4 ERATOSTHENES OF CYRENE
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1 4 ERATOSTHENES OF CYRENE BIOGRAPHY 770L
2 ERATOSTHENES OF CYRENE MEASURING THE CIRCUMFERENCE OF THE EARTH Born c. 276 BCE Cyrene, Libya Died c. 195 BCE Alexandria, Egypt By Cynthia Stokes Brown, adapted by Newsela
3 More than 2,000 years ago Eratosthenes figured out the size of the Earth with great accuracy. His tools: a stick, the Sun s rays, and simple math. 2 3
4 Eratosthenes was born in the Greek colony of Cyrene, now Libya. In Cyrene, he made a name for himself as a great scholar. The Greek ruler of Egypt decided to bring him to Alexandria to tutor his son. In 236 BCE, the chief librarian of the famous Library of Alexandria in Egypt died. Eratosthenes was given the job around age 40. Eratosthenes was a man of many talents. He was a librarian, geographer, mathematician, astronomer, historian, and poet. Most of Eratosthenes s writings have been lost. Luckily, other scholars have recorded his wideranging work. How did Greek scholars know the Earth was a sphere? They noticed that when ships disappeared over the horizon, their masts were still visible for a few extra moments. They also saw that the Earth made a curved shadow on the Moon during lunar eclipses. This happens a couple times each year when the moon passes directly behind the Earth and into its shadow. The Greeks had also noticed the changing positions of the stars in the sky. Studying the Earth Eratosthenes was the father of geography. He invented a system of longitude and latitude. He made a map of the world as it was known at the time. He also designed a system for finding prime numbers whole numbers that can only be divided by themselves or by the number 1. His system is still in use today. Eratosthenes was also the first to figure the tilt of the Earth s axis. His calculation was impressively close to being correct. Eratosthenes also calculated the distance from the Earth to the Moon and to the Sun, but with less accuracy. He cataloged 675 stars. He made a calendar with leap years. He laid the foundation of chronology, the science of arranging historical events in order by when they happened. He organized the dates of events from the siege of Troy (about BCE) to his own time. A 19th-century reconstruction of Eratosthenes s map of the known world, c. 194 BCE But he is best known for figuring the distance around the Earth. His calculation was not correct, but it was impressively close. He computed the circumference by using simple geometry and trigonometry. Most Greek scholars by the time of Aristotle ( BCE) agreed that Earth was a sphere. None, however, knew how big it was. 4 5
5 Measuring the Earth Eratosthenes heard about a famous well in the Egyptian city of Syene, now known as Aswan, on the Nile River. The summer solstice falls one day each year between June 20 and 22. At noon on that day, the Sun s rays shone straight down into the well s deep pit. On other days, the sides of the well would be lit. But not on this day. On the Solstice, the rays lit up only the water at the bottom. This proved that the Sun was directly overhead. Sun's rays cast shadow off pole at noon, June 20; angle between rays and pole = 7.2 Alexandria 5,000 stadia Sun's rays shine straight down well at noon, June 20 Syene Back in Alexandria, Eratosthenes erected a pole. On the summer solstice, he observed that it cast a shadow. The Sun was not directly overhead there. Instead, it was slightly south. Eratosthenes knew that the Earth was curved. By also knowing the distance between the two cities, Eratosthenes could calculate the planet s circumference. This angle also 7.2 as parallel lines (rays) create equal alternate angles Eratosthenes measured the angle of the Sun s rays off the vertical. He divided the length of the leg opposite the angle (the length of the shadow) by the leg adjacent to the angle (the height of the pole). This gave him an angle of about 7.2 degrees. He knew that the Earth was a 360-degree circle. He also knew the approximate distance between Alexandria and Syene. He had everything he needed to set up this equation: circumference 5,000 stadia circumference = = 360 x 7.2 5,000 stadia circumference = 250,000 stadia 360 degrees 7.2 degrees = circumference of the Earth distance from Alexandria to Syene Eratosthenes knew the distance from Alexandria to Syene was about 5,000 stadia. To us, that distance would equal about 500 miles (800 kilometers). By solving the equation, he calculated the Earth s circumference at 250,000 stadia, or 25,000 miles (40,000 kilometers). His calculations were incredibly close. The Earth s actual circumference is 24,860 miles (40,008 kilometers). How Eratosthenes measured the Earth Yet, Eratosthenes s calculations had errors. For one thing, he was using the stadion as his unit of measure. A stadion was the length of an athletic stadium. But stadiums were different lengths in Egypt and Greece. We don t know which unit Eratosthenes used. If he used the Egyptian measure, he would have been nearly spot on. However, if he used the Greek one, his calculation would have been off by about 16 percent. 6 7
6 A century after Eratosthenes, the Greek astronomer Posidonius of Rhodes (c BCE) calculated the Earth s circumference. Instead of using the Sun, Posidonius used the star Canopus as point of reference. When the star is visible at the horizon in Rhodes, it is 7.5 degrees above the horizon in Alexandria. He was very close to Eratosthenes s calculation of 7.2 degrees. Posidonius s calculations came out almost exactly correct. But then he changed the distance between Rhodes and Alexandria. This resulted in a calculation of 18,000 miles (about 29,000 kilometers). His new calculation was about 28 percent smaller than the actual circumference of 24,860 miles. The writer Ptolemy reported the calculations of Posidonius, instead of those of Eratosthenes. Christopher Columbus read Ptolemy s writings. If Ptolemy had used Eratosthenes s larger, closer figure for Earth s circumference, history might have had a different outcome. Columbus might never have sailed west. The Americas might not have been reached by Europeans until much later. Sources Eratosthenes Project. Accessed June 13, Lasky, Kathryn. The Librarian Who Measured the Earth. New York and Boston: Little, Brown, Nicastro, Nicholas. Circumference: Eratosthenes and the Ancient Quest to Measure the Globe. New York: St. Martin s, Teacher s Guide: The Eratosthenes Project. Accessed June 13, Eratosthenes died around the age of 82. He starved himself to death because he feared going blind. 8 9
7 Image credits An undated illustration of scholars at the Library of Alexandria Bettmann/CORBIS A reconstruction of Eratosthenes s c. 194 BCE map of the world, from E.H. Bunbury s 1883 A History of Ancient Geography among the Greeks and Romans from the Earliest Ages till the Fall of the Roman Empire, public domain A diagram showing how Eratosthenes measured the Earth, accessed from Simon Fraser University Online, phys/100/lectures/lecture3/eratosthenes.html. Articles leveled by Newsela have been adjusted along several dimensions of text complexity including sentence structure, vocabulary and organization. The number followed by L indicates the Lexile measure of the article. For more information on Lexile measures and how they correspond to grade levels: To learn more about Newsela, visit The Lexile Framework for Reading The Lexile Framework for Reading evaluates reading ability and text complexity on the same developmental scale. Unlike other measurement systems, the Lexile Framework determines reading ability based on actual assessments, rather than generalized age or grade levels. Recognized as the standard for matching readers with texts, tens of millions of students worldwide receive a Lexile measure that helps them find targeted readings from the more than 100 million articles, books and websites that have been measured. Lexile measures connect learners of all ages with resources at the right level of challenge and monitors their progress toward state and national proficiency standards. More information about the Lexile Framework can be found at 10
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