Pythagoras?

Question

His followers thought that ANY magnitude could be expressed as a rational number. But they discovered that this was false and were deeply upset. I need information on the discovery of irrational numbers and how this irrational number comes about. Any other information + sources would also be good. =)

Answer 1

the Pythagoreans discovered that the square root of 2 was irrational. this can be demonstrated using the method called proof by contradiction: if you assume that the square root of 2 is rational, your proof that it is leads to a contradiction. from some perspectives, a much more interesting irrational number (actually a transcendental number) is pi.

Answer 2

Here's a source for you on Pythagoras and irrational numbers.

The part that discusses irrational numbers is towards the end. It presents the standard proof - likely discovered by Pythagoreans - that the square root of 2 is irrational.

Answer 3

Indian mathematical text written in BC, named "SULBA SUTRA" mentions about Surds & its irrational nature. However the first "scientific " discussion on IRRATIONALS only appears in the commentry of " Aryabhateeya' by Nilakanta. Nilakanta was a renowed Astronomer & Mathematician who lived in Kerala(India) between 1450 &1550. In 1500 AD he wrote a the book "TANTRA SANGRAHA' . The dicussion of irrationals could be find in his "ARYA BHATEEYA BHASHYA' (SANSKRIT WORK) while he expain the irrational nature of PI while commenting on Aryabhatta's verse on PI- " Chaturadhikam satamashta gunam....". Here Nilakanta clearly says that Pi can not be expressed as a fraction of two whole numbers ( In sanskrit he says that there is no "niravayavatham" for it. Meaning is that to whatever extent we go, the "remainderlessness ' will not be there for this fraction.)

Answer 4

Click on the link Ive mentioned.
All u need to know will be there

Answer 5

wiki "irrational numbers" & are U-R-there.