Oh stop. If you have the theorem how would you not test it with sides = 1.
Of course we know it didn’t happen. The ancient stories of Hippasus don’t have anything to do with this libel. As is conveniently mentioned in the Wikipedia article you posted.
The Pythagoreans were absolutely incredible — and yet this is the only story people throw around. It’s just laziness.
They probably didn't have the modern form we use where plugging in different values like 1 is a natural and obvious thing to do. Regardless, they were a weird religious cult. They could have just regarded numbers that didn't produce rational numbers as unnatural and not something that was going to occur in the actual functioning of the world.
> They probably didn't have the modern form we use where plugging in different values like 1 is a natural and obvious thing to do.
No, but the form they used was that they thought about lines in a plane that had no particular scale other than whatever you might assign to them. "Plugging in 1" for the sides of a right triangle in that model just means that you look at an isosceles right triangle. It will always be obvious.
> Of course we know it didn’t happen. The ancient stories of Hippasus don’t have anything to do with this libel. As is conveniently mentioned in the Wikipedia article you posted.
I reread it BEFORE posting my initial comment.
Can you point me to where ON THE WIKIPEDIA PAGE this story was conclusively debunked?
It’s not about conclusively debunking. There is no evidence for it at all! They say he drowned for his impiety at publishing the dodecahedron (stated first by Iamblichus, 700 years later).
“The discovery of irrational numbers is said to have been shocking to the Pythagoreans, and Hippasus is supposed to have drowned at sea, apparently as a punishment from the gods for divulging this and crediting it to himself instead of Pythagoras which was the norm in Pythagorean society. However, the few ancient sources who describe this story either do not mention Hippasus by name (e.g. Pappus)[4] or alternatively tell that Hippasus drowned because he revealed how to construct a dodecahedron inside a sphere.[5] The discovery of irrationality is not specifically ascribed to Hippasus by any ancient writer”
You took initially took issue with the following snippet from the HN article:
> “ Two and a half millennia ago, the Pythagoreans held as a core belief that every number is the ratio of two whole numbers. They were shocked when a member of their school proved that the square root of 2 is not. Legend has it that as punishment, the offender was drowned.”
So I reference a Wikipedia page stating ancient / quasicontemporary sources describe such an event, but those ancient sources didn't attribute it to Hippasus by name. In the centuries after the supposed event authors start attributing this to Hippasus, which is under historical contention, since we don't find this attribution in writings from the same era as the event.
The HN article (just check your own snippet) describe the person as "a member of their school", which is in line with the hermeneutic interpretation of ancient texts (who said what and when).
Perhaps some day newfound libraries will be uncovered, or burnt scrolls deciphered, possibly finding contemporary (in the same lifetime) attributions of this discovery of the irrationality of sqrt(2) to Hippapus.
Basically: oldest sources already describe the events without naming the "offender" that was killed. Currently the oldest sources attributing this "offense" to Hippapus are lifetimes separated from the supposed events, casting doubt on the identity of the victim.
Of course we know it didn’t happen. The ancient stories of Hippasus don’t have anything to do with this libel. As is conveniently mentioned in the Wikipedia article you posted.
The Pythagoreans were absolutely incredible — and yet this is the only story people throw around. It’s just laziness.