1.1 Eratosthenes Measures the Earth (6 pages)

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1.1

Eratosthenes Measures the Earth

(Copyright: Bryan Dorner all rights reserved)

How big is the Earth?

The mathematician Eratosthenes (276-195 BCE) lived in the city of Alexandria in northern
Egypt near the place where the Nile river empties into the Mediterranean. Eratosthenes was
chief librarian at the Alexandria museum and one of the foremost scholars of the day -
second only to Archimedes (who many consider one of the two or three best
mathematicians ever to have lived).

The city of Alexandria had been founded about one hundred years earlier by Alexander the
Great whose conquests stretched from Egypt, through Syria, Babylonia, and Persia to
northern India and central Asia. As the Greeks were also called Hellenes, the resulting
empire was known as the Hellenistic empire and the following period in which Greek
culture was dominant is called the Hellenistic age. The Hellenistic age saw a considerable
exchange of culture between the conquering Greeks and the civilizations of the lands they
controlled. It is from about this period that the predominantly geometric mathematics of the
Greeks shows a computational aspect borrowed from the Babylonians. Some of the best
mathematics we have inherited comes from just such a blend of contributions from diverse
cultures.

Eratosthenes is known for his simple but accurate measurement of the size of the earth.
The imprint of Babylon (modern Iraq) as well as Greece can be seen in his method. He did
not divide the arc of a circle into 360 parts as the Babylonians did, but into 60 equal parts.
Still, the use of 60 reveals the influence of the Babylonian number system - the sexagesimal
system - which was based on the number 60 in the same way ours is based on the number
10. His method also uses simple ideas from Greek geometry.

The sexagesimal system became increasingly the standard for astronomical calculations.
The complete Babylonian system of degrees, minutes, seconds, etc. was introduced into
Greek mathematics by Hipparchus some 75 years after Eratosthenes. We will have more to
say about Hipparchus later. Through the Greek influence on Europe, we have adopted
their adoption and still commonly measure angles in degrees and minutes some two
thousand years after Eratosthenes and Hipparchus - as had been done in Babylon for some
two thousand years before their time.

The story goes that Eratosthenes knew that on noon of the longest day of the year (the
summer solstice) the sun was straight above the town called Syene, for travelers reported
the curious fact that a vertical pole cast no shadow at that time in that town. Eratosthenes
reportedly checked by traveling to Syene and observing that, indeed, the sun shone straight
down to the bottom of a deep well at noon on the summer solstice. (Today the spot is
called Aswan and is the location of a huge dam on the Nile river.)

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