Erastosthenes

Cyrene 215 B.C.

Q (me, the interviewer): Greetings WM Times readers! We are pleased to present to you an exclusive interview with the now-legendary mathematician, Eratosthenes, who has developed a method for measuring the earths' circumference through math, without traveling around the world in order to do so. In fact, only a fraction of travel was required. It's great to have this exclusive interview, Eratosthenes!

A (Eratosthenes): I am glad to be here. I believe this to be a great discovery and am anxious to share it with the scientific community, as well as the world!

Q: Nice to hear that. First, let us start off with a little background information. Where were you born, Eratosthenes?

A: I was born in Cyrene, which is also where this interview is taking place.

Q: How did you get into mathematics?

A: I became very interested in mathematics growing up, and met a friend that soon became my mentor, Archimedes. Challenging my intelligence, he would send me math problems on a regular basis for me to solve. He would later send the solution so I could compare with my own. My intellectual strength grew quickly.

Q: Amazing! Any early accomplishments?

A: One of my earlier works was I drew a map of the world, complete with all known lands, and included the tilt of the earth's sphere, also known as the earths' axis.

Q: We've heard you're rather popular at the library of Alexandria. How is that?

A: Well, I wouldn't say that (chuckles)! Perhaps I have gained a bit of a following there. This is most likely due to the fact that I have created a system for finding prime numbers, but that is already in renowned practice, so I do not think it is necessary to talk about that. I consider it, however, to be a great discovery (grins). I am now the director of that library.

Q: Great history. Now, would you like to explain your discovery?

A: Certainly. Well, first off, mariners have always discussed that when they sail, they always seem to do so towards a curved horizon. I believe this to be proof that the Earth is round, rather than flat, which has been a controversy over the years.

Q: How can the fact that the earth is round, if true, assist you in discovering the Earth's circumference?

A: If the Earth is round, this means that its shape is a sphere, or on paper, a circle. With the use of articulate mathematics, and thorough thought, it can be solved.

Q: What other information did you use?

A: Oh, of course. I would also need a certain distance that would act as a percentage of the circumference, and later multiplied to induce the entire circumference. Picture the following diagram as the Earth, a perfect spheroid:

Points A and B could be connected at the center (of the Earth) to create an angle that could be a certain percentage of the entire circle (a circle measures exactically 360).
The distance could then be multiplied by whatever fraction segment AB is of the Earth to get the whole circumference.

Q: It is simple to understand how to measure the distance between A and B, which is by travel or estimation, but what about angle AB, which would act as the fraction, later to be multiplied to a degree to estimate the full circumference?

A: This is where I had to really think. I soon came up with the idea that if the Sun's rays were parallel, I could use long posts at points A and B. Once the Sun's rays hit the post at B at a point where no shadow was cast, the measure of the angle is found by dividing the length of the shadow by the height of the post at point A. So this is what I did: point B became Syene and point A became Alexandria. Gathering information from acquaintances (mostly mariners), the distance between these two cities was estimated to be 500 stadia. I measured the angle of the post and the Sun at Alexandria each day until a friend at Syene contacted me when the there was no shadow at the post there. Matching the date, I found the angle to be 7 12'.
From this point, the rest of the math is just a comparison, or proportion. 7 12' is to 360 as 500 stadia is to the circumference of the Earth:



After cross multiplying, the circumference of the Earth comes out to be 250,000 stadia.

Q: That is remarkable! Well, WM Times will now begin to a worldwide measurement to see if you are correct!

A: I know I am (grins).

FOLLOW-UP REPORT Long Island, New York 2002 A.D. Well, it has been several centuries (over two millennia, actually) since we last spoke to the late Eratosthenes. But we have finished the measurement of the Earth's circumference and he was very close! His original result 46,000 kilometers (250,000 stadia) is extremely close to our measurement, 40,000 km. What was so remarkable about Eratosthenes was that his result took him only several weeks, and us thousands of years! May he go down in history as a great mathematician!


Works Cited

1. The Syene Experiment of Eratosthenes. <http://www.users.net2000.com.au/~fmetrol/giza/eratosthenes.html>.
Excellent resource, it told me what I needed to know (although that was very little). I am unsure how long it will exist because I cannot find the mother site it belongs to. Limited information, but good if you need that information; 3.5/5

2. Eratosthenes of Cyrene. http://www.eranet.gr/eratosthenes/html/eoc.html
A professional site unlike the one above. A bit oversimplified, but a simple and useful explanation at that; 4/5

3. Measuring the Earth (lesson plan). http://www.askeric.org/Virtual/Lessons/Mathematics/Geometry/GEO0004.html.
Although not a reference site, the lesson plan emulated Eratosthenes style and was therefore useful. I do not recommend this and it should only be used in the fashion I used it in; 3/5

4. Eratosthenes. http://www.bbc.co.uk/history/discovery/bypeople/eratosthenes_01.shtml.
Perhaps the best resource I have used in this entire project. It is a branch of the British Broadcasting Corporation, a company that controls most of the information and entertainment in the United Kingdom. It encompasses the qualities of all of the above resources, plus expands on all parts of his career and life; 5/5