Making sense of irrational numbers - Ganesh Pai

Like many heroes of Greek myths, the philosopher Hippasus was rumored to have been mortally punished by the gods. But what was his crime? Did he murder guests or disrupt a sacred ritual? No, Hippasus's transgression was mathematically proving the hitherto unprovable. Ganesh Pai describes the history and math behind irrational numbers.

Lesson by Ganesh Pai, animation by Anton Trofimov.

[milyon]

oh my goodness i just realized that "rational" means it can be expressed in ratios. I thought mathematicians just didn't think the numbers made sense.

[XxUginxX]

Hippasus' colleagues punished him for discovering irrational numbers? Wow, that's truly irrational!

[xmaxwell]

This should've been titled "Rationalizing Irrational Numbers".

[-.._.-_...-_.._-..__..._.-.-.-]

_"I'm sure that I will always be_
_A lonely number like root three_

_The three is all that's good and right, _
_Why must my three keep out of sight_
_Beneath the vicious square root sign, _
_I wish instead I were a nine-_

_For nine could thwart this evil trick, _
_with just some quick arithmetic_

_I know I'll never see the sun, as 1.7321_
_Such is my reality, a sad irrationality_

_When hark! What is this I see, _
_Another square root of a three_

_As quietly co-waltzing by, _
_Together now we multiply_
_To form a number we prefer, _
_Rejoicing as an integer_

_We break free from our mortal bonds_
_With the wave of magic wands_

_Our square root signs become unglued_
_Your love for me has been renewed"_

—Harold & Kumar Escape from Guantanamo Bay (2008)

[FlyAVersatran]

Great explanation.

I have a degree in applied mathematics and have never heard this pontificated so well.

Thank you.

[Stray]

> "Are you the square root of 2?"
> "Because I feel irrational around you."

How to flirt. :D

[RK-epqy]

I'm feeling a little…irrational now

[jonbenge]

This made so much more sense than when I was in high school. I wish my teacher had explained concepts like this much more clearly instead of saying "Because they are not rational"; probably would have gotten a better grade...

Thanks Ted!

[nuetralkitty]

3:43 That's a square root spiral right? I had an art integration activity in maths for that. It's seriously amazing how numbers can be connected to concepts like art, music, cosmology etc. I wonder if we will ever find a way to define irrational numbers? There IS a lot of freedom in maths after all.

[Ravr]

wow. the animation is amazing. really great for visual learners.

[TheGamerzXChannel]

Great abstract video 🙂 please make more of them, they are the juice for my brains!

[Supremebubble]

Even more interesting is that it is impossible to plot the number pi on the real number line with only using ruler and compass. Same goes for the number e. These are called transcendental numbers however the proof is rather complicated.

[lexinaut]

Quite nicely presented and relevant. As an educator, I still find that irrational numbers make people . . . nervous! However, from my reading, no one apparently knows precisely which irrational number Hippasus either proved was irrational, or revealed was irrational (if someone else proved it). Root 2, of course, is a very likely candidate, since it is present in a simple unit square. For this reason, I commonly call Root 2 "the Monster in the Unit Square (with comical yet serious intent). I agree! We should appreciate the adventure of irrational numbers rather than excessively fearing them! Mathematics is a great adventure indeed! Have a great day!

[hrag]

Wow, really so beautifully, clearly put and explained in such simplistic way. My teachers used to tell me that I should always "remember" that sqrt(2) is irrational and cannot be shown in a rational way. But after watching the proof, now everything started to make sense. I wonder if every problem has a solution, then why can't this irrational numbers have solutions too? Also there may be other numbers in the infinite set that are in a similar condition to sqrt(2) that cannot be proven.

[niory]

I have such a bad relationship with math and feel sorry for it

[BangMaster]

I wish school taught us math this way, it's so much more fun to learn this way, and now i actually want to learn about square roots and irrational numbers.

[Vnky_]

3:26 Ohhh!! That Activity did in School 👍🏼

[Saj_]

It’s insane how smart one would have to be so long ago to figure this out. Creating/discovering math is one of the most fascinating things mankind is capable of.

[thompson]

This is really cool! We're learning about Pi in class and I'm going to show this to my teacher!

[scitwi]

It only takes one look into Euclid's "Elements" to ascertain that the Pythagoreans indeed knew all well about the existence of irrational numbers and they didn't treat is as something that derails their philosophy. They also used ratios in a different way than we do nowadays: more like algebraic ratios than ratios of whole numbers only. And Hippasus's death was not a punishment for him discovering irrational numbers, but for leaking the secret to wider public.