The most dangerous number in the world

C

Cypress

Well-known member
Pythagoras and his students, through the study of musical harmonics, believed that the world was based on natural numbers (integers) or ratios of integers. This was almost a sacred belief for them. Supposedly they discovered the square root of two through the study of triangles; it is an irrational number which cannot be expressed as the ratio of two natural numbers. Legend has it, they tried to keep this number secret because it undermined and discredited the premise of their sacred mathematics.

“It's a stormy day on the sea off the coast of Greece. The date is around 520 BC. Fighting for his life, a man is heaved over the side of a boat and dropped into the open water to die. His name is Hippasus of Metapontum. His crime? Telling the world a mathematical secret. A secret only known to the school of Pythagoras. The secret of the dangerous ratio – the square root of two.”

https://nrich.maths.org/2671
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So IS there a square root of two? If so, why would it be dangerous?

Sadly my acquaintance with higher mathematics extends only so far. So I'll leave you with this horrid math pun about pi by Mr. Owl: "I know it's irrational, but I love pie." :laugh:
 
ThatOwlWoman said:
So IS there a square root of two? If so, why would it be dangerous?

Sadly my acquaintance with higher mathematics extends only so far. So I'll leave you with this horrid math pun about pi by Mr. Owl: "I know it's irrational, but I love pie." :laugh:
Click to expand...

The way I heard the story is that the Pythagoreans studied musical harmonics, and discovered that harmonic ratios are all based on ratios of integers (1, 2, 3, 4,...).

They thought harmonics were sacred and reflected some enteral truth about the universe. And that the mathematics of integers and their ratios were sacred.

The problem with the square root of two is that nobody knows prescisly what it's value is. It cannot be derived from a ratio of intergrers, and it is based on an infinite, non-recruring decimal expansion. It is an irrational number.


It's not literally dangerous, just metaphorically dangerous :). Legend has it square root of two really bothered the Pythagoreans, because it discredited their belief in the scared natural numbers.
 
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