Perhaps that a short proof of the irrationality of √2 can be obtained from the rational root theorem, that is, if p(x) is a monic polynomial with integer coefficients, then any rational root of p(x) is necessarily an integer. Applying this to the polynomial p(x) = x2 − 2, it follows that √2 is either an integer or irrational. Because √2 is not an integer (2 is not a perfect square), √2 must therefore be irrational. This proof can be generalized to show that any square root of any natural number that is not a perfect square is irrational.
The last two sentences of this video might be quoted as the important reason for worshipping nature and trying to understand the nature through science!
Isn't the story that the guy was thrown from the boat because he spilled the secret of root 2 when he was forbidden to by the Pythagorean students, not that he discovered it and was thrown from a boat because of it
you made me cry in the end
Amazing how a simple picture can summarize a complex concept.
This is a pretty cool channel. Hope you haven't stopped!
Perhaps that a short proof of the irrationality of √2 can be obtained from the rational root theorem, that is, if p(x) is a monic polynomial with integer coefficients, then any rational root of p(x) is necessarily an integer. Applying this to the polynomial p(x) = x2 − 2, it follows that √2 is either an integer or irrational. Because √2 is not an integer (2 is not a perfect square), √2 must therefore be irrational. This proof can be generalized to show that any square root of any natural number that is not a perfect square is irrational.
It might be short, but it uses more complicated maths, like the RRT, so it's definitely not the simplest proof.
The last two sentences of this video might be quoted as the important reason for worshipping nature and trying to understand the nature through science!
Apart from getting conceptual clarity, I enjoyed the way you narrated it. 👍
Isn't the story that the guy was thrown from the boat because he spilled the secret of root 2 when he was forbidden to by the Pythagorean students, not that he discovered it and was thrown from a boat because of it
Amazing!! Please continue to do more.
How to plot irrational numbers on a number line.
this video is lit af
just perfect
Wow
People think too much…