The Size of the World

I am a king in a time long ago. I have heard rumors that the earth is round. I feel that it is in my interest to find out whether or not this rumor has any truth, and I understand that great progress is often achieved when trying to learn with an open mind. As such, I have summoned my wizards and set upon them two tasks. The first is to find out what the shape of the earth is. The second is to estimate the size of the earth. Here is what they found.

Upon looking around, it appears to us that the earth is flat—despite the rumors. But accepting the earth as flat has been doubted by one of my wizards whose son is a fisherman. Each day his son sails off towards and past the horizon, appearing to have “fallen off the face of the earth,” only to eventually turn around and return home. For the observer on land, the boat does not simply fade to a dot on the horizon. Not even with our strongest distance viewers, on the clearest days, can we continue to see the fishing boats. This implies that there is a certain degree of curvature to the surface of the earth.

Another argument in favor of a degree of curvature of the earth was offered by one of my wizards who decided to take to some hills that overlook our oceans. Some fifteen to twenty miles off our shore there are two islands, whose silhouettes are easily distinguished. Further out, about sixty miles from our shores, and between these two islands, is a third, larger island. However, despite the higher mountains and larger size of this third island, it is never visible from our beaches. We can reason that, with our ability to see the heavenly stars, that if the earth was flat, and this third island lay in-between the other two, that on clear days we should be able to see it. We find that this is not the case.

The wizard who took to the hills, however, found something intriguing. Upon ascending an extremely high mountain, he found that he could see the third island. Assuming a slight curve in the form of the earth, he demonstrated with tangential lines of sight, that the most probable explanation was that the earth was round—or rather, he corrected me—spherical.

My astronomers supplied a final piece of evidence supporting the idea that the earth is spherical. They noticed that on the occasion that the sun, moon and earth lined up in such a manner that the earth cast a shadow upon the moon, the form of the earth’s shadow took on the form of a circular section.


This first question answered, my wizards next set out to try to measure the circumference of the earth. After some struggling with problems of measurements of distance and time, a pair of them came up with a potential solution. With the help of our expert astronomers, who have been studying the heavens for some time now, my wizards determined a day when the noontime sun would be directly overhead in my kingdom. With this the case, if a stick were planted perfectly perpendicular to the earth, there would be no shadow.

Once the date was determined, we set up three observers each an equal distance apart—say 150 miles, all directly north (or south) of our location. The experiment would not work if the stations were to the west or east since these locations would be along the path of the sun. Each station would have the identical setup of the stick planted perpendicular to the earth. At noon, those attending these latter stations should observe a shadow cast by the stick. We can then use the shadows to figure out the angle of the sun to our second and third locations. We know there are 360 degrees in a circle, and dividing that figure by the estimated angle to the earth should give us an idea of the proportion of each 150-mile stretch to the diameter of the earth.

The calculations are yet to be performed, but I have faith in my wizards that they would provide me with their solution shortly.

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