ERATOSTHENES OF CYRENE

Eratosthenes of Cyrene (c. 276 BCE–192 or 194 BCE) was an ancient Greek mathematician, poet, and astronomer who is known as the father of geography. Eratosthenes was the first person to use the word "Geography" and other geographical terms that are still in use today, and his efforts to calculate the circumference of the Earth and the distance from the Earth to the Sun paved the way for our modern understanding of the cosmos. Among his other many accomplishments were the creation of the first map of the world and the invention of an algorithm known as the sieve of Eratosthenes, which is used to identify prime numbers.
Eratosthenes was born around 276 BCE in a Greek colony in Cyrene, a territory located in present-day Libya. He was educated at the academies of Athens and in 245 BCE, after earning attention for his skills, he was invited by Pharaoh Ptolemy III to run the Great Library at Alexandria in Egypt. This was a major opportunity, and Eratosthenes was excited to accept the position.

In addition to being a mathematician and geographer, Eratosthenes was also a very gifted philosopher, poet, astronomer, and music theorist. He made several significant contributions to science, including the discovery that a year is slightly longer than 365 days, requiring an extra day—or leap day—be added to the calendar every four years to keep it consistent.

Geography

While serving as the Head Librarian and scholar at the Library of Alexandria, Eratosthenes wrote a comprehensive treatise about the world, which he called "Geography." This was the first use of the word, which in Greek means "writing about the world." Eratosthenes' work introduced the concepts of torrid, temperate, and frigid climate zones. His map of the world, though highly inaccurate, was the first of its kind, featuring a grid of parallels and meridians used to estimate distances between different locations. Though Eratosthenes' original "Geography" did not survive, modern scholars know what it contained thanks to reports by Greek and Roman historians.

The first book of "Geography" contained a summary of existing geographical work and Eratosthenes' speculations about the nature of the planet Earth. He believed it was a fixed globe whose changes only took place on the surface. The second book of "Geography" described the mathematical calculations he had used to determine the circumference of the Earth. The third contained a map of the world in which the land was divided into different countries; it is one of the earliest examples of political geography.

Calculating the Circumference of the Earth

Eratosthenes' most famous contribution to science was his calculation of the circumference of the Earth, which he completed while working on the second volume of his "Geography."

After hearing about a deep well at Syene (near the Tropic of Cancer and modern-day Aswan) where sunlight only struck the bottom of the well on the summer solstice, Eratosthenes worked out a method by which he could calculate the circumference of the Earth using basic geometry. Knowing that the Earth was a sphere, he needed only two critical measurements to calculate the circumference. Eratosthenes already knew the approximate distance between Syene and Alexandria, as measured by camel-powered trade caravans. He then measured the angle of the shadow in Alexandria on the solstice. By taking the angle of the shadow (7.2 degrees) and dividing it into the 360 degrees of a circle (360 divided by 7.2 yields 50), Eratosthenes could then multiply the distance between Alexandria and Syene by the result to determine the circumference of the Earth.

Remarkably, Eratosthenes determined the circumference to be 25,000 miles, just 99 miles over the actual circumference at the equator (24,901 miles). Although Eratosthenes made a few mathematical errors in his calculations, they canceled each other out and yielded an amazingly accurate answer that still causes scientists to marvel.

A few decades later, the Greek geographer Posidonius insisted that Eratosthenes' circumference was too large. He calculated the circumference on his own and obtained a figure of 18,000 miles—about 7,000 miles too short. During the Middle Ages, most scholars accepted Eratosthenes' circumference, though Christopher Columbus used Posidonius' measurement to convince his supporters that he could quickly reach Asia by sailing west from Europe. As we now know, this was a critical error on Columbus' part. Had he used Eratosthenes' figure instead, Columbus would have known he was not yet in Asia when he landed in the New World.

Prime Numbers

A noted polymath, Eratosthenes also made notable contributions to the field of mathematics, including the invention of an algorithm used to identify prime numbers. His method involved taking a table of whole numbers (1, 2, 3, etc.) and striking off the multiples of each prime, beginning with multiples of the number two, then multiples of the number three, etc. until only the prime numbers remained. This method became known as the sieve of Eratosthenes, as it works by filtering out the non-prime numbers in the same way that a sieve filters solids out of liquids.

Death

In his old age, Eratosthenes became blind and he died of self-induced starvation in either 192 or 196 BCE in Alexandria, Egypt. He lived to be about 80 to 84 years old.

Legacy

Eratosthenes was one of the greatest Greek polymaths, and his work influenced later innovators in fields ranging from mathematics to geography. Admirers of the Greek thinker called him Pentathlos, after the Greek athletes known for their prowess in a number of different events. A crater on the Moon was named in his honor.


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