[left]Eratosthenes wanted to estimate the circumference of the earth.[br][br]At the time Eratosthenes was in the city of Alexandria in Egypt. He read[br] that in a city named Syene south of Alexandria, on a particular day of [br]the year at noon, the sun’s reflection was visible at the bottom of a [br]deep well. This meant the sun had to be directly overhead. (Another way [br]to think about this is that perfectly vertical objects would cast no [br]shadow.) On that same day in Alexandria a vertical object did cast a [br]shadow. Using geometry, he calculated the circumference of Earth based [br]on a few things that he knew (and one he didn’t):[br][/left][list][*]He knew there are 360 degrees in a circle.[/*][*]He could measure the angle of the shadow cast by a tall object in Alexandria.[/*][*]He knew the overland distance between Alexandria and Syene. (The two[br] cities were close enough that the distance could be measured on foot.)[/*][*]The only unknown in the equation is the circumference of Earth![/*][/list][br]The resulting equation was:[left][br][br][math]\frac{angle.of.shadow}{360}=\frac{distance.between.cities}{x}[/math][br][br][math]\frac{7.2}{360}=\frac{800}{X}[/math][/left]To solve we cross multiply and solve for x.[br]7.2x = 360(800)[br]7.2x = 288000[br]x = 40000[br][br]This estimate of 40,000 km is close to the actual circumference of 40,075km![br]