This man just turned a parabola into a multiplication table.

@user-he4ef9br7z

3 жыл бұрын

I was amazed. I never thought of it that way, took me pen and paper to understand how that was happening.

@K1lostream

3 жыл бұрын

If you can describe 2,000 years ago as 'just' then yeah! Pretty neat!

@mediocreman6323

3 жыл бұрын

In fact, it always has been a multiplication table, only people like you and me did not know about it. Now we do. I am officially amazed by this. I mean, we did conic sections in school and such, but this here never came up. Amazing, just amazing.

@Bodyknock

3 жыл бұрын

Yeah, it’s a neat trick! You can derive it pretty quickly too. Assume you have points a and b and the parabola y = x^2. Then the line between them is x (b^2 - a^2)/(b - a) + C For some C which is the y-intercept. Notice this simplifies to x (b + a)(b - a) / (b - a) + c = x(b + a) + c = y Now substitute x=a and y=a^2 and you get a(b + a) + c = a^2 = ab + a^2 + c So 0 = ab + c and therefore c = -ab, meaning the intercept is negative the product of a and b. P.S. Had a sign error that I corrected above.

@syc8066

3 жыл бұрын

@@Bodyknock c = -ab

This video felt too short! I could listen to this wise old man tell stories of other wise old men until I myself am a wise old man.

@boynet2

3 жыл бұрын

Yes Please Yes

@billob1305

3 жыл бұрын

or as i am,a mere confused old man

@iliketurtles4463

3 жыл бұрын

@@billob1305 ahh but an old man none the less Bill, which is half the battle. If you have managed to survived long enough to be an old man, there is likely to be much more wisdom within you than you realize my friend. Without a doubt you could teach us all something!

@beningram1811

3 жыл бұрын

if you'd like to do a little more relaxing watching this particular man, he used to do a show when i was a kid, called "Johnny Ball explains it all". You may be able to find videos of it, somewhere.

@iliketurtles4463

3 жыл бұрын

@@beningram1811 I will have to do just that then wont I! I don't remember such a show although there was a time when not a lot of TV stuff made it to our shores here in NZ. Thank you very much for this information Ben. I appreciate you taking the time to share, I shall endeavour to make it worth your effort by searching right now. Cheers.

If only Archimedes had algebra to formalise the idea of infinitesimal lines summing to finite weight, he almost surely would have made the connection to what we now know as calculus.

@destructfashion

3 жыл бұрын

Another related missing piece is the Greek rejection of zero as a number. This caused them to miss concepts like infinitesimals "approaching zero". Interesting to think about the quantum leaps that could have been made in math with the addition of a couple of key concepts!

@lennart-oimel9933

3 жыл бұрын

Interesting! Maybe there would be only something like "approaching to nothing" and still no actual zero.

@sonaruo

3 жыл бұрын

@@destructfashion the rejection was that math was to solve problems so if something end up been zero meant it was not possible and you do not need zero to do things the quadratic equation instead of making equal to zero take c to the other side and equal it with that the formula can still work also greeks had ZERO when used for LOGISTICS since when you do inventories of warehouse you may end up not having something so they had to show that

@christopherpape4823

2 жыл бұрын

Am I the only one who finds it interesting that the Greeks or those before weren't clever enough to invent/discover algebra? I mean algebra, at least the basics, is kinda just introducing the concept of variables and then shuffling them around, no?

@sonaruo

2 жыл бұрын

@@christopherpape4823 you are the only one since greeks where dealing with different kind of problems and also 90% of greek text is gone so we do not know how much is lost

Something Archimedes never said was "Excuse me." or "I'm sorry." Some might argue that it was because he was rude or stubborn. But I think it was probably because he didn't speak English.

@kwanarchive

3 жыл бұрын

I think you're onto something...

@themeditatingdog6402

3 жыл бұрын

@@kwanarchive Shhhh! Don't tell him that. He'll become too powerful.

