Mathematics in Context
Eratosthenes’ Procedure for Measuring the Earth’s Circumference
North Pole
Tro
pic
of
Ea
r
th
’s
Eq
u
Rays from the Sun
Ca
nce
Ce
nt
e
ato
r
r
x
r
Alexandria
x
d
Rays from the Sun
is
Syene
Ea
rth
’s
Ax
d
Circumference
=
x
360
Homework
Modify Eratosthenes’ approach to get a procedure for measuring the circumference of the
Earth when taking shadow measurements at Santa Barbara, CA and Prosser, WA. Use the
information given in the figure below. Hint: Use Proposition I.29 to get a formula for
calculating angle x based on angles α and β.
Rays from the Sun
β
Prosser, WA
Rays from the Sun
α
d = 813 miles
Santa Barbara, CA
x
Rays from the Sun
Earth’s Center