1.1 Eratosthenes Measures the Earth (6 pages)

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

.