As an astronomer and scientist in general, Eratosthenes made quite a few important measurements and calculations. Not only did he calculate the circumference of the Earth, but also the tilt of its axis, as well as the diameter of the Sun (though this last measurement was significantly less accurate than the former).
Eratosthenes also furthered mathematics by creating a method to look for prime numbers, which is still one of the most important area's of Number Theory even today. His most touted mathematical accomplishment however, is his solution to the Doubling of the Cube: attempting to construct the edge of a cube whose volume is double that of a given cube.
To call Eratosthenes a geographer is a little vacuous, in that he was the father of geography. He wrote a vast trilogy of encyclopedias called Geographika, which encompassed many details of the known world at the time, including climate zones as well as the division of the earth via meridian and parallel lines.
Meridians and Parallels
Despite his many contributions to the scientific and mathematical community, Eratosthene's greatest success was probably his estimation of the circumference of the Earth. To accomplish this astounding feat, he used the power of shadows. Eratosthene was told that looking down a well in Syene at noon during the summer solstice would result in one's shadow blocking out the reflection of the Sun at the bottom of the well. Upon hearing this, he deduced that, the Sun must be directly overhead. Then by using a gnomon, the part of a sundial that casts the shadow, at noon in Alexandria he observed the length of the shadow. Using this information, and some trigonometry, Eratosthene deduced that Alexandria must be roughly 7.2 degrees from Syene. Since 360/7.2 = 50, and Alexandria is roughly 800 km from Syene, Eratosthene estimated the circumference of Earth by multiplying 50 x 800 km = 40000 km (of course he did not use km as his unit of measure).
The accuracy of this method is truly astonishing, with the true circumference of Earth being 40008 km (meaning the relative error of his calculation is only 8/40008 = 0.00019996 or 0.02% approx, although depending on the exact value of his unit the stade).
This is an incredible accomplishment and a great success, given the number of variables, estimates and assumptions that he had to make, such as the distance from Syene to Alexandria and the assumption that the Earth was spherical.
References:
- http://www.famousscientists.org/eratosthenes/
- http://www-history.mcs.st-and.ac.uk/Biographies/Eratosthenes.html
- http://www.britannica.com/EBchecked/topic/191064/Eratosthenes-of-Cyrene
- http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm
- http://www.encyclopediaofmath.org/index.php/Duplication_of_the_cube
Images:
-https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhfnpxj1PaCL_DEPDvYWdLRGThOAgov3xb1yVc3ee-HKbrAlvupaANWaiDU5nNdzgLFCrGVPU_kayGPacrtvjnUS3SAm_aHNAEDYUkcs6p7hyphenhyphenpylT8GQvz5i5NpdW5QMC_raizPznfHt_SE/
600/Doubling%2Bthe%2BCube.png
-https://regardingmeasurement.files.wordpress.com/2010/10/eratosthenesmap.png
-http://astrosun2.astro.cornell.edu/academics/courses//astro201/eratosthenes.htm
