The only limit to creation is the extent of a person’s imagination and curiosity. Every day, new ideas are formed and some are brought into existence. Hundreds of thousands of scientists and innovators got recognition for what they have discovered or invented. All of these creations wouldn’t have been possible if not for our predecessors. What we know as modern day technology would not have come for another thousand years without the marvelous discoveries of geniuses like Pythagoras. This term paper expounds on the life and contributions of Pythagoras of Samos along with his followers that is recorded in history.

**Biography**

Pythagoras lived around 570 BCE in Samos and is very influential in the field of mathematics mainly because the Pythagorean theorem is named after him. There are two versions of his death. One is that he died of old age at Metaponto around 500-490 BCE. The other version is that he was killed by someone who was rejected the chance to join his exclusive society and revolted against him and his followers, the Pythagoreans, in Croton (The Editors of Encyclopaedia Britannica, 2020).

Pythagoras accompanied his father Mnesarco, a merchant of the city of Tyre, on his trips. During those trips, Pythagoras’ wrote poetry, recited Homer, and played his lyre. All of those activities are inclined more to the field of arts rather than science but in the early days, knowledge is knowledge. As soon as he was old enough, his father took him to Anaximander, Ferécides of Siros, and Thales all of whom became his teachers.

Thales is the one who influenced Pythagoras in his interest in astronomy and mathematics. Meanwhile, Pythagoras, attended lectures on geometry and cosmology given by Anaximander, a long time student of Thales. After that, he travelled to Egypt and Persia to gather more knowledge. He learned about their rituals aside from mathematics. This is why Pythagoras was initially known as an expert of the fate of soul after death and religious ritual, as someone who is omnipresent, and as the founder of a society where a strict and extremely disciplined way of life is being practiced (Huffman, 2018).

It was not until the age of 40 that he migrated to Croton that he began teaching. Pythagoras is a deeply religious man who formed a society, known as Metematikoi, where a strict code of conduct being imposed. Among those is vegetarianism, the use of animal skin as clothing, secrecy, and avoidance of beans. They also firmly believed that everything in the universe is number-related. The number of his followers reached 300 and came to be known as Pythagoreans.

**Contributions**

There are no written records of Pythagoras’ teachings nor of his followers’ discoveries and contributions because of the secrecy he demanded from his student followers. What is known about Pythagoras and his followers are only based on collective accounts from ancient Greek scientists and philosophers.

Although there are fragments of detailed accounts about Pythagoras, it was written 150 years after his death. Some of the information recorded in those accounts contradicted with the data on other accounts. Following that, a large collection of books was found to be forged in the name of Pythagoras and his followers. It was from these texts that prominent ancient Greeks like Plato and Aristotle obtained some of their ideas.

Because of this, historians and even ancient Greeks were unsure of how to distinguish what Pythagoras himself contributed personally and what the Pythagoreans developed. As a result, whatever the Pythagoreans discovered was credited to their teacher even if those discoveries occurred following his death.

**In Mathematics**

As mentioned earlier, Pythagoras and his followers believed that everything is number-related. It is no surprise that their circle’s biggest and greatest contributions are centered in the study of mathematics. The most widely-recognized mathematical contribution of Pythagoras is the Pythagorean Theorem.

First, let’s start with how Pythagoras had a theory that numbers exist in their own right and had certain qualities assigned to it. For example, odd numbers are believed to be masculine, imperfect, and is also associated with divinity and harmony while even numbers are believed to be feminine and perfect. Number one is believed to be reason, two is opinion, four is justice, and five for marriage.

In his visit to Egypt, Pythagoras learned that the sum of the squares on a right angle triangle’s shorter sides is equal to its hypotenuse squared. The Pythagorean Theorem can be stated as the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides. Pythagoras proved that if triangle ABC is a right triangle with C being the longest side, then a^{2}+b^{2}=c^{2}. Professor David Joyce of Clark University discovered that the theorem can be expanded beyond a calculation of triangles and used in fields ranging from astronomy to construction and even social networking (Wills, 2019).

His proving of the Pythagorean Theorem along with his obsession with perfect numbers ultimately led to the discovery of the existence of irrational numbers. If side A and B has the length of 1, then the length of side C, the hypotenuse, is √2. It was then discovered that no ratio of whole numbers can produce √2 and if √2 is rewritten in decimal form, the digits after the decimal form wouldn’t end. They have called √2 an irrational number as this discovery has shaken their belief of a ratios in this number-based universe.

**In Astronomy**

It is also known that Pythagoras is a religious man in a sense and is also learned in the study of the cosmos. In astronomy, the Pythagoreans were well aware of the periodic numerical relations of heavenly bodies. He managed to observe and take note of the movement or rotation of the planets, sun, moon, stars, and other heavenly bodies. He then noticed that the celestial bodies are spherical. He was the one who proposed that the Earth is in fact round and not flat and that the Earth was the center of the universe. He also discovered that the planet Venus is both the morning and evening star.

**In Music **

Pythagoras’ contribution to music and his love for the Greek god Apollo isn’t known to many. He had discovered music as he was listening to the pounding of four blacksmith’s hammers which produced different tones. When he approached the blacksmiths, he saw that their anvils were of different sizes but is the ratio of the other. He then discovered that the intervals between harmonious musical notes is rooted in the ratio 2:1. Pythagoreans studied this discovery on stringed instruments and were able to determine the musical notes’ mathematical conversion.

The most basic musical interval is the octave, which occurs when the frequency of any tone is doubled or halved. Two tones set one octave apart create a feeling of identity, or the duplication of a single pitch in a higher or lower register. Pythagoras also discovered the simple ratios for other intervals. These acoustically other intervals, however, gave dissonant sound.

Various tuning systems in which minor adjustments are made in the size of Pythagorean intervals have been devised to deal with this problem. The interval between any two adjacent tones is called a half-step. An interval equal to two half-steps (such as between two white keys separated by a black key) is termed a whole-step. This contribution to music was appreciated first by the Greeks, but now, it is recognized all over the world as being the most vital step in music history.

Pythagoras achieved important discoveries out of a collection of rules that had been found by observation of trial and error. Pythagoras managed to master several subjects and share his acquired knowledge to his students. He combined mathematics with astronomy, music, and philosophy. The possibility of the number of his contributions throughout those fields to happen in our time is unthinkable. We focus on a certain area and we master it. That is not the case for Pythagoras and that’s what made him one of the most prominent ancient Greek philosophers.

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## References

Huffman, C. (2018). Pythagoras. In *The Stanford Encyclopedia of Philosophy.* https://plato.stanford.edu/entries/pythagoras/

The Editors of Encyclopaedia Britannica. (2020, May 15). Pythagoras. In *Encyclopædia Britannica. *https://www.britannica.com/biography/Pythagoras

Wills, P. (2019, July). *Notable Contributions Made by Pythagoras to Know on Pythagorean Theorem Day.* Study.com. https://study.com/blog/notable-contributions-made-by-pythagoras-to-know-on-pythagorean-theorem-day.html