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 Chapter 3 : Perpendicular and Parallel Lines Measuring Earth's Circumference Measuring Earth's Circumference Some ancient cultures imagined that Earth was a flat disk; others thought it to be a box-shaped object. They did not realize that Earth was circular in three dimensions, making it a sphere. Egyptians hypothesized that Earth was egg-shaped, and Greeks of about 2,500 years ago realized that Earth was in fact spherical in shape. In one instance, Aristotle observed the shadow of Earth on the moon during an eclipse and reasoned that Earth must be a sphere. By the second century A.D. the idea that Earth was spherical was widely accepted, although the concept of a flat Earth was still held by many. Once it was determined that Earth was spherical, curiosity led to the attempt to determine its size. Around 200 B.C., the Greek philosopher Eratosthenes noticed that the sun shone directly into a well located in the city of Syene on the first day of summer, casting no shadow. He found that, at the same time, a shadow was cast from a vertical stick located in the city of Alexandria. From this information, he was able to create a geometric model of the situation. Eratosthenes then estimated the circumference of Earth to be 29,000 miles. His estimate was about 16% higher than the actual circumference of 24,902 miles. Another Greek philosopher, Posidonius, used the star Canopus and a calculation similar to that of Eratosthenes to calculate the circumference of Earth to be 20,700 miles. The Greek astronomer Claudus Ptolemy, born in Egypt around 85 A.D., made profound contributions to astronomy and geography in his written works Geography and Almagest. Ptolemy was credited with developing some of the most extensive maps ever created, and also theorized that unknown lands lay beyond the far reaches of the oceans. He attempted his own estimate for the size of Earth. As it turned out, Ptolemy's estimate for the circumference of Earth was 28 percent low. The estimate was low enough that, centuries later, Christopher Columbus would convince the queen of Spain that his voyage to India would take only 30 days. Columbus was fortunate that "unknown lands" did exist, otherwise his trip to India would have proven to be futile. The size of Earth has been accurately measured several times since the days of Christopher Columbus. In the late 1700's, the French Academy of Sciences introduced a new unit of measure while calculating the distance from the pole to the equator. This unit of measure is called the meter. Today, sophisticated measuring techniques have determined the circumference of Earth with a high degree of precision. It should be noted that Earth is actually not perfectly spherical. For example, the radius of Earth measured at the equator exceeds that from either pole by about 13 miles. Because of this and other surface irregularities, Earth is better described as being a geoid, which means "earthlike." You can get some more information about the History of Mathematics in Greece from the Clark University Mathematics and Computer Science Department .

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