# Free Math In Ancient Greece Essay Example

Type of paper: Essay

Topic: Archimedes, Athens, Greece, World, Discovery, Mathematics, Time, History

Pages: 3

Words: 825

Published: 2020/10/12

Ancient Greece has long been known as the intellectual center of the ancient world. Also attributed to the development of basic democracy, Greece’s many academic contributions to the world are seemingly insurmountable. Greece’s most notable academic pursuit was philosophy, as most basic history classes include at least an overview of Plato or Aristotle. Their philosophy would, for many centuries, be the dominating philosophy of Western civilization. However, while less known, there were several Greek mathematicians who made equally noteworthy and revolutionary discoveries. Euclid and Archimedes are two of these famous mathematicians who changed both their world, and future generations.

Euclid of Alexandria developed a revolutionary take on geometry and number theory. While Euclid himself was Greek, he did live in Alexandria for much of his life, due to the fact Alexander the Great conquered much of the known world. Alexandria contained many museums which had thousands of Greek manuscripts, which preserved its influence on this Egyptian city (Lewinter, 2002). It is with this historical background that Euclid makes his mathematical discoveries.

Around the year 300 B.C.E., Euclid was able to summarize and develop over 300 years of Greek thought. Euclid first started developing definitions. These included things like “a point has location without extension,” and “parallel lines don’t meet no matter how far they are extended (Lewinter, 2002).” While these ideas seem basic today, everything had to be proven at some point in time, and that is exactly what Euclid managed. His idea about parallel lines was the mainstream idea up until the nineteenth century, where new ideas were finally discovered. However, for around 2,000 years, Euclidean geometry was the common approach.

Another area in which Euclid helped further the development of mathematics was his work with prime numbers and number theory in general. He was most interested in proving that there were an infinite amount of prime numbers. Euclid achieved this by first assuming there were a finite number of prime numbers and hope this yielded a contradiction. He managed to do this, after much study, and also provided a formula for finding the greatest common factor. During his work with prime numbers Euclid realized that if a number can go into, for example, x and y, then it will also work with x – y. He found it works to subtract the smaller number from the larger one as many times as needed to compute the greatest common factor of the remaining smaller number (Lewinter, 2002). This discovery, revolutionary at this time, still holds true today. Therefore, Euclid provided timeless contributions in the field of geometry and number theory. It took a great amount of time an energy to completely validate his proofs, and his ability to do so serves as a witness to his genius.

Archimedes was another great Greek scientist. He was born around 287 B.C.E in the port of Syracuse, Sicily. He had grown up in a scientific household, as his father was an astronomer. Archimedes did study under Euclid in Alexandria for a time, but otherwise remained on the island of Sicily for most of his life. Archimedes was another scientist who was naturally curious about the real world, and because of this, developed many mathematical and scientific tools which still impact life today (“Archimedes of Syracuse”).

Archimedes most practical discovery during his time was arguably the fulcrum. Because he lived during the Punic Wars, any technological advantage he could give his home town over the Romans would prove invaluable. Therefore, Archimedes found a way to discover the basic principles of a fulcrum, and compound pulley system. These devices helped him to fortify the cliffs of Syracuse as they could hoist Roman ships out of the water and let them drop, smashing them. Consequently, this caused less of a need for slave labor in defense, so these resources could be used elsewhere. Archimedes discovered these scientific devices through math. He found a mathematical formula for counterbalancing weight, which he then applied practically to a defense system (Lewinter, 2002).

However, Archimedes achievements do not stop here. He also discovered many properties of geometry during his lifetime. His revolutionary discovery revolved around the idea to inscribe a square in a circle. It was considered preposterous at the time, but by putting a square inside a circle, Archimedes was able to discovery many geometric properties. Archimedes discovered the formula A= 1/2Ph through his inscribed square experiment, and later started working around an octagon. Through these two shapes, Archimedes was able to come up with the first idea about circumference of a circle, as he found the diameter to be constant. He continued to build on this idea, and thanks the Archimedes, the principles were set in place to discover how to find the area of a circle (Lewinter, 2002). Archimedes research greatly impacted geometry today.

In conclusion, Euclid and Archimedes were extremely influential in the world of math and science, and for Greek culture of their time. While not as universally known as Aristotle or Plato, their practical achievements in their field have helped the development of Western civilization. They are further proof of how Greek influence was the intellectual center of the ancient world.

## References

Lewinter, M., & Widulski, W. (2002). The saga of mathematics: A brief history. Upper Saddle River, N.J.: Prentice Hall.

The History of Archimedes. (n.d.). Retrieved January 26, 2015, from http://archimedespalimpsest.org/about/history/archimedes.php

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