Eratosthenes, now more than ever

As it turns out, the world is round. There are some who may disagree with this statement, but it was proven just the other day.

As it turns out, the world is round. There are some who may disagree with this statement, but I stand by it. It has been proven with mathematics, and it was proven just the other day. I know, I was there — on an international occasion.

Well, to be precise, it was first proven more than 2,000 years ago, back when the Greeks ran Egypt, by Eratosthenes — mathematician, poet, astronomer, and music theorist, among other things.

Eratosthenes was one of the most intelligent humans who ever lived. He invented the discipline of geography, for one thing, and created an algorithm for finding prime numbers, still in use today, and still known in mathematics as the sieve of Eratosthenes. His day job was chief librarian at the Library of Alexandria, the greatest library of all time.*

One day, Eratosthenes read how in Syrene, far to the south, at precisely noon, columns would cast no shadows and the sun would shine directly down into the water of the well. At that moment the sun was directly overhead. Eratosthenes found that at the same moment in Alexandria, 5,000 stadia (800 kilometres) to the north, a column or stick cast a very definite shadow. The only way there could be no shadow in Syene and a distinct shadow in Alexandria was if the Earth was curved, and not flat, as so many people believe — even today, remarkably.

Eratosthenes estimated the angle of the shadow to the stick to about seven degrees, about one fiftieth the full circumference of the earth (360 degrees). Given the distance between Alexandria and Syene was 800 km it meant the distance around the earth must be about 40,000 km. This is correct with only a small percent error. **

People like Eratosthenes are suspect in some powerful circles these days. Experts are frowned upon. Some people consider emotion and rumour to be a truer gauge of reality than science. I think that every now and then, it should be proven again that the earth is round.

So does Dr. Robert Stauffer, a science teacher at Somerset College Prep Academy in Las Vegas, who recently invited Mount Baker Secondary School to take part in re-creating Eratosthenes’ experiment. Las Vegas is due south of Cranbrook.

So on Monday, Oct. 16, at exactly 1:28 pm (solar noon — exactly halfway between sunrise and sunset), math students at Baker and Somerset, repaired to the outdoors. The sun broke out, casting long vivid shadows. The students created a right triangle with a vertical stick and its shadow as its legs and to measure the acute angle subtending to the shadow.

Taking the Earth as spherical, and knowing both the distance and direction of Las Vegas (1,485 kilometres due south — or 8,000 stadia), the students at both Baker and Somerset could prove and pinpoint the Earth’s circumference using Tagent (theta) equals opp/adj.

I watched this process, seeing mathematics turned into action. Eratosthenes was there himself in spirit.

I’m looking forward to the next time mathematics makes the news in Cranbrook.

* The Library of Alexandria was a repository of ancient knowledge the likes of which the world has never seen since. Its destruction in the early years of the first millennium set back the course of human intellectual and social development by centuries. Some say it was burned by Julius Caesar. Some say anti-pagan rulers of Egypt had it gradually destroyed. Some say it was destroyed during the Islamic invasions. Some say it was struck by lighting. In any case, the Library at Alexandria has become a symbol of the loss of irretrievable knowledge. I wish I still had that library card!

** As recounted by Carl Sagan

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