@tobiaslawrence5199

2 жыл бұрын

you are the "para" and not the "bolic", which is excelent either way

@patrickadu-amankwah1660

Жыл бұрын

Kwasia 😂

@anapina6723

Жыл бұрын

Pretty sure the words “Excuse me” and “I’m sorry” didn’t exist back then, because English hadn’t even been made when he was alive.

Archimedes must have been one of the most brilliant minds of all time

@jasondoe2596

3 жыл бұрын

He was an intellectual giant, up there with Gauss and Euler.

@anthonyparsotam3611

3 жыл бұрын

Just imagine what his mind would do for humanity if he were alive today

@GlorifiedTruth

3 жыл бұрын

Someone once asked me what you do in Calc 3. I said, "Basically, prove everything that Archimedes figured out 2,500 years ago."

@frostyusername5011

3 жыл бұрын

@@anthonyparsotam3611 opens up tiktok.. immediately rolls back into grave

@anthonyparsotam3611

3 жыл бұрын

@@frostyusername5011 🤣🤣🤣

Video: "What is the ratio of the parabola's area to the rectangle's?" Me: "Well, this would be trivial to compute with an integral, but the Greeks didn't have Calculus, so let's see." Archimedes: *basically does a Riemann sum Me: "Well color me impressed."

@stephenbeck7222

3 жыл бұрын

The Greeks had a lot of calculus. They were obviously missing some of the algebra that was developed later. Newton and Liebniz are credited with summarizing the fundamental theorem, i.e. connecting derivatives and integrals, not with developing derivatives and integrals themselves.

@leif1075

3 жыл бұрын

@@stephenbeck7222 But Newton did develop it himself didnt he?

@tahmidislam5208

3 жыл бұрын

@@leif1075 Newton refined it and leibnitz helped with the notation , but integration and derivation predated those two

@vikraal6974

2 жыл бұрын

Differential calculus was first discovered by Newton. Bhaskara II knew derivative of sine function but he couldn't generalize it to other function. He was calculating speed of stars when time interval was very small.

@sumdumbmick

2 жыл бұрын

@@vikraal6974 nobody has generalized it. you can generalize the concept, but there is no generalized algorithm. so ultimately it takes somebody who's not really doing the mathematics, but just bored and poking around at stuff to recognize the connections between different derivatives.

I love the manner he explains things, pure tranquility.

@kirannigade8200

2 жыл бұрын

Like David Attenborough of mathematics

@shy-watcher

2 жыл бұрын

I honestly find it distracting. He didn't explain a crucial step and hardly anyone noticed. "Let me tell you a story" indeed. Math is not a fairy tale, too bad many treat it like one - the best-told story wins, just like in journalism...

@Andrew-fv4sj

2 жыл бұрын

@@shy-watcher You love listening to yourself speak it seems

@shy-watcher

2 жыл бұрын

@@Andrew-fv4sj It seems you like reading people's minds? How do you know what I do and don't like? I just don't like when people ignore problems with a proof just because the presenter's voice is nice.

@Bronco541

2 жыл бұрын

the point is the presenters attitude should inspire a hunger for learning and creativity. They might make mistakes, everyone does. this channel isnt about perfection. Nobodys watching this so they can become a mathematician, thats what college is for.

Gauss is probably the only one I can allow to get away with calling Archimedes an idiot :)

@tonylee1667

2 жыл бұрын

And no one can get away with calling Gauss an idiot. Although you can call him an asshole.

@piratesofphysics4100

2 жыл бұрын

And Ramanujan is the only one I can allow to get away calling Gauss an average genius.

@RodelIturalde

2 жыл бұрын

Archimedes to Gauss: Isn't this so called calculus thing obvious to most casual mathematician?

@insertcreativenamehere492

2 ай бұрын

@@piratesofphysics4100 look guys we found another delusional indian

Johnny Ball is a legend to my generation.

