptic to the celestial equator. Eratosthenes served as chief librarian of the museum at Alexandria, Egypt. His method of measuring the Earth's circumference reflects the Hellenistic way for mathematical solutions.
Measuring the Earth
Pictures showing Eratosthenes in Alexandria and Syene One of the many brilliant mathematicians who taught in the city of Alexandria was Eratosthenes. About 240 B.C., as librarian of Alexandria's already unsurpassed library of scrolls, he learned that Syene, near what is now called Aswan, stands almost exactly on the Tropic of Cancer. At noon the reflection of the midsummer sun was there visible in the water of a deep well. This showed that the sun was directly overhead and that its beams therefore pointed in a straight line toward the middle of the earth. On the same day, measurement of the noon shadow cast by a pillar at Alexandria shows that the sunbeam strikes the earth at an angle of 7.2 degrees off the vertical. Sunbeams travel in parallel, so we may account for the difference only by the curve of the earth.
If we draw two parallel straight lines, one to show the sunbeam at Alexandria and the other to show the sunbeam at Syene, we see that the line on which the vertical pillar stands cuts through both of them. It cuts the first at the surface of the earth, and the second at the middle of the earth. The Greeks knew that when a straight line cuts across two parallel straight lines, it makes equal angles with both of them. Eratosthenes thus knew that the angle between Alexandria, the middle of the earth, and Syene must be 7.2- one fiftieth of the 360 degrees circle.
Syene lies nearly due south of Alexandria, and the road between them therefor lies almost exactly on a great circle passing through the North and the South poles. Since it is almost exactly 480 miles long, the great circle is 50 times 480 miles in length: that is, the circumference of the earth is about 24,000 miles. Eratosthenes gave this remarkably accurate estimate of the size of our earth more than 1700 years before Magellan's ships first sailed around it.
