# Question about Eratosthenes method for calculating the circumference of the earth

1. Jan 23, 2013

### marcusau

My professor was showing us how to calculate the Circumference of the earth using Eratosthenes method, as shown here. I completely understand this method. http://www.bsin.k12.nm.us/Curriculu...nomy/completed files/eratosthenescircumf.html

However he told us he had an easier method and to use it. I'm not sure if it works, however. I have attached the slide from his lecture that explains what he was saying to do. I understand Eratosthene's method because the sun's rays are directly over the southern most stick and the shadow cast by the northern stick then can be used to find the angle that subtends the arc, which is the distance between the two sticks.

I suppose using his method you have to measure the angle cast by both sticks using a protractor, rather than having the option to use geometry like in the original.

Also, I am not sure about the direction of the shadow cast by the sun based on the way he has the sticks are oriented, given the cardinal directions given in the diagram.

Thanks for any help or input.

#### Attached Files:

• ###### eratosthene.jpg
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2. Jan 24, 2013

### Simon Bridge

The diagram looks like the same method, just that the Sun need not be directly overhead as in your description and the one in your link. It is the difference between the two shadows that counts - if you wait for one of the shadows to have no length, then the math is probably easier.