Impossible Squares - Numberphile

Ben Sparks shows us a simple problem that takes some fascinating twists.
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NUMBERPHILE

Videos by Brady Haran

[numberphile]

This was filmed BEFORE the lockdown but edited during it! :) - Brady

[howsjimmysocool]

I was yelling at my computer asking why the area wasnt being solved using pythagoras - and then he surprised me with it being a proof for pythagoras...

[chrismcdonald]

"We're getting square numbers because we're drawing squares."

FINALLY - something on Numberphile I kinda know already!

[itwasinthispositionerinoag]

Rubik's cube in the background feeling all superior with its extra dimension

[MozartJunior]

8:52
It's amazing how Brady has developed a mathematician's mind after all these years of doing these vidoes. This is exactly the question a mathematician would ask

[CursedJoker]

I'm sure that if you go and film Matt Parker long enough, he'll come up with some "kinda possible" Squares.

[craigmcqueen]

7:03 That was a real pleasure to see how such an elegant proof of Pythagoras' theorem just popped out like that.

[edwardstennett]

Ben Sparks is by far my favourite Youtube mathematician. His knack for explaining things in a way that's easy to understand for pretty much anyone makes maths so much more accessible. I regularly rewatch his videos - would love to see him do even more videos on Chaos.

[midwinter]

As soon as I saw the square-in-a-square diagram, I started yelling "that's the square on the hypotenuse!"

[Peetzaahhh]

5:41 in and I'm bewildered how Pythagoras didn't come up

EDIT: 7:24 oh it’s because he’s proving it

[mariosonicfan]

"suddenly there's this deep glimpse of maths that goes way beyond what they're ready for"
you make it sound like math is some ancient forbidden arcane knowledge or something

[HonkeyKongLive]

Ben has this knack for taking something we all know about and hitting from a different direction and I love it.

[Wigglemice]

6:42 as soon as I saw this, I was like, "Ohhh of course! That's how you visualize the Pythagorean theorem! I should have seen that sooner!" Man, I love those ah ha moments.

[Dude-srji]

7:20 why do I feel like I just got rickrolled by Pythagoras?

[dylanwolf]

I think this is my most FAVOURITE Numberphile video ever, I keep coming back to watch it, ever few months. I think it's because it is so simple and so beautiful but leads quickly into the real business of maths. It's a super outline for a maths lesson for children who are sick of tables, compound interest and long division.

[waltercisneros]

7:10

"We prove Pythagoras"

*drops mic*

[chrisbersabal]

3:10 i thought i am the only who does that pen cover thing

[DouglasZwick]

At 11:20, I was really hoping he was going to circle the number on his screen with that marker.

[notoriouswhitemoth]

@7:30 not only does it prove the Pythagorean theorem, it proves it in the same way the Pythagoreans discovered it in the first place.

[AdamBomb]

That one 3Blue1Brown video of which coordinates are on a circle just popped into my mind.