Measuring the Earth circumference: Eratosthenes' method
4. Circumference Arc
If you apply the mathematical formula of the Arc of the circumference, the arc length (L) in a circle, knowing the radius (r) and the angle (ɸ) between the two radius is L = r * ɸ.
In our case we do not know the value of the radius, which is just what we want to find out (since once known this value we can know the length of the "circle" land, as well as its diameter).
In our case we do not know the value of the radius, which is just what we want to find out (since once known this value we can know the length of the "circle" land, as well as its diameter).
 According to the picture above "L" corresponds with the arc of the circle, and we can find this distance browsing, for example, different websites  [See how to achieve this information on the page corresponding to the practical examples]


 Finally, the value of "r" is what we want to know, as it corresponds to the radius of the Earth.
Therefore, to find the radius of the Earth we must to know in advance the length of the arc of the circle which separates the two points of observation.
In our example (see next pages) we will try to find the distance between our study center and a point situated on the Ecuador at the same longitude as our.
In our example (see next pages) we will try to find the distance between our study center and a point situated on the Ecuador at the same longitude as our.
Well, it seems that some of you are a bit confused and did not understand what we wanted to explain, right?
If this is your case do not be discouraged ! On the next page we will show you some practical examples of how to perform the experiment. In any case, those of you who do not have some mathematical skills please do not give up, just applied what we said in the following examples. Maybe in a couple of years you will think that all of this is very easy ! But before that we can see another way, probably easier for you, to calculate the circumference of the Earth and, therefore, the radius of it. Go to the next page to figure it out. 