@numberphile

3 жыл бұрын

More Numberphile videos with Johnny Ball: bit.ly/Johnny_Ball

@Koisheep

3 жыл бұрын

@@numberphile i reas tommy ball and thought for a moment there was a tommyball reference snuck into the animations

@axelperezmachado3500

3 жыл бұрын

@@Koisheep well, we all know that Johnny Ball was actually one of the first people to ever play tommy ball when it wasn't even invented

@honorarymancunian7433

3 жыл бұрын

Who? (What why where when)

@tp3960

3 жыл бұрын

@@numberphile whenever you get a chance, more of Johnny Ball is a MUST thank you!

If Johnny Ball hadn't been on the TV when I was small it is a certainty that my career track would have been different. He was the first person to show me the emotional payoff you get from understanding a piece of mathematics. He set the stage for the idea that there could be such a thing as mathematical exposition for a mass audience. It's not too much of a leap to say that Numberphile could not really exist without him.

You think this is amazing? Archimedes’ calculation of the volume of a sphere is even more incredible. Please ask prof. Ball to do do another video on Archimedes calculation of the volume of the sphere using levers/balancing! Pleaseeee

@Tytoalba777

3 жыл бұрын

So, how you liking their new video?

@neoxus30

3 жыл бұрын

Heyyyy)

@willjohnston2959

3 жыл бұрын

Numberphile released a travesty of a video on the volume of sphere. Ball makes it sound like Archimedes dunked shapes in water to "prove" their volumes add up. Completely skips the actual law of levers method Archimedes wrote in "Method" (the palimpsest).

I love how the Greeks figured out mathematics in such a visual, geometric way. I didn't understand why, at 6:43 , he said "it will only balance at the balance point". Why is that?

@epicsmashman6806

3 жыл бұрын

The triangle “sits” on the lever at its center of mass

@Fazupala

3 жыл бұрын

I think this is a severe issue with the video - that is one large leap of reason that I can't imagine archimedes making but from the video it is not clear what the reasoning would be

@eyalrotem8547

3 жыл бұрын

@@epicsmashman6806 Still didn't got it. Why will the parabola balance it at 3 times the distance?

@chiragadwani1875

3 жыл бұрын

"the proof is left for the reader as an exercise"

@annaclarafenyo8185

3 жыл бұрын

This is explained in coordinates on Wikipedia with a straight parabola and triangle under "Method of Mechanical Theorems", which is the Archimedes work where this argument and diagram come from. The quadratic relations are difficult to see intuitively on a skewed parabola.

WOW Numerphile. It's Johnny Ball, bless his cotton socks.

@HotBoySinatra

3 жыл бұрын

this comment brings me an endless amount of joy

@codycast

3 жыл бұрын

Huh?

@Triantalex

5 ай бұрын

??.

I'm 55 and this gentleman was presenting "playschool" when I was 4 and "think of a number" when I was 11. Still educating and with the same passion and energy. It's wonderful to see him again ❤

This man was quite a big part of my childhood, he's an amazing story teller.

For those asking how Archimedes figured out that the triangle would balance the parabola at 6:43, the proof is skipped in the video. He used a known property of parabolas that PO/NF = MO/CF, and thus PO x CF = MO x NF but by definition CF = FH and so PO x FH = MO x NF which means that if each PO segment is placed at H, it would balance its corresponding MO segment, and thus the parabola placed at H balances the big triangle.

@wbfaulk

3 жыл бұрын

It's too bad in a Numberphile video that you have to go to the comments to find the actual math.

@vsm1456

3 жыл бұрын

thank you! your comment completes the video

@alexrvolt662

2 жыл бұрын

thanks, I really didn't get where it came from

@12388696

Жыл бұрын

This comment is underrated

@myexflower

6 ай бұрын

Thanks for the explanation and the identity you provided here, but it also took me time to conclude even after your statements. Do you not think you also forgot to finalize the proof? You did not mention the relation between N and X.

