# The Development of the Concept of Irrational Numbers

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The Development of the Concept of Irrational Numbers

Irrational numbers are real numbers that cannot be written as a simple fraction or a whole number. For example, irrational numbers can be included in the category of √2, e, Π, Φ, and many more. The √2 is equal to 1.4142. e is equal to 2.718. Π is equal to 3.1415. Φ is equal to 1.6180. None of these numbers are “pretty” numbers. Their decimal places keep going and do not end. There is no pattern to the numbers of the decimal places. They are all random numbers that make up the one irrational number. The concept of irrational numbers took many years and many people to discover and prove (I.P., 1997).
There are many people that contributed to the discovery of irrational numbers. Some of these people include Hippasus of Metapontum, Leonard Euler, Archimedes, and Phidias. Hippasus found the √2. Leonard Euler found the number e. Archimedes found Π. Phidias found the golden ratio. Hippasus found the first irrational number of √2. In the 5th century, he was trying to find the length of the sides of a pentagon. He successfully found the irrational number when he found the hypotenuse of an isosceles right triangle. He is thought to have found this magnificent finding at sea. However, his work is often discounted or not recognized because he was supposedly thrown overboard by fellow shipmates. His work contradicted the Pythagorean mathematics that was already in place. The fundamentals of the Pythagorean mathematics was that number and geometry were not able to be separated (Irrational Number, 2014).
Zeno of Elea was the next person who attempted to prove irrational numbers by challenging the Pythagorean mathematics as well. He lived from 490BC to 430BC. Zeno had influence from Socrate...

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...r position in mathematics and their relation until about the 5th century. People began to have a drive to find more about the irrational numbers. Euler put a symbol with Π and e, but he was not the first to discover these wonderful numbers that help people in every day activities and jobs.

Works Cited

Burton, D. (2011). The History of Mathematics: An Introduction. (Seventh Ed.) New York, NY. McGraw-Hill Companies, Inc.
I.P. (1997). Assessing irrational irregularity. Science News, 151(22), 340.
Irrational Number. (Apr. 4, 2014). Irrational Number. .
O’Connor, J. J. & Robertson, E. F. (Sept. 2001). The Number e. .
Ramasinghe, W. (2005). A Simple Proof e2 is Irrational. International Journal of Mathematical Education in Science and Technology, 36(4):407-441