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Pythagoras and Pythagoreans Contribution

Medina Fetai 13-A

Intro

Pythagoras was a Greek mathematician and philosopher who lived around 570 BC in Samos, which is now an island in Greek. Around 530 BC, Pythagoras and his family moved to Croton, Southern Italy, where he started his school. He taught his student how to save the human soul through mathematical principles. His followers were known as Pythagorean.

Philosophy and Science

1.Metempsychosis

2. Numerology

3. Cosmology

4. Pythagoras Reasonings

5. Tetractys

Metempsychosis

1.

Metempsychosis means the transmission of the soul from one body to another. Pythagoras mentioned that after death, the soul gets transferred into another bodys, Pythagoras used to claim that he could remember his previous four lives in detail. He also mentioned in one of his poems that he could recollect his former incarnation. According to him, his first incarnation was Aethalides as the son of Hermes, the second was a minor hero of the Trojan war, Euphorbus. His third incarnation was as a philosopher of Hermotimus and last was as Pyrrhus, a fisherman from Delos.

Numerology

2.

The principle of Pythagoras school was “All is number” or “God is number.” As mentioned by Aristotle, They believed that each number has its meaning and character. They used to worship numbers and very strongly practice numerology. For example, number 1 was called a generator as it can generate all other numbers, number 2 represents matter, number 3 represents harmony, number 4 signifies four seasons and four elements, number 5 represents marriage because it is the sum of two and three, number 6 represents creation; number 7 was sacred as it was the number of 7 planets. Odd numbers were considered as female and even numbers as male.

Cosmology

3.

Before Pythagoras, it was believed that Earth was the focal point of the universe with everything revolving around it. He was the first person who discovered planet Earth to be a sphere. He also suggested that the morning star and the evening star are the same, i.e., Venus. Pythagoreans believed that all planets move in a large circle and when they come in contact with each other, they produce melodious sounds. These sounds were known as the music of spheres. He also discovered that the orbit of the Moon was leaning towards the Equator of the Earth.

Pythagoras Reasoning

4.

There are chances that both Plato and Pythagoras believed that the science of mathematics can change the way we look at the world. It is believed that Plato might have learned that mathematical ideas are behind logic and morality from Pythagoras.

Tetractys

The Tetractys is a triangular structure also known as an equilateral triangle that consists of 10 dots arranged in four rows. One point in the first row, two points in the second, three points in the third, and four points in the fourth row. The four rows add up to number 10. Pythagoreans gave a very special place to the number 10. According to them, 10 is a holy number. Tetractys represents the four classical elements – fire, air, water, and earth.

5.

Mathematics of Pythagoras

Mathematics

1. Pythagoras Theorem

2. Five Regular Solids

3. Properties of Triangle

4. Irrational numbers

5. Amicable Numbers

6. Perfect number

Pythagoras theorem

1.

He is mainly credited for the theorem that is named after him, i.e, the ‘Pythagoras Theorem’. This theorem states that:

In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of length of other two sides that contains the right angle.

Five regular solids

2.

Proclus credited Pythagoras with the discovery of five regular solids, i.e., cube, triangle, octahedron, dodecahedron, icosahedron. Properties of these solids were further elaborated by Plato, hence these are named after him like Plato’s regular solids.

Properties of triangle

3.

Adding further to his achievements, Pythagoras and his followers gave the idea about the angles of the triangle. They stated that the sum of all angles of a triangle is equal to two right angles.

Irrational numbers

4.

Inspired by the inventions of Pythagoras, one of his students named Hippasus discovered a new set of numbers, i.e., Irrational numbers. One day, Hippasus tried to calculate the value of "root 2" and found out that it was impossible to express this number in terms of fractions. So, he proposed a new set of numbers in mathematics. This discovery shattered the Pythagoreans as it was against their belief that ‘All is number,’ and every number can be expressed as the ratio of God’s creation.

Amicable numbers

5.

Pythagoreans are credited for the discovery of the first pair of amicable numbers. Amicable numbers are those pairs of numbers for which the sum of divisors of one number is equal to the other number and vice versa. For example, (220,284), here, sum of perfect divisors of 220 is 1+2+4+5+10+11+20+22+44+55+110=284 and sum of perfect divisors of 284 is 1+2+4+71+142=220.

Perfect number

6.

Pythagoreans were the first to identify the perfect numbers. Perfect numbers are those numbers that are equal to the sum of their proper divisors. For Example, 6, 28, 496, and 8128. It is believed that Pythagoreans studied the ‘mystical’ properties of these numbers.

Music and lifestyle

Life style

Pythagoras and his followers believed that music produces the same effect on the body as medicine does. They found music to be the best source for purifying and saving one’s soul.

Pythagoras was the first person to link music to self-improvement and peace of mind. According to historians, one day, he was passing by a blacksmith, and suddenly, he noticed the sound of a hammer and found it to be musical. He rushed inside the shop and started beating hammers of different sizes on the table. He observed that the tune played by the hammer was directly proportional to the size of the hammer, hence he proved that music was mathematical.

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