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Table of Contents
Pythagoras was known as the first pure mathematician because of his contribution to the field of mathematics. He was also a philosopher who influenced Plato and Aristotle. His life remained a mystery. After his death, the accounts of his life were slowly unearthed, while some remain controversial.
See the fact file below for more information on Pythagoras, or you can download our 30-page Pythagoras worksheet pack to utilize within the classroom or home environment.
Key Facts & Information
PYTHAGORAS AND HIS EARLY LIFE
- Pythagoras, also known as Pythagoras of Samos, is often described as the first pure mathematician because he served as a very significant figure in the development of mathematics.
- Despite this, his life remained a mystery because there was a very limited account. Most of these life accounts came from his students, while some came out years after his death.
- According to some of the accounts collected about him, Pythagoras was born in Samos, Greece, around 570 BCE. His father was Mnesarchus, a merchant from Tyre, while his mother was Pythias, a native of Samos. It was believed that Mnesarchus brought corn to Samos during the time of famine, and this granted him the citizenship of Samos as a form of gratitude.
- There is very little information about his childhood, including his physical descriptions. However, it is believed that he had a striking birthmark on his thigh.
- Some accounts also say he had two or three brothers.
- Because his father was a merchant, Pythagoras studied, was able to read and play the lyre, was able to learn poetry, and was able to recite Homer.
- It was also believed that Pythagoras had great tutors like philosopher Thales and his student Anaximander, who used to give lectures in Miletus. Anaximander took a great interest in geometry, which may have influenced Pythagoras.
- Years later, when the tyrant Polycrates took control of Samos, Pythagoras went to Egypt. He visited many temples and was accepted into the priesthood in Diospolis after completing the rites required for admission.
- Ten years later, when the relationship between Samos and Egypt fell apart, Pythagoras was taken as a prisoner to Babylon.
- However, Pythagoras was not treated as a prisoner, which allowed him to continue his education in mathematics and music.
- Pythagoras eventually went back to Samos, where he founded a school called the Semicircle in the third century.
SCHOOLS FOUNDED BY PYTHAGORAS
- In this school, the Samians would hold political meetings to discuss questions about goodness, justice, and expediency.
- However, the Samians did not seem keen on Pythagoras’ method, which he learned from Egypt, and rudely responded to him.
- Then he went to Crete to study their legal system and founded another school in Croton.
- Pythagoras was also dragged into different diplomatic missions by his fellow citizens and forced to participate in public affairs. Because of this, he decided to escape.
- Pythagoras founded a philosophical and religious school in Croton (now known as Crotone in Southern Italy), where he became the head of the society of the inner circle known as mathematikoi. These followers lived with the society. They had no personal possessions and were vegetarians.
- Pythagoras taught these people, and they obeyed strict rules.
- Some of the beliefs that Pythagoras taught were the following:
- At its deepest level, the reality is mathematics in nature.
- Philosophy can be used for spiritual purification.
- The soul can rise to unite with the divine.
- Certain symbols have a mystical significance.
- All brothers of the order should observe strict loyalty and secrecy.
- Pythagoras contributed many concepts in mathematics, which made him known as the first pure mathematician.
CONTRIBUTIONS OF PYTHAGORAS
- Pythagoras spearheaded the idea of a numerical system which was the beginning of mathematics. For Pythagoras, numbers were vital, and they made up the world.
- Pythagoras also studied the properties of numbers, such as even and odd numbers.
- In the field of geometry, Pythagoras became famous with a mathematical formula that is even named after him, the Pythagorean Theorem.
- The formula shows how the square of the hypotenuse of the right-angled triangle is equal to the sum of the squares of the other two sides.
- Pythagoras also taught the principle of “All is number” or “God is number”. This shows how sacred numbers are, and they represent significant things. For instance, seven was for the number of plants at that time; three represented harmony, and four for seasons and elements.
- Metempsychosis was also one of the teachings of Pythagoras, which is a belief that all spirits are godlike and a soul moves from one body to another after death. He believed that he was reincarnated four times. First, he was Aethalides, the son of Hermes; second was Euphorbus, a minor hero of the Trojan war; next was Hermotimus, a scholar; and lastly, Pyrrhus, a fisherman from Delos.
- Pythagoras was also the first to discover that the planet Earth is a sphere. Pythagoreans also believe that planets move around in a circle, and when they get close to each other, they produce a melody. They believe that the Earth, stars, and planets all move in a circle around a central flame.
CONTRIBUTIONS OF PYTHAGORAS
- Pythagoras was given credit for discovering the five solids: cube, triangle, octahedron, icosahedron, and dodecahedron. Plato elaborated on these and published them in books.
- Pythagoras and his followers also proposed a generalization that the sum of the interior angles of a polygon with n sides is equal to (2n-4) right angles, and the sum of its exterior angles is equal to four right angles.
- Pythagoreans also forwarded the idea of Tetractys. It is a triangular structure known as an equilateral triangle consisting of 10 dots arranged in four rows.
