Tag Archives: Pythagoras

The Mysterious Pythagoras

Introduction
               The first time I heard of the Pythagorean theorem was in my high school geometry class in ninth grade. As a young child, I never thought of it as anything else but a strange name. It was simply another formula that I needed to memorize in order to get a good grade on the upcoming test. Many of you can relate to this, as I’m sure everybody was required to learn about the theorem. Everyone has been through the “drill and kill” method where “A squared plus B squared equals C squared” can be said without effort. But there is actually a heavy history behind the name Pythagorean, and it derives from a historical influential Greek named Pythagoras. Surprisingly, the life of Pythagoras can be seen as a legend or myth with ambiguity. As I studied and read about him, I was amazed at how influential he was and the people that he moved with his teachings. Every country he visited, he obtained followers who were inspired and motivated to better themselves and contribute to mathematics, philosophy, and music. Truly it is unquestionable why his name has been discreetly implanted into mathematics and our modern day culture.

Sculpture of Pythagoras in the Capitoline Museums, in Rome. Image: Galilea, via Wikipedia

Sculpture of Pythagoras in the Capitoline Museums, in Rome. Image: Galilea, via Wikipedia

Background
             There is great controversy among historians about the origins and early life of Pythagoras. All scholars can agree that he was born in the island of Samos. Aristoxenus, a Greek philosopher and pupil of Aristotle, stated that Pythagoras lived in Samos for about 40 years and then left during the reign of Polycrates. As we trace it back, it could be estimated that he was born around the year 570 BC what is today Italy in what was then a part of Greece At around 530 BC, he emigrated to Croton and spent the rest of his life there until his death at around 510 BC. Throughout his early life, he had the opportunity to travel and learn from many different cultures and obtained their knowledge. He traveled to Egypt where he learned about their religious practices and geometry. He also visited the Phoenicians, the Chaldeans, and the Magians to learn about arithmetic, astronomy, and religious practices. Along with knowledge about religion, he had the privilege to be taught ethics by a Delphic priestess named Themistoclea. Unquestionably, Pythagoras was a revered individual who knew how to communicate with others and connect with them. The talent and knowledge he obtained throughout his life had influenced many and created an exclusive secret society called the Pythagoreans. This society made Pythagoras a God-like figure and they strictly practiced his teachings. They consisted of a group of individuals who studied philosophy and were serious mathematicians and scientists.

Pythagoras in the center teaching music. Image from “The School of Athens” by Raphael, via Wikipedia.

Great Teacher or Renowned Mathematician?
             Surprisingly, there is no clear record of Pythagoras being a mathematician and his famous theorem being proved by him. I mentioned previously that he obtained knowledge in mathematics, but there is actually no clear record of his works contributing to geometry. Although this is the case, Aristotle’s pupil Eudemus wrote a history of geometry in the fourth century. He did not mention anything about the Pythagorean theorem, but he did note that Pythagoras played a role in the use of geometry in education for people who were considered freemen and not slaves. Proclus, who at the time preserved and commentated the works of Plato and Euclid, later rebuked Eudemus’ proposal that Pythagoras contributed to mathematics. So when it came down to it, Pythagoras was not known as a geometer during the time of Plato or Aristotle. But because of his influence and teaching towards the Pythagoreans, it is likely that they attributed their works to him. It may even be possible that his followers gave homage to his name when the Pythagorean theorem was founded. There are unfortunately many more claims and theories about Pythagoras that can either support him or not support him as a mathematician. Because of all of these different opinions and perspectives, it is difficult to say whether or not he actually contributed anything to geometry. But it is safe to say that he was a highly religious person and taught a particular way of life. He believed that the soul was immortal and went through a series of reincarnations. He taught a peculiar strict way of life that emphasized on dietary restrictions, religious ritual, and rigorous self-discipline. His expertise in religious ritual gave notice to many and he was recognized as someone who could be at two different places at the same time. Unquestionably, because of his acquired education and communication skills, he was popular among his peers and followers.

