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Question: ricci math 142 homework 1 written homework l due wed...

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Ricci Math 142 Homework 1 Written Homework l Due Wed Jan 22th, in class Show all work and use another sheet of paper! Eratosthenes was a Greek mathematician who lived 276-194 BC. At summer solstice he waited until noon, when the sun was directly overhead in Aswan. He placed a gnomon (basically a stick) at the bottom of the well at 90° to the ground, and noticed that it cast no shadow. Then at the same time he had others place a gnomon in Alexandria. He found that the tip of the gnomon made an angle of 7° to the edge of the shadow, where the gnomon was again at 90° with the ground. Based on records at the Library of Alexandria, he knew that the distance from Aswan to Alexandria was 5,000 stadia. 1. Draw a picture (or several), and then make a calculation for the circumference and radius of the earth, in stadia. Explain all your steps. 2. One assumption that Eratosthenes made was that the earth was a perfect sphere. What are 5 other assumptions critical to this calculation? 3. Some historians believe that an Olympic stade which is 176.4 meters. What % error would this make his calculation off by, when compared to the modern value?
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