Wednesday, March 29, 2023

# How is it known that the earth is not flat?

Long before Elcano and Magellan made the first circumnavigation of the earth; before affirming during the Greek philosopher Pythagoras classic greece that the Earth was round about 500 BC; Earlier Aristotle Around 350 BCE, based on his observations of the constellations, declared that the Earth was a sphere, We have to go back a bit earlier, around 200 B.C. Greek mathematician and astronomer, Eratosthenes of Cyrene to find, Who was the first to measure the circumference and diameter of the earth. that’s how it is; This is a discovery that we owe to the ancient Greeks. Therefore, We have known for 2,000 years that the Earth is spherical.

## But how did you know?

Curiously without leaving the city of Alexandria. Not with more tools than math. amazing thing about His data is that he has an incredible accuracy for timing and available technology.

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

His reflection led him to assume – and quite correctly – that this was because the Earth was curved. And, therefore, there was this difference in the form of shadows of the two cities. Thus, if the shadow in Siena had a certain length and the shadow in Alexandria had the same length, it would also mean that the Earth was flat. But it was not so. To test this, Eratosthenes did a very simple but effective experiment.

## 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.

## Reference:

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.

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