Over 2,000 years ago, an ancient scholar used a stick to calculate the approximate circumference of the Earth with an accuracy of 99%.
Around 2,240 years ago, a scholar named Eratosthenes was able to determine the Earth’s circumference using just a wooden stick. Remarkably, the figure provided by Eratosthenes had an error margin of only about 1% compared to modern calculations.
Eratosthenes, the ancient scholar, estimated the circumference of the Earth with just one stick. (Image: Ancient Pages).
Eratosthenes (276-194 BC) was born in Cyrene, a region in present-day Libya. After studying in Athens, he moved to Alexandria (Egypt), one of the prosperous cities and intellectual centers of the time. Under the patronage of King Ptolemy, Eratosthenes managed the famous Library of Alexandria.
In the city of Syene, there was a very famous well. The remarkable feature was that at noon during the summer solstice, the sun would shine directly down into the well without casting a shadow. The reason for this phenomenon is that Syene is located right on the Tropic of Cancer. On the summer solstice, the sun shines directly overhead.
Of course, the scholar Eratosthenes had heard of this and saw an opportunity. Moreover, Alexandria (where Eratosthenes worked) is situated just north of Aswan. Thus, the two locations lie on the same meridian and share the same longitude.
Eratosthenes discovered that Alexandria and Syene share the same meridian. (Image: The Cultural Tutor).
At Alexandria, during noon on the summer solstice, Eratosthenes placed a stick in the ground and measured the angle of sunlight based on the shadow of the stick. At that time, Eratosthenes found an angle of 7 degrees, which is approximately 1/50 of the circumference of a circle.
Therefore, Eratosthenes calculated that the distance between Alexandria and Syene (where the angle is 0 degrees) represented 1/50 of the total circumference of the Earth. He then multiplied that distance by 50, resulting in 250,000 stadia (an ancient unit of measurement).
Ultimately, Eratosthenes estimated the Earth’s circumference to be a figure ranging between 24,300 and 25,000 miles (39,100-40,300 km). Currently, scientists estimate the Earth’s circumference to be 24,900 miles (40,075 km). This demonstrates that Eratosthenes’ calculations had an error margin of less than 1%.
Eratosthenes’ estimate of the Earth’s circumference has an error margin of less than 1% compared to today’s figures. (Image: The Cultural Tutor).
Eratosthenes documented all his calculations in a book. However, it was lost for many years until Cleomedes, a Greek astronomer (10-70 AD), rewrote Eratosthenes’ calculations in a simplified form. This is also the method we know today.
Cleomedes noted that Eratosthenes’ original methods were much more complex than the simplified version. In the end, Cleomedes expressed admiration for how Eratosthenes could calculate the Earth’s approximate circumference using just a stick, a well, and relevant geographical knowledge.
