Finding the Circumference of the Earth (2000 Years Ago) 
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Finding the Circumference of the Earth (2000 Years Ago) 

By Layla Kluth

Over 2,200 years ago, with a lot of free time and basic geometry, the ancient Greek mathematician Eratosthenes calculated the circumference of the Earth with impressive accuracy. His answer was only 75 kilometers off. How in the world did he do this?

Eratosthenes was in Alexandria, Egypt when he learned that no shadows were cast in Syene, Egypt at noon on the summer solstice. However, Eratosthenes found that on the same day in Alexandria, objects did cast shadows. The sun, he realized, was directly overhead in Syene, but not in Alexandria.  Eratosthenes concluded that this was only possible if the surface of the Earth was curved. 

He figured that at noon on the summer solstice in Alexandria, the angle the sunlight makes with a pole is the same as the central angle between Alexandria and Syene, which he measured as 7.2 degrees. 

Knowing the proportional relationship between arc lengths and central angles, he created an equation. The circumference of the Earth divided by the north-south arc length between the two cities (which was 800 kilometers) = 360 degrees divided by the central angle between the two cities (7.2 degrees). Using cross multiplication, he determined that the Earth’s circumference = 360/7.2 * 800 km, which is 40,000 km! The modern measurement for the circumference of the Earth is 40,075 km, which means he was only off by 75 km!


References

Hutchens, G. (2021, September 4). This measurement is more than 2,200 years old, and its accuracy is remarkable. This measurement is more than 2,200 years old, and its accuracy is remarkable – ABC News. https://www.abc.net.au/news/2021-09-05/eratosthenes-measured-circumference-of-the-earth-2200-years-ago/100434560

YouTube. (2019, September 11). Carl Sagan explains how eratosthenes calculated circumference of the Earth. YouTube. https://www.youtube.com/watch?v=f-ppBtuc_wQ