Original Post: A long, long time ago there was a man who had some special knowledge about a water well. What he knew about this well was that once a year, right at noon, the sunlight shone straight down the well so that you could see the water at the bottom in a perfectly lit up circle. always happened at summer solstice. Actually, this was common knowledge in that particular city, because on that special day and at that specific time, everyone's shadow was directly beneath them. No slanting shadows at all. The man's name was Eratosthenes, and the city was Syene, a town on the Nile river, which Eratosthenes knew to be (the equivalent of) 496 miles from the bustling city of Alexandria. At some point it struck Eratosthenes that he could use this information to get a good approximation of the radius of the earth. (Do you know the radius of the earth?) At noon of summer solstice, he calculated the angle of the sun's rays in Alexandria by using a vertical stick, measuring its shadow, and applying basic trigonometry (of right triangles). He found that the sun's rays fell 7 degrees and 12 minutes from vertical. Now imagine the earth as a large circle with the cities of Syene and Alexandria lying on the circle. They can be represented by two points separated by a distance of 496 miles. The 496 miles is the measure of the arc length from one point to the other on the circle. Go ahead and sketch this picture with Syene directly at the top of the circle and Alexandria a little to the right of Syene. Now draw a line from the center of the circle straight through Syene and another from the center through Alexandria. The line through Syene points directly to the sun at noon of summer solstice. The line through Alexandria represents the stick Eratosthenes used to calculate the sun's rays. This stick and its shadow form two sides of a right triangle whose hypotenuse is parallel to the sun's rays. The shadow of the stick forms the base of this right triangle. We know the top angle of the triangle is 7 degrees and 12 minutes based on the calculation of Eratosthenes. Now use our arc length formula to get an approximation of the radius of the earth. (Hint: What is the angle formed at the center of the circle by the two lines that pass through Syene and Alexandria?) In your post, give us your reasoning and your calculations that led you to your final answer. Feel free to attach your sketch and your handwritten work to support your claim. I fully expect that there will be confusion about this assignment, and I don't plan to clean up the confusion. Just give it a solid attempt and see if your answer makes sense based on the actual radius of the earth and based on the posts of your classmates.