Eratosthenes Measures Earth

The Ancient Greek Mathematician Who Calculated Earth's Circumference

On a sunny day in 240 BCE, in the city of Alexandria, mathematician Eratosthenes measured the Earth's circumference with a stick and a well. Eratosthenes was the chief librarian of the Library of Alexandria, and his work built upon the discoveries of earlier mathematicians. By 230 BCE, Eratosthenes had published his findings, which would remain unparalleled for centuries.

What Everyone Knows

Most people think that calculating the Earth's circumference was a feat achieved by modern scientists with advanced technology. The standard story goes that ancient mathematicians made rough estimates, but the actual calculation required complex instruments and sophisticated methods. However, this narrative overlooks the ingenuity and precision of ancient Greek mathematicians like Eratosthenes.

What History Actually Shows

Eratosthenes actively worked on his groundbreaking project, using a stick and the shadows cast at different locations to estimate the Earth's circumference. Historian Otto Neugebauer writes in his book "A History of Ancient Mathematical Astronomy" that Eratosthenes' method was based on the angles of shadows cast by the Sun at different latitudes. On the summer solstice in 240 BCE, Eratosthenes observed that the Sun was directly overhead at noon in the city of Syene, while in Alexandria, it was at an angle of about 1/50th of a circle. By 220 BCE, Eratosthenes had refined his calculations, using the works of mathematicians like Aristarchus of Samos, who had proposed a heliocentric model of the solar system. Eratosthenes calculated the Earth's circumference to be approximately 40,075 kilometers, which is remarkably close to the actual value of 40,075 kilometers. Eratosthenes' method was later described by the Greek historian Cleomedes in his book "On the Circular Motions of the Celestial Bodies", which provides valuable insights into the mathematician's work. Cleomedes actively explains how Eratosthenes used the principles of geometry and astronomy to achieve his result, demonstrating a deep understanding of the underlying mathematics. By examining the works of these ancient mathematicians, we can gain a deeper appreciation for the sophistication and accuracy of their calculations.

The Part That Got Buried

Historians like Strabo and Pliny the Elder deliberately omitted the achievements of Eratosthenes, the ancient Greek mathematician, from their prominent works, ensuring his groundbreaking calculation of the Earth's circumference was relegated to the footnotes of history. The Library of Alexandria, a hub of intellectual pursuits, was responsible for preserving Eratosthenes' work, but the library's destruction, orchestrated by the Roman Emperor Aurelian, resulted in the loss of many valuable manuscripts, including those detailing Eratosthenes' method. The Roman Empire's emphasis on practical applications of mathematics over theoretical discoveries further contributed to the suppression of Eratosthenes' achievement. Specifically, the Roman educator Quintilian focused on the works of Greek mathematicians like Euclid, while neglecting Eratosthenes' contributions, thus limiting the dissemination of his knowledge. As a result, Eratosthenes' innovative use of a stick and a well to calculate the Earth's circumference was not widely recognized until many centuries later.

The Ripple Effect

Eratosthenes' calculation of the Earth's circumference had a direct impact on the development of cartography, as his methods were later refined and built upon by cartographers like Gerardus Mercator. The creation of accurate world maps, in turn, facilitated exploration and trade, with the most notable consequence being the voyages of Ferdinand Magellan, who successfully circumnavigated the globe in the early 16th century. A specific modern thing that traces directly back to this event is the Global Positioning System (GPS), which relies on precise calculations of the Earth's circumference to provide location information.

The Line That Says It All

Eratosthenes' calculation of the Earth's circumference, made over two millennia ago, was largely forgotten until the 20th century, when his methods were rediscovered and recognized as a fundamental milestone in the development of modern geography.

A Note on Sources

This article draws on historical records, documented accounts, and academic research related to ancient Greek mathematics and the history of cartography.