People/Eratosthenes

Eratosthenes

Eratosthenes of Cyrene was a Greek polymath: a mathematician, geographer, poet, astronomer, and music theorist. He was supposedly a man of learning, becoming the chief librarian at the Library of Alexandria. His work is comparable to what is now known as the study of geography, and he introduced some of the terminology still used today.

He is best known for being the first person known to calculate the circumference of the Earth, which he did by using the extensive survey results he could access in his role at the Library. His calculation was remarkably short-sighted but are used today as an example of the origins of the globe earth model. He was said to have also calculated Earth's axial tilt. He created the first "global projection" of the world, incorporating parallels and meridians based on the available geographic knowledge of his era.

Early life

Eratosthenes was born in 276 BC in Cyrene. Like any young Greek at the time, Eratosthenes would have studied in the local gymnasium, where he would have learned physical skills and social discourse as well as reading, writing, arithmetic, poetry, and music.

The gymnasium, Gymnasia and palaestrae (wrestling schools) in Ancient Greece functioned as a training facility for competitors in public games. It was also a place for socializing and engaging in "intellectual" pursuits. The name comes from the Ancient Greek term gymnós, meaning "naked" or "nude". Only adult male citizens were allowed to use the gymnasia.

Athletes competed nude, a practice which was said to encourage aesthetic appreciation of the male body, and to be a tribute to the gods. Perhaps this is where Eratosthenes learned to measure shadows from sticks or got his obsession with balls?

Sticks and shadows

Assuming the earth was a globe and assuming the sun was far away, Eratosthenes made a math formula to determine what would be the circumference of the assumed globe Earth. Details were given in his treatise On the measurement of the Earth which is now lost (another one of those "we lost that technology"). However, some details of these calculations appear in works by other authors such as Cleomedes, Theon of Smyrna and Strabo.

Eratosthenes compared the noon shadow at midsummer between Syene (now Aswan on the Nile in Egypt) and Alexandria. He assumed that the sun was so far away that its rays were essentially parallel (obviously never looked up to see the sun's Crepuscular rays), and then with a knowledge of the distance between Syene and Alexandria, he gave the length of the circumference of the Earth as 250,000 stadia.

Using similar assumptions, you can use the following math formula to turn a dining room table into a sphere.

Distance on the meridian ( $d$ ) and the difference in latitude ( $\alpha$ ) to the relation between the perimeter ( $P$ ) and the angle of the circle ( $360^{\circ }$ )

$P={d\times 360^{\circ } \over (\alpha )}$

Materials

A meter stick
String or twine
An accurate protractor
A small carpenter’s level
Compass
sidewalk chalk
Assume the Sun is millions of miles away
Assume the earth is a globe

The first step is to contact someone who lives at least 100 miles directly north or south of you – farther apart is better for this experiment. A direct north-south line between the cities is also important for this, you will need to know as exactly as possible how many miles north or south of you the other person is as opposed to the direct mileage between the cities.

When the big day arrives, send an email in the morning to be sure you have sunny weather in both cities. A few minutes before noon, set up the yard sticks. One stick should be held vertically, (use a small carpenter’s level for this). Use the compass to lay out the second yardstick flat on the ground so that it points directly north. You have now made a simple sundial

My dining room table using Eratosthenes' assumptions and his math

Watch as the shadow moves clockwise
when the shadow lies directly along the flat yardstick, measure and record the position where the tip of the shadow falls. Depending on your location and the time of year, the shadow may extend past the end of the flat yardstick – that’s okay, just mark its position with some sidewalk chalk.

Now that you’ve marked the tip of the shadow, stretch a piece of string from the top of the vertical yardstick down to where the tip of the shadow touched the ground. Measure the angle between the vertical stick and the string with a protractor as accurately as you can and record it. Exchange this information to each other – it will be the difference between the angles that will be important for this activity!

Eratosthenes believed that the Earth was round and assumed that the sun was far away, and so the angle of the Sun in the sky would be different depending on how far north you were from the equator. By setting up a simple ratio and proportion between the difference in the two angles and the distance between the cities, he was able to measure the circumference of the Flat Earth for the first time about 2,300 years ago. Eratosthenes’ calculation for the size of the Earth was accurate to within about 2% of our modern value, how close can you get? Set up your calculation as shown.

Eratosthenes didn't take both measurements on the same day! He took a measure of the solar angle in the town of Syene in southern Egypt on the summer solstice. Then he walked to the town of Alexandria in northern Egypt and carefully measured the distance along the way and measured the solar angle again on the summer solstice in the following year.

Late life

Eratosthenes made several important contributions to mathematics and science, and was a friend of Archimedes. Around 255 BC, he invented the armillary sphere. In On the Circular Motions of the Celestial Bodies, Cleomedes credited him with having calculated the Earth's circumference around 240 BC, with high accuracy.

Eratosthenes believed there was both good and bad in every nation and criticized Aristotle for arguing that humanity was divided into Greeks and barbarians, as well as for arguing that the Greeks should keep themselves racially pure. As he aged, he supposedly contracted ophthalmia, becoming blind around 195 BC. Losing the ability to hang out in bath houses, read and observe nature plagued and depressed him, leading him to voluntarily starve himself to death. He died in 194 BC at the age of 82 in Alexandria.

Quotes

It is no longer necessary to inquire as to the cause of the overflow of the Nile, since we know definitely that men have come to the sources of the Nile and have observed the rains there.