- Furthermore, Pythagoras also inspired irrational and perfect numbers. Hippasus, one of Pythagoras’ students, discovered and proposed irrational numbers which contradicted the Pythagoreans’ theory. Because of this, Hippasus was sentenced to death. On the other hand, the Pythagoreans also discovered that perfect numbers are equal to the sum of their proper divisors. Euclid further developed the explanation.
- Pythagoreans were also given credit for the discovery of amicable numbers. These are two numbers where each is equal to the proper divisors of the other.
CONTRIBUTIONS OF PYTHAGORAS
- Pythagoras was the first who believed that music had an effect similar to what medicine has on the body. Therefore, he was also the first one who recommended it. Pythagoreans believed music was the best source of purifying and saving one’s soul. Pythagoras also linked music to self-improvement and peace of mind.
- It was also believed that Pythagoras inspired Plato and Aristotle’s reasonings. Plato may have obtained his morality from Pythagoras. Plato and Pythagoras both had a way of dealing with the spirit and its place in the material world. These were both impacted by Orphism, a set of religious beliefs and practices originating in the ancient Greek world.
PYTHAGOREAN THEOREM
- The Pythagorean Theorem is one of the most fundamental geometric theorems.
- It is one of Pythagoras’ contributions to mathematics.
- Pythagorean theorem claims that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse, hence the algebraic notation, a2+b2=c2.
- In the algebraic notation, a is the altitude, b is the base, and c is the hypotenuse which is the longest side of the right-angled triangle.
- This formula can be applied to any triangle with one 90-degree angle. This triangle produces Pythagoras’ theorem.
- Another way of understanding this is by using the square of the length of the longest side of the triangle. This is equal to the sum of the area of the squares formed by the other two sides of the right-angled triangle.
- This theorem can be proven by using algebraic methods and using similar triangles methods.
PYTHAGORAS’ DEATH
- The cause of Pythagoras’ death remains a mystery, but some concluded that he died in 495 BCE.
- According to some accounts, he died at the age of 75.
- One of the cited assumptions stated that the house of Milo in Croton was ransacked and burned. There were 50 to 60 Pythagoreans who were killed, and the others who survived took refuge in Thebes and other places.
- Another theory was Pythagoras died at the hands of an angry mob who targeted him.
- Others say that Syracusans may have killed him because he was part of the war between the Argentum.
- Another story stated that he died in Metapontum, starving himself for 40 days because he was grieving the persecution of the Pythagoreans.
- Even though Pythagoras’ life was unclear and remained a mystery, his impact on philosophy and mathematics was indeed remarkable.
Pythagoras Worksheets
This fantastic bundle includes everything you need to know about Pythagoras across 30 in-depth pages. These ready-to-use worksheets are perfect for teaching kids about Pythagoras, a Greek mathematician and philosopher born on the island of Samos in 570 BCE and is best known for the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Complete List of Included Worksheets
Below is a list of all the worksheets included in this document.
- Pythagoras Facts
- True or False
- Match the Concept
- Identification
- Pythagorean Profile
- Pythagorean Rhymes
- Pythagorean Beliefs
- Pythagorean Influence
- Great Contributions
- Letter to Pythagoras
- Portraying Pythagoras
Frequently Asked Questions
Who was Pythagoras, and what was his contribution to mathematics?
Pythagoras was a Greek mathematician, philosopher, and founder of the Pythagorean school of thought. He is most famous for the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This theorem is a fundamental result in mathematics used in various fields, including trigonometry, geometry, and engineering.
What was the Pythagorean school of thought?
The Pythagorean school was a religious and philosophical society founded by Pythagoras. Its members, called Pythagoreans, believed that mathematical concepts were the basis of all things in the universe and that numbers held a special significance. They also believed in the transmigration of souls and practiced vegetarianism.
What was Pythagoras’ view on mathematics?
Pythagoras believed that mathematics was a fundamental aspect of the universe and that numbers held a special significance. He thought that mathematical relationships were the key to understanding the world and that mathematical concepts such as proportion, ratio, and harmony could be applied to both the natural world and human behavior.
How did Pythagoras’ ideas influence later philosophers and mathematicians?
Pythagoras’ ideas profoundly impacted the development of philosophy and mathematics. Plato was heavily influenced by Pythagorean thought and used mathematical concepts in his philosophical writings. Pythagoras’ theorem was used by the ancient Greeks to calculate the distance between points and was later rediscovered and proved by Euclid.
What is the legacy of Pythagoras today?
Pythagoras’ legacy continues today, with the Pythagorean theorem still being an actual result in mathematics and widely used in various fields. His ideas about the relationship between mathematics and the universe influenced later philosophers and scientists, including Galileo Galilei and Johannes Kepler. Additionally, the Pythagorean school of thought and its emphasis on the importance of mathematics has had a lasting impact on Western philosophy and science development.
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