PYTHAGORAS

We chose to work with Pythagoras because we had heard about his school and his strange community. We wanted to know more about this strange and mysterious man.

And we have indeed found a lot of information! We had no idea when we started that there are so many words written about numbers… Our problem has not been only the extent of the info, but also that some if it gives different facts. Was Pythagoras born in 580 BC or 569 BC? Did he get killed when his school burnt down or as an old man in the northern Italy? We have written what we believe is closest to the truth. These details don’t really matter. The most important is what he did for the history of mathematics.

Pythagoras’ life - From he was born in Greece

Thinking and being - He was a strange man…

The Pythagoreans - Pythagoras’ school and community

Special numbers - The Pythagorean way to see numbers

Astronomy - A little bit about their assumptions

The Pythagorean Theorem - What his is world famous for

Conclusion & Source list

One day about 580 BC the great Greek philosopher and mathematician Pythagoras was born on the isle of Samos. Here he spent his childhood - and he is now known as "the Samian". He was the son of Mnesarchus, and grew up in a moderately wealthy family. (Though other accounts says he was born a son of the god Apollo...)

Once when he was in Egypt, the great mathematician Thales recommended him to study there to enlarge his knowledge. On the way back to Samos, Pyhtagoras travelled to Lebanon. There he studies in the temples of Tyre, Sidon and Byblos for about 3 years, after being initiated into the Ancient Mysteries of the Phoenicaians. Afterwards he did as Thales had recommended him, and studied for 22 years in Egypt.

When he tried to return back to Greece, he was for some reason captured - which made him study in Babylon for another 13 years.

At the age of 50, he finally got home to Samos. Then he found that the island was subdued under the tyrannical yoke of Polycrates. Despite of him being there, Pythagoras tried to found a school there. But he failed, and decided to leave and go to Crotona, in Southern Italy instead.

There he succeeded with establishing a famous school of philosophy, mathematics and natural science. Later on he married one of the female pupils there, and together they got at least two daughters.

Around 500 BC the school was attacked and burned down. It is yet uncertain weather Pythagoras was killed then, or if he died later.

His way of thinking seams to be influenced by the East.

I.e., he believed that ones soul was going to be reincarnated. That is also what the Hindu religion tells as the truth. Pythagoras himself said that he had once before lived as a warrior in the Troja-war.

Also he believed that animals have got a soul.

He was a vegetarian, and he also refused to eat beans, as he thought human-souls were in them. Another thing he refused was to eat bread unless it was cut in a certain way.

His way of dressing was rather unusual for the time. He wore a gold diadem, a sweeping white robe and trousers, which was not common.

Of his work, nothing is left. All we know about what he found out is second-hand. That is why no one can be sure if the discoveries from his school came from him or from his students.

When Pythagoras settled in Crotona in 530 BC, he established his famous school -said to be the creator of mathematics as a science. This movement of his, known as the Pythagoreans, was almost like a religion were the numbers were regarded as gods.

This secret society was not a 'brotherhood', but a community of families. (Some believe that it later became the model of Plato's ideal society.) Everything was passed on by word of mouth; written accounts were forbidden. All Pythagoreans were under oath not to speak about their sacred knowledge. It is know that one of the men once told someone from the outside that the number of can't really be told. He was killed.

The community was authoritarian and ultra-conservative, but they accepted women as equals on all terms. At least 28 of the students were female. It is also known that when Pythagoras died, his wife Teano (who had been a teacher at the school) ran the school together with her two daughters.

All property was held in common. The Pythagoreans lives were lead ascetic, and they were all vegetarians. They dressed simple, and it was important to examine your inner self frequently. The leaders were expected to live in celibacy and devote all of their time to numbers.

The Pythagoreans are known for the Pythagorean Theorem*, their knowledge about strings and harmony in music, the prime numbers*, the gyldne snitt* and they knew a lot about astrology*. (-This does not necessarily mean that the were the first to think all of this!)

* See other part of the project for more information about these subjects.

