Скачать или смотреть PROVE SQUARE ROOT 2 IS IRRATIONAL » proof by contradiction | Math Hacks

Brett nerds out talking about the history of irrational numbers, the mathematical mysticism of the Pythagoreans of ancient Greece, and shows you how to prove that the square root of 2 is an irrational number using a proof by contradiction.

Ah good ole Pythagoras, the man of high school geometry class legend. Although he definitely wasn’t the first person to discover his namesake theorem, his legend lives on nonetheless. Surely, if he lived in modern times we’d probably all think he was straight-up crazy. As you may be familiar with, Pythagoras was the leader of the Pythagoreans, a religious, philosophical society that worshipped the beauty of numbers in their wholeness.

In 6th century BC, there were only two kinds of numbers that humans knew about: counting numbers and ratios of counting numbers (i.e. rational numbers or fractions). And to the Pythagoreans these numbers weren’t just cool, they were holy. They were divine. They were worthy of undergoing years of study, austerity and initiation into a special society led by their beloved Pythagoras.

If you’ve ever had the opportunity to study right triangles and use the Pythagorean Theorem you’re probably thinking one thing right now…irrational numbers show up all the time in right triangles!

Yep. In fact, you probably stumbled upon irrational numbers on the very first day you were introduced to the Pythagorean Theorem. You know that famous 45–45–90 degree isosceles right triangle, the one with side lengths of 1, the diagonal of a 1-by-1 square, oh yeah that hypotenuse is an irrational number: square root 2.

That’s bad news bears for the Pythagoreans. You see, their most-valued equation leads you straight into the world of irrational numbers... Oh, the irony.

More on the Pythagoreans, that pesky square root 2, and most importantly a logical proof of how we know-as-a-matter-of-fact that the square root of 2 is irrational in this week's episode of Math Hacks.

Skip to the proof » 2:10

NEXT LESSON:
Geometric Proof that Square Root 2 is Irrational »    • GEOMETRIC PROOF: SQUARE ROOT 2 IS IRRATION...  

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