what is the number feared by pythagoreans?

Question

help please... i know it has to be between 1 and 31 thanks

Answer 1

√2

Pythagoreans were the followers of Pythagoras. In Ancient Greece, mathematics and philosophy were one and the same. Pythagoras a prominent figure in a philosophical world where rationality and order were highly important.

Rationality here was not only meant philosophically, but numerically: they believed fractions were the ONLY numbers allowed. However, √2 is not a fraction ("rational number"). It cannot be expressed as the ratio of two whole numbers.

There is a simple proof:
http://en.wikipedia.org/wiki/Square_root_of_2#Proof_by_unique_factorization

But this was known to some Ancient Greeks
http://en.wikipedia.org/wiki/Square_root_of_2#Geometric_proof

The existence of such a number was denied by Pythagoreans, except that Pythagoras himself proved one existed (construct a right triangle with legs of lengths 1 and 1 - it has hypotenuse of length √2).

They knew √2 must exist, but as it became known that √2 cannot be rational, it was very upsetting. They even killed people for it.

The Pythagoreans, like other Greek geometers, understood how to make pleasing tones. If you have a 1 meter string, and a 1/2 meter string, they harmonize. 1/3 meters would also harmonize with the two.

However, if you had a string of length 1 and of length √2, they would be completely unharmonious. This is due to the fact that there is no rational relationship between the two lengths.

I've seen this often as "17" because of the reason about area=perimeter rectangles, however, I've only seen it anecdotally among random meaningless websites written by 5th grade math teachers. The explanation I gave is repeated (essentially) in several texts on the history of mathematics.

Who would you trust? Mathematical historians who understand mathematical history and have well-referenced texts in publication? Or a couple of random people on the internet who claim to be 5th grade teachers, whose bizarre answer to this question floats around on the internet, despite being unreliable, unverifiable, and dubious at best?

Answer 2

The number feared by Pythagoreans is the one that lies halfway between the only two integers that can be both the perimeter and the area of the same rectangle.

Those integers are 18: 3*6 =2*(3+6)
and 16: 4*4 =2*(4+4).

The dreaded number is 17.

Answer 3

17

Answer 4

Well there's a story that a man was drowned for proving root 2 was irrational.

It was certainly true that pythagoras hated the idea of irrational numbers, and as such thought them impossible.

Whether the actually 'feared' a number, I'm not sure, but they didnt like irrationals.

Answer 5

17
It lies half way between 16 and 18
16 is a number which is both the area and perimeter od a rectangle whos sides = 4
18 is a numbet that is the area and perimeter of a rectangle with sides = 6 and 3.