# Pythagoras

By: Mariana Castillo, Denise Mojica & Cecilia Gregory

Early Life and How he Came to Be

Pythagoras was born in 570 BCE in Samos, Ionia. There isn’t much known about what his childhood was like, nor is there a lot of information on what he physically looked like. Pythagoras learned his skills from three famous philosophers who served as his teachers; Pherekydes, Thales, and Anaximander. Thales in particular contributed to Pythagoras’ fascination with astronomy and mathematics. Pythagoras traveled to Egypt to learn more about the topics that Thales intrigued him with. During his travel, he learned the Egyptian culture and then traveled back to Samos. Upon his return he then left to Croton, a city in the southern part of Italy. There he established a school called “the semicircle” and gained followers under the name of mathematikoi, that were taught by Pythagoras himself. With this, he was able to further his interests and become an influential Greek figure to not only the people he taught, but to many others around the world as well. After years of studying and furthering his work, Pythagoras died in 500 BCE in Metapontum, Italy; leaving behind a legacy that is forever known. Mathematical Discoveries

Pythagoras and his followers sought to explain many explanations of the world through patterns and numbers. He and his followers believed numbers held truths, specific characteristics, and representations; for example, odd numbers were female and even were male. However, his most popular findings were geometric relationships and patterns.

A very special number to the Pythagoreans, Pythagoras and his followers, was the “teractys” which was an equilateral triangular line-up of points. It’s a visual relationship with four rows of points starting with one point in the first row, two in the second, and so on. The sum of all the points is 10. Pythagoras’ most useful finding was the “Pythagorean Theorem” in which a right triangle’s side lengths’ squares are related; the sum of squares of the two legs (sides creating the right angle) is equal to the square of the hypotenuse, a2+b2=c2. Stemming from this theorem are “Pythagorean triples,” sets of three numbers with the first two having their sum of squares equal the third number’s square. The most popular triple being (3, 4, 5). Also dealing with triangles was the discovery that all the angles of the shape add up to 180 degrees. This finding led to the generalizations of polygons and their interior and exterior angles.

Another notable finding is by one of Pythagoras’ students who was interested in the square root of two. It could not be written as a fraction which led to the establishment of irrational numbers, numbers that could not be expressed as fractions. This contributed to much of geometry which is continuous with much its planes, lines, and angles.

Number theory was started by the Pythagoreans, in which along triangles and their squares, perfect numbers were looked at. Perfect numbers could be divided by two numbers, and the sum of those numbers also add up to the perfect number.
Another discovery by Pythagoras was the ratios among musical tones in harmony. Creating the common intervals, are the first four overtones: the octave, perfect fifth, perfect fourth, and the major third (1:1, 3:2, 4:3, and 5:4, respectively ).

Influence on Society

Pythagoras has influenced today’s in several way. Because of the Pythagorean Theorem, we have been tortured by our grade school math teaches, but most importantly, we have been able to mathematically determine very important questions that help all aspects of society. The Pythagorean Theorem is essential to many fields of mathematics. The Pythagorean Theorem is constantly used by architects, engineers and surveyors. The triangle also has its place in Computer Aided Drafting and military application.  For example, a rescue worker can use the Pythagorean Theorem to determine the necessary length of a ladder.

Sources

http://www-history.mcs.st-and.ac.uk/Biographies/Pythagoras.html

http://www.britannica.com/biography/Pythagoras

https://prezi.com/dqfwhqr9hjfk/pythagoras-and-his-contributions-to-modern-society/

“Pythagoras – Greek Mathematics – The Story of Mathematics.” Pythagoras – Greek Mathematics – The Story of Mathematics. N.p., n.d. Web. 01 Dec. 2015.