But how did you know?
It is very curious how it all began. While in the Library of Alexandria, Received a report of observations on Sienna, city about 800 km south of Alexandria (though he did not know how far that was at the time), which was said to have On the day of the summer solstice (June 21) at noon there were no shadows of objects and sunlight was visible at the bottom of the well. Reflecting on this in Alexandria, on the same day and at the same time, he saw the same thing didn’t happen, He could not repeat what was said in the library document. Because
running the experiment
by measuring the length of the shadow cast by a vertical pole During the afternoon solstice (when the shadow was shortest) in Alexandria, he was able to calculate what angle the Sun makes with the vertical in Alexandria. Answer was: One fiftieth part of a circle, or 7.2 degrees. At that time, in Siena, the angle that the sun made with a uniform vertical rod was zero degrees.
With these figures and taking into account the distance between the two cities Eratosthenes paid a man to walk from Siena to Alexandria to find out how many kilometers it was from one to the other. (5,000 stadia, ancient unit of length, 800 kilometers to convert), He calculated that the radius of the Earth must be about 6,000 kilometers -The estimate would be between 6,244 and 7,358 km. In its measurement it failed within a very small percentage of the value accepted today (the accepted terrestrial radius is 6,371 km).
to end, He concluded that the Earth’s circumference was equal to 250,000 stadia, the average stadia being 160 m, giving him a figure of 40,000 km; A figure that is higher than the estimated actual, which is 40,075 km. Regardless of the average stadium size chosen (we do not know which stadium size Eratosthenes used in his estimation as ancient measurements were not standardized)Accuracy is still underwhelming. The outcome of the mathematical experiment is impressive and thanks to him being the first geographer on the planet, we have the concepts of latitude and longitude that we still use today and Made the first model and map based on the spherical earth.
The only tools the Greek sages used were sticks, eyes, feet, and a brain, and with only these elements, they estimated the circumference of the Earth with a fairly small margin of error. By merely observing the difference in the angles of the Sun from two different locations, he was able to calculate the circumference of the Earth and at the same time show that it is indeed round and not flat.
5th World Conference on Educational Sciences – WCES 2013
Basic astronomy concepts in the footsteps of Eratosthenes
Hüseyin Kalkan, Kasim Kıroglu, Kumhur Turka
Lucio Russo. The longitude of Ptolemy and the measurement of the circumference of the earth by Eratosthenes.
Mathematics and Mechanics of Complex Systems, 2013, 1(1), pp.67-79. ?10.2140/memox.2013.1.67?. Hall-03279971,
Lamont-Doherty Earth Observatory at Columbia University.