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ERATOSTHENES
OF CYRENE
BIOGRAPHY
770L
ERATOSTHENES
OF CYRENE
MEASURING THE
CIRCUMFERENCE OF
THE EARTH
Born
c. 276 BCE
Cyrene, Libya
Died
c. 195 BCE
Alexandria, Egypt
By Cynthia Stokes Brown, adapted by Newsela
More than 2,000 years ago
Eratosthenes figured out
the size of the Earth with
great accuracy. His tools:
a stick, the Sun’s rays, and
simple math.
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Eratosthenes was born in the Greek colony of Cyrene, now Libya. In Cyrene,
he made a name for himself as a great scholar. The Greek ruler of Egypt
decided to bring him to Alexandria to tutor his son. In 236 BCE, the chief
librarian of the famous Library of Alexandria in Egypt died. Eratosthenes
was given the job around age 40.
How did Greek scholars know the Earth was a sphere? They noticed that
when ships disappeared over the horizon, their masts were still visible for a
few extra moments. They also saw that the Earth made a curved shadow
on the Moon during lunar eclipses. This happens a couple times each year
when the moon passes directly behind the Earth and into its shadow.
The Greeks had also noticed the changing positions of the stars in the sky.
Eratosthenes was a man of many talents. He was a librarian, geographer,
mathematician, astronomer, historian, and poet. Most of Eratosthenes’s
writings have been lost. Luckily, other scholars have recorded his wideranging work.
Studying the Earth
Eratosthenes was the father of geography. He invented a system of longitude
and latitude. He made a map of the world as it was known at the time. He
also designed a system for finding prime numbers — whole numbers that
can only be divided by themselves or by the number 1. His system is still in
use today.
Eratosthenes was also the first to figure the tilt of the Earth’s axis. His calculation was impressively close to being correct.
Eratosthenes also calculated the distance from the Earth to the Moon and to
the Sun, but with less accuracy. He cataloged 675 stars. He made a calendar with leap years. He laid the foundation of chronology, the science of
arranging historical events in order by when they happened. He organized
the dates of events from the siege of Troy (about 1194 — 1184 BCE) to his own
time.
A 19th-century reconstruction of Eratosthenes’s map of the known world, c. 194 BCE
But he is best known for figuring the distance around the Earth. His calculation was not correct, but it was impressively close. He computed the circumference by using simple geometry and trigonometry. Most Greek scholars
by the time of Aristotle (384 — 322 BCE) agreed that Earth was a sphere.
None, however, knew how big it was.
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Eratosthenes measures the Earth: June 20, many years ago
Measuring the Earth
5,000
stadia
Back in Alexandria, Eratosthenes erected a pole. On the summer solstice,
he observed that it cast a shadow. The Sun was not directly overhead there.
Instead, it was slightly south. Eratosthenes knew that the Earth was curved.
By also knowing the distance between the two cities, Eratosthenes could
calculate the planet’s circumference.
Eratosthenes measured the angle of the Sun’s rays off the vertical. He divided
the length of the leg opposite the angle (the length of the shadow) by the
leg adjacent to the angle (the height of the pole). This gave him an angle of
about 7.2 degrees. He knew that the Earth was a 360-degree circle. He
also knew the approximate distance between Alexandria and Syene. He had
everything he needed to set up this equation:
Sun's rays shine
straight down well at
noon, June 20
Syene
Alexandria
Eratosthenes heard about a famous well in the Egyptian city of Syene, now
known as Aswan, on the Nile River. The summer solstice falls one day each
year between June 20 and 22. At noon on that day, the Sun’s rays shone
straight down into the well’s deep pit. On other days, the sides of the well
would be lit. But not on this day. On the Solstice, the rays lit up only the water
at the bottom. This proved that the Sun was directly overhead.
Sun's rays cast
shadow off pole
at noon, June 20;
angle between
rays and pole = 7.2°
This angle also 7.2°as parallel lines
(rays) create equal alternate angles
circumference
360°
=
5,000 stadia
7.2°
circumference = 360° x 5,000 stadia
7.2°
circumference = 250,000 stadia
360 degrees
7.2 degrees
=
circumference of the Earth
distance from Alexandria to Syene
How Eratosthenes measured the Earth
Eratosthenes knew the distance from Alexandria to Syene was about 5,000
“stadia.” To us, that distance would equal about 500 miles (800 kilometers).
By solving the equation, he calculated the Earth’s circumference at 250,000
stadia, or 25,000 miles (40,000 kilometers).
His calculations were incredibly close. The Earth’s actual circumference is
24,860 miles (40,008 kilometers).
Yet, Eratosthenes’s calculations had errors. For one thing, he was using the
“stadion” as his unit of measure. A stadion was the length of an athletic
stadium. But stadiums were different lengths in Egypt and Greece. We don’t
know which unit Eratosthenes used.
If he used the Egyptian measure, he would have been nearly spot on. However, if he used the Greek one, his calculation would have been off by about
16 percent.
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A century after Eratosthenes, the Greek astronomer Posidonius of Rhodes
(c. 135 — 51 BCE) calculated the Earth’s circumference. Instead of using the
Sun, Posidonius used the star Canopus as point of reference. When the
star is visible at the horizon in Rhodes, it is 7.5 degrees above the horizon in
Alexandria. He was very close to Eratosthenes’s calculation of 7.2 degrees.
Posidonius’s calculations came out almost exactly correct.
But then he changed the distance between Rhodes and Alexandria. This
resulted in a calculation of 18,000 miles (about 29,000 kilometers). His new
calculation was about 28 percent smaller than the actual circumference
of 24,860 miles.
Sources
Eratosthenes Project. Accessed June 13, 2011.
http://eaae-astronomy.org/eratosthenes/documents.
Lasky, Kathryn. The Librarian Who Measured the Earth. New York
and Boston: Little, Brown, 1994.
Nicastro, Nicholas. Circumference: Eratosthenes and the Ancient Quest
to Measure the Globe. New York: St. Martin’s, 2008.
Teacher’s Guide: The Eratosthenes Project. Accessed June 13, 2011.
http://www.physics2005.org/projects/eratosthenes/TeachersGuide.pdf.
The writer Ptolemy reported the calculations of Posidonius, instead of those
of Eratosthenes. Christopher Columbus read Ptolemy’s writings. If Ptolemy
had used Eratosthenes’s larger, closer figure for Earth’s circumference,
history might have had a different outcome. Columbus might never have
sailed west. The Americas might not have been reached by Europeans until
much later.
Eratosthenes died around the age of 82. He starved himself to death because
he feared going blind.
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Image credits
An undated illustration of scholars at the Library of Alexandria
© Bettmann/CORBIS
A reconstruction of Eratosthenes’s c. 194 BCE map of the world,
from E.H. Bunbury’s 1883 A History of Ancient Geography among
the Greeks and Romans from the Earliest Ages till the Fall of the
Roman Empire, public domain
A diagram showing how Eratosthenes measured the Earth,
accessed from Simon Fraser University Online, http://www.sfu.ca/
phys/100/lectures/lecture3/Eratosthenes.html.
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