Download e-book for iPad: A Century of Mathematics in America (History of Mathematics, by Peter Duren

By Peter Duren

ISBN-10: 0821801368

ISBN-13: 9780821801369

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Godel destroys mathematics. Hiroshima. electric motor. 1855 Einstein publishes Special Theory 1922 blood. 1633 Curies awarded Nobel Prize for of Relativity. Revolution oJ the Celestial Spheres. 1628 Marconi receives first radio discovery of radioactivity. Columbus discovers America. Copernicus publishes The of transmission across Atlantic. Closing down of Plato's Academy marks start of Dark Ages. Freud publishes Interpretation Dreams. knowledge. experimental physiology. International agreement establishes Greenwich meridian.

Another great secret which the Pythagoreans c did their best to keep to themselves was the discovery of irrational numbers, such as >12, which could not be calculated. This discovery came as a tremendous blow. It meant that the entire structure of mathematics, which was based on rational numbers, simply couldn't explain everything. Pentagram -58- Pythagorean theory never -59- overcame this PYTHAGORAS & HIS THEOREM LIFE AND WORKS devastating discovery, which perhaps explains But according to Pythagoras' disciples, he fre- why the Pythagoreans went to such great lengths quently displayed miraculous powers.

These were certainly known to the Pythagoreans. Euclid's Elements (IX, 36) contains a formula for discovering 'perfect' numbers, which may have been discovered by the Pythagoreans: When 2n - 1 is a prime number -74- Perfect numbers led Pythagoras to the discovery of 'amicable' numbers. ,.. bers where each is equal to the sum of the factors of the other. The lowest amicable numbers are 220 and 284: 220 can be divided by 1, 2, 4, 5, 10, 11,20,22, 44, 55 and 110. These divisors add up to 284. 284 can be divided by 1, 2, 4, 71 and 142.

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A Century of Mathematics in America (History of Mathematics, Vol 3) by Peter Duren


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