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Pythagoras and His Countless Discoveries

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Pythagoras was born in 569 BCE in the island of Samos. As a kid, Pythagoras had 2 or 3 brothers. He and his brothers learned how to recite poetry, recite Homer, and play the lyre. He was raised with his mom, Pythias, and father, Mnesarchus. Often, he went on business trips with his dad where he was taught by scholars. With these scholars, he learned geometry and cosmology. Some scholars say Mnesarchus once took him to Tyre, where he studied under scholars from Syria. They also suggest they might have gone to Italy in those years. Along with that, Pythagoras studied with many other teachers. He also studied with many wise people in Chaldea. In addition, Pherecydes of Syros was somebody he studied philosophy from. In addition, he studied with the philosopher Thales and his student Anaximander. Later in his life, his astronomical and geometrical discoveries had developed from theories of Thale.

34 years after he was born, Pythagoras left for Egypt to study with priests. Some say he did this in order to escape the tyranny of Polycrates, the ruler of Samos. Also, it is believed the Egyptian priest Oenuphis studied with him for a few years. For 10 years, he stayed here. Finally, he gained admission into priesthood. In 525 BCE, Persia invaded Egypt and Pythagoras was taken prisoner and brought to Babylon. Here, he learned with Bablyonians unlike a typical prisoner would be treated. Later, he escaped and came back to Samos. In Samos, he founded a school called the Semicircle. A group of travelers from his island were killed. Later, people from that same country came. Pythagoras begged the leaders of his island and they listened to him. This upset many politicians and made him many enemies. In just 500 BCE, his school was raided. Buildings were set on fire killing many of his followers and students known as Pythagoreans. Some say when Pythagoras wouldn’t step on plants even though his life was on the line because he believed that all living things have a soul. After a few years, he went to Crete to study more. In addition, he founded another here. Also, he worked with a secretive group discussing math, philosophy, metaphysics, and religion. They believed a soul is immortal and can’t be harmed. Also, Pythagoras urged to follow a code of conduct that all Pythagoreans followed. Pythagoreans all wore simple linen clothing. They were not allowed to urinate in public. Also, they were encouraged to have children and to reject wealthy material. Pythagoras focused his rules on day to day life. Also, they were known for maintaining silence. New members of the society would have to remain silent for 5 years. This was due to their code of not wanting to speak about their discoveries. He then returned to Samos and rebuilt his school, the Semicircle, burnt down earlier. He then shared his mathematical and philosophical discoveries with his students.

Pythagoras is known for his countless discoveries. One of them are the platonic solids. The five platonic solids are the tetrahedron (4 triangles), cube (6 squares), octahedron (8 triangles), Dodecahedron (12 pentagons), Icosahedron (20 triangles). These are the only polyhedrons, 3-dimensional solids with the same regular polygon as its sides. In Pythagoras’ lifetime, he constructed the first 3 platonic solids. Also, Pythagoras is known for designating odd and even numbers. He called odd numbers masculine and even numbers feminine. Also, Pythagoras gave characteristics to many other numbers. For example he defines what would become modulo, a commonly used math concept today. He defined a remainder system which is used today as well. He also defined square numbers. In addition, he defined tetraktys to be the sum of the numbers from 1 to n. For example, the third tetrakyt is 1 + 2 + 3 = 6. Today, these are known as triangular numbers. They are considered to be a special number for this reason. This is because the tetraktys represented the number of points needed to define the universe. The first 2 make a line, add a third point and the line becomes 2 dimensional. Add a fourth point not on the plane of the first 3 gives a 3 dimensional figure. Today scientists have used this information further to develop higher dimensions. Scientists think the universe could have more than 3 dimensions. One of Pythagoras’ most profound and well known discovery is the Pythagorean theorem. Although he wasn’t able to prove it, he discovered the sum of squares of the legs of a right triangle equals the square of the hypotenuse of a triangle. To right this as an equation, we let the legs of the right triangle have lengths of a and b and the hypotenuse have a side length of c.

The simple geometric formula is one of the main foundations of mathematics and Euclidean geometry. This formula remained unproven till Euclid’s time. Some say that it was actually discovered by the Egyptians and Pythagoras just popularized the formula and showed a use case of it. This remarkable discovery led to another conspiracy. At the time, they believed all lengths could be expressed as a ratio a:b. The pythagorean theorem showed that this wasn’t necessarily true. This value can’t be expressed as a ratio. This contradicts the beliefs of all Pythagoreans. Today we know that lengths are either rational or irrational.

Pythagoras’ discoveries weren’t limited to math. He had many discoveries in music and cosmology as well. For example, he discovered that planets are spherical. He discovered that due to gravity, matter was packed together to form an almost sphere. He figure out that there were 9 planets and claimed there was another directly opposite of Earth that wasn’t visible in order to get a total of 10 planets, a perfect number at the time. These discoveries led the fundamentals for cosmology today. His belief of a 10th planet was later proved false. Also, he discovered music is composed of ratios. A ratio of 1:2 makes an octave. A ratio of 3:2 produces a fifth and a ratio of 4:3 makes a fourth. The ratio of the length of the string held to the length of the total string determines the pitch of the music. Today, music instruments use this principle today in order to create different pitch sounds.

The cause of Pythagoras death is unknown. Some say it was because of a raid causing his school to be burnt down. Others say he was killed by an angry mob. Others say he was caught up in war between Agrigentum and Syracusans and killed them. Eitherways, his legacy is long lasting. I truly enjoy math and without Pythagoras, over half of mathematical discoveries wouldn’t exist. In addition, he helped with many fundamentals of cosmology and philosophy. His legacy is long lasting and will never be forgotten. In addition, Pythagoreans continued developing Pythagoras work further. After his death, his followers soon finished constructing the remaining 2 platonic solids. In addition, there were many mathematicians who used Pythagoras discoveries to further develop outstanding theorems. His presence will never be forgotten off the face of our planet.

Pythagoras was a man of wonders and intelligence. We can not only honor his remarkable discoveries in mathematics, cosmology, and philosophy, but also, his obedience of life. Even with many enemies and haters of his community, he pulled away many times remaining loyal to his code. He is the true meaning of making utmost use of life. Next time in your math class, rather than being bored learning about the Pythagorean theorem and his other discoveries, think about what would have happened without Pythagoras.

Works Cited

  • Greene, Nick. “The Life of Pythagoras.” ThoughtCo, ThoughtCo, 10 Oct. 2019,
  • Mark, Joshua J. “Pythagoras.” Ancient History Encyclopedia, Ancient History Encyclopedia, 24 Feb. 2020,
  • Staeger, Rob. Ancient Mathematicians. Morgan Reynolds Pub., 2009. 

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