He was supposed to be born in an island named 'samos' near the coast of Asia minor and guessed to be born between 580-560 BC. He probably visited Egypt on the advice of his teacher. Pythagoras was one of the pupil of Thales "the father of Greek mathematics, astronomy and philosophy". After his travelling he finally settled at 'Crotone' - a town on the southern coast of Italy about 529 BC. There he found a religious, scientific and philosophical brotherhood. It was a form of school, where the members were divided into two categories -
(1)Probationers
(2) Pythagorean
The Pythagorean formed themselves into a form of secret society with the idea of sharing and they were governed by disciplinary binding themselves strictly by an oath not to reveal the secrets and teachings of the school.
Pythagoras never embroided his findings or doctrines due to the lack of good writing material. He followed the customs of his time in passing his philosophy along by the words of mouth.
However, Pythagoras may be said to be credited with some of the following contributions in the field of science and mathematics : -
1. He was the first who declared that the Earth is sphere in shape.
2. He had discovered even and odd numbers.
3. The famous "Pythagoras theorem" bears his name although it was long ago known to Indians and Egyptians.
4. He proved the proposition relating to the sum of the angles of a triangle is 180°.
5. He is credited for creating geometry, a science based on axioms and postulates and also defined them by setting down the methods of prove.
6. He discovered that a plane surface about a point may be filled by six equilateral triangles, four squares or three regular hexagons.
7. He studied the properties of areas and volume, and he was the first person who proven that the circle occupies a greater area than any plane figure with the same perimeter, while the sphere contains a greater volume than any other shape bounded by the same surface.
8. Pythagoras was able to prove that √2 is incommensurable i.e. irrational for the first time.
9. Pythagoras was very much interested in playing with numbers, his interest can be summarised as below -
(i) For him numbers were no more attributes but have valuable meaning. Numbers for themselves is to stuff out with all of objects we see or handle and can make rational reality.
One was identified with reason. Two with opinion of a wavering fellow (he doesn't know his own mind), Four with justice, stead fast and square. Five suggested marriage, the union of first even with the first genuine odd number. His ideology had given birth to too many new superstitions like considering odd number male, divine and lucky, even number as female, earthly and unlucky.
(ii) He classified numbers as odd and even.
He pointed that any odd number say 2n+1, could be expressed as the difference of two squares i.e. 2n+1= (n+1)^2-n^2
= n^2+2n+1-n^2 = 2n+1
(iii) He was acquianted, what are known as triangular numbers and square numbers. He maintained that the sum 1+2, 1+2+3, 1+2+3+4,........................... gives the triangular numbers.
Similarly, numbers like 4,9,16,25,36,............ we're called as square numbers because the dots depicting these could be arranged as squares.
10. Many mathematical terms are traced by him and his associates related to lines, sides, parabola, ellipses etc.
Conclusion :
In every sense, he was one of the great maker of the civilization of his parents. Pythagoras fled to neathy island "Metapontum" and was considered there till 497 BC. The world of mathematics, astronomy and science will always remember his contributions as "the torch bearer" of the advancement of modern civilization.
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