Eudoxus' Contribution To Calculus Essay

641 words - 3 pages

Eudoxus was a notable mathematician and astronomer of ancient times, particularly 408 – 355 BC. He lived in Greece and studied under Plato, one of the most notable philosophers ever. In Calculus, Eudoxus is known for advancing Antiphon’s ideas on the method of exhaustion. The method of exhaustion is very important to calculus because one of the fundamental themes of calculus is sending variables (or whatever it happens to be) to infinity, which is a branch of the method of exhaustion. This is known as taking the limit.
Eudoxus used the method of exhaustion to calculate volume and area. One example of this is his work with the area of a circle. At the time they hadn’t established this yet. If you didn’t know the formula for finding the area of a circle, you would need to approximate it, just like how we have learned to approximate the area under a curve with Rieman Sums. First, you could inscribe a circle in a triangle, and use the area of the triangle to approximate the area of the circle. But that would not give you a very accurate answer, so next you would draw a square around your circle. Still, this is not very accurate, so you would keep adding to the number of sides of your polygon until you approached infinity, giving you the most accurate answer possible without the formula. This is how Eudoxus would have figured out the area of a circle – with limits.
It seems thus that Eudoxus was the first person to develop the definition of a limit. This definition has evolved through the centuries, and today we know a limit as “f(x) gets close to L as x gets close to a” (taken from mathisfun.com). In simpler language, as x approaches a, y approaches L. L and a are the constants that you would already know. After Eudoxus came Archimedes, another Greek philosopher. He used Eudoxus’ ideas but furthered them by drawing regular polygons in and tangent...

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