Eratosthenes was a Greek born in Cyrene in modern-day Libya. As a mathematician, poet, athlete, geographer, astronomer, and music theorist, his vast knowledge made him an ideal fit for the post of librarian at the Museum (Library) of Alexandria.
Eratosthenes lay claim to a number of significant achievements. He invented the Sieve of Eratosthenes, an algorithm for finding prime numbers still used today. He sketched the course of the Nile River and correctly predicted its source. He also may have accurately calculated the distance from the Earth to the Sun and invented the leap day. He even created the first map of the world incorporating parallels and meridians.
Eratosthenes was also the first person to calculate the circumference of the Earth with stunning accuracy and remarkable logic.
In the mid-20th century, we began launching satellites into space that would help us determine the exact circumference of the Earth: 40,030 km. But over 2000 years earlier, a man in Ancient Greece came up with nearly the exact same figure using just a stick and his brain.
In the mid-20th century, we began launching satellites into space that would help us determine the exact circumference of the Earth, 40,030 km.
But over 2,000 years earlier in ancient Greece, a man arrived at nearly that exact same figure by putting a stick in the ground. That man was Eratosthenes. A Greek mathematician and the head of the library at Alexandria.
Eratosthenes had heard that in Syene, a city south of Alexandria, no vertical shadows were cast at noon on the summer solstice. The sun was directly overhead. He wondered if this were also true in Alexandria.
So, on June 21 he planted a stick directly in the ground and waited to see if a shadow would be cast at noon. It turns out there was one. And it measured about 7 degrees.
Now, if the sun’s rays are coming in at the same angle at the same time of day, and a stick in Alexandria is casting a shadow while a stick in Syene is not, it must mean that the Earth’s surface is curved. And Eratosthenes probably already knew that.
The idea of a spherical Earth was floated around by Pythagoras around 500 BC and validated by Aristotle a couple centuries later. If the Earth really was a sphere, Eratosthenes could use his observations to estimate the circumference of the entire planet.
Since the difference in shadow length is 7 degrees in Alexandria and Syene, that means the two cities are 7 degrees apart on Earth’s 360-degrees surface. Eratosthenes hired a man to pace the distance between the two cities and learned they were 5,000 stadia apart, which is about 800 kilometres.
He could then use simple proportions to find the Earth’s circumference — 7.2 degrees is 1/50 of 360 degrees, so 800 times 50 equals 40,000 kilometers. And just like that, a man 2200 years ago found the circumference of our entire planet with just a stick and his brain.
What is Earth’s circumference? In the age of modern technology this may seem like an easy question for scientists to answer with tools such as satellites and GPS—and it would be even easier for you to look up the answer online. It might seem like it would be impossible for you to measure the circumference of our planet using only a meterstick. The Greek mathematician Eratosthenes, however, was able to estimate Earth’s circumference more than 2,000 years ago, without the aid of any modern technology. How? He used a little knowledge about geometry!
At the time Eratosthenes was in the city of Alexandria in Egypt. He read that in a city named Syene south of Alexandria, on a particular day of the year at noon, the sun’s reflection was visible at the bottom of a deep well. This meant the sun had to be directly overhead. (Another way to think about this is that perfectly vertical objects would cast no shadow.) On that same day in Alexandria a vertical object did cast a shadow. Using geometry, he calculated the circumference of Earth based on a few things that he knew (and one he didn’t):
-He knew there are 360 degrees in a circle.
-He could measure the angle of the shadow cast by a tall object in Alexandria.
-He knew the overland distance between Alexandria and Syene. (The two cities were close enough that the distance could be measured on foot.)
The only unknown in the equation is the circumference of Earth!
The resulting equation was:
Angle of shadow in Alexandria / 360 degrees = Distance between Alexandria and Syene / Circumference of Earth.
There is a geometric rule about the angles formed by a line that intersects two parallel lines. Eratosthenes assumed the sun was far enough away from our planet that its rays were effectively parallel when they arrived at Earth. This told him the angle of the shadow he measured in Alexandria was equal to the angle between Alexandria and Syene, measured at Earth’s center.
In 200 B.C. Eratosthenes estimated Earth’s circumference at about 46,250 kilometers (28,735 miles). Today we know our planet’s circumference is roughly 40,000 kilometers (24,850 miles). Not bad for a more than 2,000-year-old estimate made with no modern technology.
NovoScriptorium: A careful reader of Ancient Greek literature -especially Mythology- will soon realize that the Ancient Greeks knew well that the Earth is round and not…flat since very ancient times. Otherwise, various astronomical references they provided us with in their texts would be complete nonsense; on the contrary though, they are purely scientific and allow us to date historical or ‘mythical’ incidents with extreme accuracy. Archaeoastronomy is a branch of Science that deals with this fact lately.
Of course, there were other ancient nations -if not all really- that knew the truth about the shape of the Earth. For example, in India lived Aryabhata* (476–550 CE), a great mathematician that clearly referred to the spherical shape of the Earth. Many ancient monuments, if examined Archaeoastronomically, provide us, indirectly at least, with ancient astronomical knowledge which definetly includes ‘the shape of the Earth’.
Eratosthenes is considered to be the ‘first’ to have measured the Earth’s circumference simply because we haven’t found any other relevant source/text of older age, so far. We are positive though that humans had acquired that knowledge much earlier than the 3rd or 5th century B.C.
Last but not least, as image is very powerful, let’s look at a photograph of an ancient statue (Roman era) that displays Atlas (a very ancient mythological figure) holding the spherical Earth.
*(more info here: https://www.britannica.com/biography/Aryabhata-I)
Research-Selection-Comments for NovoScriptorium: Philaretus Homerides