Shape
Copyright David & Cynthia Thomas, 2009
Circumference and Area of Circles--Challenge: Measuring the
Circumference of the Earth
Approximately 2300 years ago, Eratosthenes (275-194 BC), chief librarian in Alexandria, Egypt, conducted an experiment in which he determined the shape of the Earth to be a sphere with a circumference of 250,000 stadia (1 stadia = 157 meters). While reading a report from Syene (now called Aswan), he learned that, at noon on June 21st, vertical sticks cast no shadow. On a subsequent June 21st in Alexandria, Eratosthenes observed that vertical sticks did cast a shadow at noon, the sun making an angle of 1/50th of a circle relative to the stick. On the basis of this observation and with the knowledge that the distance from Alexandria to Syene was approximately 5000 stadia, Eratosthenes concluded that the world was a sphere with a circumference of 25000 stadia.
· Learn more about Eratosthenes’ experiment by visiting the Noon Day Project website http://www.k12science.org/noonday/
· How did Eratosthenes’ observation lend support to the theory that the Earth is a sphere?
· Thoroughly explain the geometry used to justify Eratosthenes’ calculation.
· Convert Eratosthenes’ estimate to miles and compare it to the accepted circumference of the Earth at the equator. Determine the percent error in his calculation.
Directed Activity Diameter, Circumference, and Pi
Focus |
The meaning and value of p |
Technologies |
Fathom, MS Excel, or a graphing calculator. |
Background |
A group of students is given a set of seven cylinders. Using a measuring tape, they obtained the centimeter measurements for diameter and circumference seen in Table 3.9.
Table 3.9: Diameter vs. Circumference
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Tasks |
Using appropriate computing and graphing tools … · Plot the data and graph a line of best fit; · Find the slope of the line of best fit; · Interpret your findings. |