Why north/south and not just the direct distance?
The distance from one location to another is NOT the "as the crow flies" distance, but rather the north/south distance. As a result this can be more of a challenge. To calculate this, use map scales to determine the distance or you can determine the north/south distance from the site's latitude.
Though the math is good here, the need for using the actual circumference of the earth as part of the calculation is a bit of deception since you are using information that you are setting out to show. What the ancients did was hire surveyors or behamists to measure the distances needed. A modern solution would be to drive from one site to another and use the speedometer as your measuring device. Of course, the sites would have to be on the same longitudinal line. A compromise would be to use scale methods for estimating the distance, then comparing them to the more accurate methods to see how they did. The compromise would be to choose the more accurate measurement for the purposes of this activity.