Closing
            There is so much more that can be discussed about Pythagoras and the more I read about him, the more fascinated I become. It’s amazing to me how one individual can be so popular that no one really knows his true origins or who he was exactly. Clearly he has made himself exalted in the form of his name among mathematics and other fields of study. I never thought that something that I used in almost all of my math classes would be connected with so much history and mystery. I feel even more impressed by the Pythagorean theorem as I researched deeper about Pythagoras and his background. There is definitely more information that can be gathered about him and I’ve only shared just a small portion of what he actually is. For further reading, I recommend looking into his secret organization and their discoveries. In closing, my take home message is to encourage everyone to look deeper into the math formulas and theorems taught in our education. It will definitely give deeper insight and provide meaning to them to the point where we can all appreciate frameworks of our mathematical world.

References:
http://plato.stanford.edu/entries/pythagoras/#ChrChaSouPyt
http://en.wikipedia.org/wiki/Pythagoras

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The mysterious life of Pythagoras

A bust of Pythagoras. Image: Gavin Baker, via Flickr.

Pythagoras. Image: Gavin Baker, via Flickr.

The Pythagorean Theorem is a well-known theorem that we study in math. We all probably learned about it in high school during our geometry class. It is a simple theorem: a2 + b2= c2, which we use to find the hypotenuse of a right angle (90 degrees) triangle. What we did not learn about was the man who this theorem is named after. What was he like, how did he live his life, and what was he famous for?

Pythagoras was an Ionian Greek philosopher and a mathematician. He was from a Greek Island  called Samos. He made many contributions in his life, one of which was a movement called Pythagoreans. Pythagoras strongly believed that the soul was immortal and went through a series of reincarnations; he was also thought to be knowledgeable about various religious rituals and for his strict way of living his life.

Pythagoras created a school in Croton (now known as Crotone and is located in Calabria, Southern Italy) which not only allowed male but also female students (he ended up marrying one of them). The school was divided into four sections: arithmetica ( the number theory), harmonica (music), geometra (geometry), and astrologia (astronomy). The members of the school were not allowed to share the knowledge they gathered with those who did not go to that school. Therefore there are not many written documents about the Pythagoreans’ ideas and any findings that they might have made. For this reason we cannot tell what is true and what is a myth in the information we have about him. Scholars are not even sure if Pythagoras created the Pythagorean Theorem or whether it was merely named after him.

Pythagoras had many interests in different fields. From his work many scholars, such as Nicholas Copernicus, Plato and his student Socrates, were inspired. For example, in Plato’s Phaedo, Socrates talks about the possibilities related to the soul’s existence and how it went through a series of lives after death. Nicholas Copernicus did not refer his view on the earth’s relationship with the sun as the ‘Copernican System’ but he refers it as Astronomia Pythagorica because he was greatly inspired by Pythagoras’ ideas on the cosmos, which gave him and other philosophers various views on different topics. In Copernicus’ case, this was astronomy.

One of the articles I read states that Pythagoras helped with the discovery of harmonious intervals of the musical scale. He found the fourth, the fifth and the whole tones. This indicates that mathematics can also change the way we perceive different sounds. Pythagoras uses ratios to change these sounds, for example, by dividing a string in half which is a ratio of 2:1, the shorter string gives off a tone that is an octave higher than the longer string. Similar with the fourth, the ratio of 3:4; and the fifth, a ratio of 2:3 change the octave. The ratio of 9:8 (a pitch) characterizes the whole tone. In this way mathematics helped in discovering the musical sound system.

Because of a lack of documents, Pythagoras’ entire life is a mystery, including his death. No one seems to know how, when and where Pythagoras really died. Some believe that Pythagoras went back to Croton and lived up to 100 years. Others believe that the Pythagoreans (including Pythagoras, himself) was surrounded and set to fire during a revolt, but it is also a possibility that he may have escaped, as people made a ‘bridge’ of their bodies over the flames. It is believed that after the escape he went to Metapontum (a city located in Sothern Italy) where he died on a sacred bean field rather than choosing to die at the hands of his enemies.

Work cited:

https://philosophynow.org/issues/78/The_Death_of_Pythagoras

http://www.math.wichita.edu/history/men/pythagoras.html

http://plato.stanford.edu/entries/pythagoras/

http://plato.stanford.edu/entries/pythagoras/

https://www.flickr.com/photos/naufragio/793278893/

http://www.philosophybasics.com/philosophers_pythagoras.html