**Determining the earth's size**

By the
fifth century

The
philosopher Plato (400

Observations
and calculations by two later Greeks, Eratosthenes and Posidonius,
finally resulted in accurate estimates of the size of the earth.

In the
third century

**Eratosthenes' methods**

Eratosthenes
determined the earth's size by observing known phenomena and applying basic
arithmetic and geometry to them. Here's how he did it.

Eratosthenes' methods were simple but effective. All he needed to know was the distance between two locations and what percentage of a circle this distance constituted.

While in

Eratosthenes
then divided 360° by 7° 12' and determined that 7° 12' was 1/50th of a circle.
Now all he had to do was find the distance from Syene
to

Many
scholars believe Eratosthenes measured the distance by measuring a single pace
and then counting the number of paces from Syene to

Next, he
multiplied this distance by 50 to get 40,250 kilometers (25,000 miles). Today,
most scientists set the earth's circumference at 40,096 kilometers (24,901
miles). This gives Eratosthenes' estimate less than a one percent error—an
excellent approximation of the earth's circumference.

**Eratosthenes'
errors**

Syene is not on the Tropic of Cancer, where the sun's
rays are directly overhead during the summer solstice. It is actually 37
kilometers (23 miles) north of the Tropic of Cancer.

All in all, it's amazing that his calculations came as close as they did to the earth's true circumference.

Posidonius
used the stars to determine the earth's circumference. He observed that a given
star could be seen just on the horizon at

In the
second century CE (Common Era) in Alexandria, a philosopher named Claudius Ptolemaeus, or Ptolemy, revised Posidonius'
calculations and set the earth's circumference at 28,985 kilometers (18,000
miles)—an error of nearly 28 percent. Because of Ptolemy's contributions to
geography and cartography, his circumference was used throughout the
Renaissance. It is believed that Christopher Columbus used Ptolemy's number to
plan his voyage to the

With the circumnavigation of the globe and subsequent scientific calculations, the accepted value of the circumference of the earth returned from Ptolemy's calculation back to that of Eratosthenes. After countless millennia, scientists, explorers, clergy, and laymen finally knew the "true shape" and "true size" of the earth. Of course, this geographic euphoria wouldn't last.

**Refining the earth's shape**

It seems that nothing is perfect, and that goes for the earth's shape as well. As explorers and scientists of the past investigated the earth more closely, they realized that it is not a perfect sphere but an ellipsoid—and an imperfect one at that.