On math, logic, and the simple ability to think and reason

Sorry, no spanking. I was looking in an old text today, and came upon this again. I've always liked this story. Just imagine the reasoning that went into this whole process, and, simply doing the math alone! I know many high school, as well as college students, who still don't get it, even when it's explained how he did it.

In Egypt, around 200 B.C., the Greek Eratosthenes correctly estimated the circumference of the earth.

On the longest day of the year, when at high noon the sun's rays hit the water at the bottom of a deep well in the city of Syene, Eratosthenes measured the length of the shadow of a tall obelisk in the city of Alexandria, which was about 800 km to the north.

Because he knew the distance between the two cities, and the height of the obelisk, he was able to employ the principals of Euclidian geometry to correctly estimate the circumfrence of the earth.


Step by step how he did this.
1. On the day when sunlight shown directly into the well, he measured the length of the obelisk shadow.
2. The shadow's length, and the obelisks's height formed two sides of a triangle. From principles of Euclidian geometry he was able to use the height and length to deduce the angle a. It proved to be 7 degrees 12 minutes, exactly 1/50 of a circle.
3. If angle a = 1/50 of a circle, then the distance between the obelisk in Alexandria, and the well in Syene must equal 1/50 of the circumfrence of the earth.
4. Eratosthenes had heard that it was a 50 day camel trip to the well, and figured that a camel travels about 18.5 km a day (he used different units of measurements) , and he estimated the distance between well and obelisk to be as 925 km.
5. Eratosthenes thus estimated the circumference of the earth to be 50 x 925 = 46,250km. In reality, the distance from the well to obelisk is just over 800 km, 15% less then Eratosthenes crude estimate. Substituting 800 km x 50= 40,000km.
The actual value is 40,075 km.
Angie