Posted by Ryan Pilling on Dec 3, 2009 in Interesting Facts |

The time is 250 BC, about 1500 years before what we call “*modern science*” took it’s first baby steps. The Egyptian city of **Alexandria**, on the northern coast of Egypt, was home to the greatest library that ever existed, filled with the wisest people of the day, and the birthplace of many fundamentals of mathematics, geometry, and other sciences.

The head librarian was **Eratosthenes** who was a talented generalist of knowledge, dabbling in many fields. Colleagues joked he was “the second best in the world at everything”, but in today’s story he got the jump on everyone. As he was reading one of the hundreds of thousands of books (scrolls) in his library collection, he found a rather mundane observation from the city of **Syene**, further south in Egypt.

It was reported on the longest day of the year (summer solstice, June 21), as it came to midday columns in Syene would cast no shadow. The sun was so directly overhead that the light would shine straight down to the bottom of a well. Eratosthenes did his own experiments in Alexandria and found that on the same day, at the same time, there were shadows. The sun shone straight down on Syene, but Alexandria was at an angle. Curious!

Time to apply those math and geometry skills that were floating around the library. By measuring the shadow cast from his sticks, and determining the distance from Syene to Alexandria (he hired somebody to pace out, on foot, the 5000 stadia, or 800 kilometers!) he had the numbers required for his calculation.

His shadow suggested that Alexandria was “tilted” a little over 7 degrees from Syene. Knowing there are 360 degrees in a circle, that meant the distance between the cities was about 1/50th of the total. Multiply the walking distance (800 km) by 50 and you end up with 40,000 kilometers around the whole earth.

Eratosthenes was using rough measurements, and even rounding his numbers for easier calculation. However the idea was solid, and his estimate revealed great accuracy when the true circumference of the earth was measured to be 40,075 kilometers around. Not bad for some sticks and piece of paper.

Sadly the great library of Alexandria was destroyed, along with most of the knowledge housed within. For over 1500 years after Eratosthenes the earth was still generally believed to be flat until the great ships actually set out to make the impossible voyage.

### 40,075.0240,075.02 kilmoeters around!

I’m old enough to remember when this was taught in 5th grade science class.

As for the method — do you think Kent Allard might be interested?