Assignment 1: Eratosthenes

Eratosthenes

Eratosthenes, born in 276 BC out of the town Syene, was an ancient Greek scholar who was educated in philosophy and mathematics. He is most well known for his discovery on the measurement of the circumference around the earth with great accuracy. Some of his other achievements include producing the first map of the world which included meridian line and parallel lines. He was able to mark the equator and the size of the polar zones. He also invented geography which we use today. He invented an efficient method to discover prime numbers. Overall Eratosthenes was a well rounded scientist and contributed a lot to our civilization.




Measuring The Earth: 

The story of how Eratosthenes measured the circumference of the earth with great accuracy is very interesting and simple to comprehend. According to www,famousscientists.org Eratosthenes was the director of the library in Alexandria, one of the biggest libraries at the time, so he had access to an enormous amount of information during the ancient Greek period. Syene was a city, about 500 miles away from Ahclexandria where he lived, located in Egypt known as Ashwan in modern day. The people of Syene knew that midday on a certain day of the summer the sun shined directly over Syene. This mid summers day is known as the summer solstice. It was said the Eratosthenes confirmed this fact by looking into a well located in Syene and identifying the sunlight hitting the bottom of the well. He also realized there were no shadows at this time in Syene because the fact that the sun was directly above. He did notice that at the time where there were no shadows in Syene, there were small shadows in Alexandria.

Eratosthenes then made the observations and assumptions that:
1. The earth is assumed to be a sphere similar to the moon or sun
2. The sunlight is parallel when it hits the earth
3. Measuring the angle of shadows in Alexandria during the mid summer day of the summer solstice
4. The distance between Alexandria and Syene

Eratosthenes knew that the sunlight coming straight down on Syene would hit the center of the earth and the sunlight hitting Alexandria would not hit the center and therefore caused a shadow. Eratosthenes then set up a pole straight up from the ground as if it came up from the center and measure the angle of the shadow.



Eratosthenes measured the angle (angle A in diagram) to be approximately 7.2 degrees using simple geometry property of alternate interior angles. Due to the assumption that the earth is spherical, he could assume that the circumference around the earth was 360 degrees. He then went on with a simple calculation...

~ 360 / 7.2 = 50
~ distance between Alexandria and Syene was approx. 5000 stadia or 500 miles
~ 500 miles x 50 = 25000 miles or 250000 stadia

His calculation arrived to the estimation that the circumference of the earth was 25000 mile. Using today's technology the earths current polar circumference is 24901.55 miles which shows how amazingly accurate Eratosthenes was.  

Sources Used 
http://www.famousscientists.org/eratosthenes/
http://www.eg.bucknell.edu/physics/astronomy/astr101/specials/eratosthenes.html
https://www.youtube.com/watch?v=8On7yCU1EjQ
https://www.youtube.com/watch?v=O6KOSvYHAmA
http://en.wikipedia.org/wiki/Summer_solstice