Worksheet
Name _______________________
Calculating the earth
Diagram taken from A Short History of Scientific Ideas to 1900, Charles Singer
Taken from An Introduction to the History of Mathematics, Howard Eves.
Eratosthenes, in 240 BCE made a famous measurement of the earth. He observed at
Syene, at noon and at the summer solstice, that a vertical stick had no shadow, while at
Alexandria (which he believed to be on the same meridian with Syene) the sun’s rays
were inclined 1/50 of a complete circle to the vertical. He then calculated the
circumference of the earth from the known distance of 5000 stades between Alexandria
and Syene. There is reason to suppose that an Eratosthenian stade was equal to about
170.5 m.
Recreate Eratosthenes’ calculation. Compare your result with with the accepted value.
Measuring the distance to the moon
Diagram and excerpt from Mathematics for the Non-Mathematician, Morris Kline.
Calculate the distance from the surface of the earth to the moon. The radius of the earth
is 6380 km. Compare your result with the accepted value.
Measuring the radius of the moon
Diagram from Mathematics for the Non-Mathematician, Morris Kline.
From a point the Earth, E, measure the angular separation of two lines: one to the center
of the moon and one to a point tangent to the moon. This angle is found to be 15°.
Use your result from above to calculate MR.