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The Story of Eratosthenes – Critical Thinking Adventure Part 1

In this critical thinking adventure we intend to place you in the shoes of inventors and historical figures and ask you to try and solve the problems they faced with only the same observations and information available to them. In short, we will pit your creative mind against that of scientists who lived hundreds, or in the case of Eratosthenes, over 2,000 years ago. Is your modern brain power up to the challenge? You could Google their discoveries, but that is not in the spirit of the effort which is to give you a break from SHSAT preparation and get your creative juices flowing to solve a puzzle while hopefully having a little fun. 

Eratosthenes was an accomplished inventor and intellectual who at the young age of 30 in 245 B.C. was hired by the Pharaohs to be librarian for the Alexandria (Egypt) Library, one of the prestigious centers of intellectual history and pursuits at the time. While rubbing elbows with the likes of Archimedes, Eratosthenes most likely read library documents indicating that during the summer solstice, June 21, there could be observed no shadow from columns or a vertical stick in any direction at high noon in the city of Syene approximately 500 miles from Alexandria also in Egypt. If a person looked down a water well, they would observe no reflection from the water below. This was notably not the case in Alexandria at the same time. Vertical columns did cast a shadow. Eratosthenes used these observations to calculate the first accurate measurement of the distance around the globe to 252,000  stadia (a Greek unit of distance). The question to students is how did he do it based on the observations made? Could you make the same discovery and measurement with only the information and tools available to Eratosthenes in 245 B.C.?

Some background information is required as Eratosthenes was a leading scientist of the age and not flying completely blind. For example, and this may surprise you, it was already well know to Eratosthenes and others for over two centuries prior to 245 B.C. that the earth was round. Pythagoras asserted the earth was round in 500 B.C. based on the round shape of the moon and others came to the same conclusion based on different means including Aristotle who determined from the movement of constellations in 350 B.C. that the earth was round and he even estimated its size as 400,000 stadia around. Eratosthenes knew rays from the sum came to earth in parallel and he knew the earth rotated on a tilted axis where the northern hemisphere was tilted closest to the sun on June 21, the summer solstice. In fact, Eratosthenes is credited also with the first accurate measurement of the earth’s axial tilt. He knew the distance from Alexandria to Syene fairly accurately. He understood mathematics of the day which included analysis of right triangles and the work of Pythagoras and others who lived before him. 

Given similar information, what conclusions can you draw from the observations of shadows and how would you design a measurement of the earth’s circumference?

Feel free to share thoughts and ideas below, but not answers sourced from Google or elsewhere. The objective is to put on your own thinking cap and proceed. Keep an eye out for Eratosthenes Part 2 on an upcoming Lectures page at the start of each lesson group for answers to these questions and more.

Part 2 continues on the Lesson 1: Lectures page.

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