1.1 Eratosthenes Measures the Earth (6 pages)

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However in Alexandria, which lies pretty much due north of Syene, Eratosthenes measured
the angle of the sun's rays at noon on the summer solstice to be (in "modern" units) 7

o

12'.

Now the distance from Alexandria to Syene was known to be about 5000 stades.

We can easily complete Eratosthenes' determination of the size of the earth in the following
steps:

Exercise:

1. First note that the angle at the center of the earth determined by Alexandria and
Syrene is equal to the angle

α

measured by Eratosthenes. Explain why the angles

are equal.

2. A proportion is an equation of the form:

M
N =

P
Q . Write a proportion that

relates the following four quantities:

d, the distance bewteen Alexandria and Syene,
c, the circumference of the Earth,
a, the angle that Eratosthenes measured, and

360

o

.

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