The Pythagoreans believed in five basic ideas:

1. The university was created, and continues to exist on the basis of a divine plan. The ultimate reality is not material but spiritual; it consists of the ideas of number and form.
1. The human souls are spiritual entities; a self-moving number which passes from body to body. All souls are eternal.
2. There is an inner harmony and order in the universe, resulting from the union of opposites.
3. Friendship and modesty are most important in human relations.
4. The divine ideas, which created and maintain the universe, are those of numbers.

The last principle was the most important one, and sprung from the Pythagoreans experiences with possibility to explain music (how the harmonies are related to the length of the strings) and astrology from numbers.

As the Pythagoreans' recognition increased politically, so did their enemies. There were several attacks at the school, as the dissatisfaction among the 'outsiders' grew stronger. Then, around 500 BC the enemies of the school put it on fire, and killed many of the Pythagoreans. Some of them managed to escape, and even though they did not have a school any more, the Pythagoreans continued to exist as a group until 400 BC.

The number one was very special to the Pythagoreans. It was the first number to be created, and they considered it much more than a number. Like Adam in the Old Testament, the number one was created in the image of God. This number had divine qualities; it was a symbol of unity, wholeness and priority.

Two was the first of the even numbers, which were considered as the 'male numbers'. This was a special number too, but it didn't have as many divine qualities as number one.

The fact that the sum of the four first numbers is ten (1+2+3+4) meant something special to the Pythagoreans. In Greek they called this sum teatraktos, and this was one of the innermost secrets of the group.

They also operated with so-called perfect numbers. A perfect number is a number who's factors sum up to the number itself. (6: 1+2+3) Between one and 10,000 there are only four of these; 6, 28, 496 and 8,128. The Pythagoreans compared this to humans: very few are perfect, good and beautiful. But imperfection in numbers is common, just like evil and ugliness in people.

The division of numbers started with even ('male', who can be divided by two) or odd ('female', not dividable by two) numbers. Then the numbers were separated into even-odd numbers (dividable by two only once), even-even numbers (can be divided by two until one is reached) odd-even numbers (can be divided by one several times without ever reaching one) and odd-odd numbers (products of two odd numbers). Like this they found out that some numbers can not be reduced by any number but the number itself or one. These are the prime numbers.

Even 4 6 8 10 12

Odd 3 5 7 9 11

Even-odd 6 10 14 18 22

Even-even 4 8 16 32 64

Odd-even 12 20 28 36 42

Odd-odd 9 15 21 27 33

Prime numbers 3 5 7 11 13

The Pytagoreans developed some important ideas in Astronomy. They were the first to think that the earth is round. They came to this because they looked at the shadow of the moon during a lunar eclipse.

As they knew the earth was round, they used this and math to develop the idea that the sun and the other planets were round too and that they went in circles around a central fire.

Pythagoras was the first to see that Venus as an evening star is the same as Venus as a morning star.

The Pythagoras theorem states that the sum of the squares of the lengths of the two adjacent legs of a right triangle is equal to the square of the length of the hypotenuse.

The sum of square C is equal to the sum of square A and B. ( 25 = 9 + 16 )

The Egyptian surveyors, the Chinese and Babylonians knew this rule already about 2000 BC, but they couldn’t prove it. The first people we know proved it is the Pythagoreans, it might have been Pythagoras himself. Thereby they raised the rule to the status of a theorem.

The theorem is important to the evolution of the Greek concept of number and the proof demonstrates how the Greeks used such proofs.

Pythagoras theorem can also be used for triangles that aren’t right. Then it goes:

It was interesting for us to work with the person and the stories behind the numbers for once.

Mathematics is more than numbers!

• Problems in paradise- numbers according to Pythagoras

John McLeish

• The story of numbers

Carl B. Boyer

• A history of Mathematics

Jamie H. Eves

• An introduction to the history of mathematics with cultural connections

Jan K. Sanander

• Alt er tall- Innføring i matematikk for barn

• Aschehoug & Gyldendals leksikon
• Britannica
• Kunnskapsforlagets matematikk leksikon

• www.geocities.com/Cape Canaveral/Haugar/3736/pytagora.htm
• homepage of Seth Yoshioka-Maxwell
• and other different pages