I just read the wikipedia article on this, and boy can I say this video did not at all do justice to the proof. Trying to represent this proof in two dimensions makes it practically impossible to tell what’s going on. I didn’t even notice him *attempting* to prove the most important part of the demonstration. Basically, for anyone confused, imagine on a lever, the triangle is placed starting at the fulcrum, following along the lever to the left, increasing in height. On the other side, the parabola will be placed *sideways* (extremely important part that was not clearly explained due to the lack of 3D) meaning it rests on a single point of the ruler. One can then pair up, line by line, pieces of the triangle and that of the parabola, and using the property of levers that states force=mass*(distance to fulcrum) and prove that they apply the same force. The triangle has mass x and distance x, and the parabola has mass x^2, but a constant distance of 1. Since these both multiply to the same thing, they apply an equal force, and balance. Notice how this *only works* in three dimensions where the parabola can lie sideways, unlike the triangle. With every line being equal, the entire shapes must be equal. Archimedes didn’t just say, like this video suggests, “I bet it will balance”. He actually demonstrated it in a really beautiful way that this video just does not offer.

@vsm1456

3 жыл бұрын

Oh, that's a great and an elegant approach! I still have questions, though, but I can't find the article you're talking about. Can you tell me its name? Upd: Never mind, I found one: The Method of Mechanical Theorems

His voice is so soothing

@mazza420

3 жыл бұрын

johnny ball is a legend

@bhargavdesai7984

3 жыл бұрын

That's as British accent as it can get.

@brianmiller1077

3 жыл бұрын

Reminded me of the Geico gecko a bit.

@ViratKohli-jj3wj

3 жыл бұрын

I really love this accent.

5:57 I absolutely love the mathematical discoveries where it's like "By definition I cannot" but then the genius goes "But what if I did anyways?"

I’ve never been lost in a numberphile video before but I have no idea what just happened

@maxxie8058

3 жыл бұрын

Yeah, same here. I love Numberphile because it takes complicated math things and makes them accessible, but this video didn't achieve that at all.

@proloycodes

3 жыл бұрын

@@maxxie8058 same

@QuantumHistorian

3 жыл бұрын

@@maxxie8058 Indeed, it took a fairly simple geometrical concept and dressed it up so it became incomprehensible

@e2DAiPIE

3 жыл бұрын

I feel the reasoning behind Archemides' intuition as to why the parabola's "weight" balanced that of the triangle at the "fulcrum" was not explained at all. We got all this beautiful setup for a punchline that said Archimedes' guessed this was true and it turns out he was right. Unfortunately the video does not clearly explain WHY Archimedes was correct. It left me feeling like there is an itch I can't reach to scratch.

@marcel87688

3 жыл бұрын

@@e2DAiPIE because he was doing an integral without knowing it

Among other things, back in the day on the BBC, this chap did a couple of series for kids called 'Think of a Number' and 'Think Again'. They were inspiring and engrossing. As far as I know there has never been anything else quite like them. I doubt if they would be made now with the BBC the way it has become.

@peterfireflylund

3 жыл бұрын

"Look Around You".

at first i was think "how he is going to figure it out without integrals at that time" and than he uses integral mindblown.

@GreylanderTV

3 жыл бұрын

Except he didn't. He only almost did. He knew the answer approximately (no doubt from measurement) and assumed the exact solution. Here he "almost" invented calculus which would have allowed him to prove it. I put "almost" in quotes, because this is more like the first step to inventing calculus -- there's three or four more big insights or ideas needed to get to calculus.

@jasondoe2596

3 жыл бұрын

@@GreylanderTV Well, if there was only one person intellectually capable of these insights, that would be Archimedes. But he was a few centuries too early, and lacked the mathematical tools.

@GreylanderTV

3 жыл бұрын

@@jasondoe2596 Yes, no knock on Archimedes. See my main comment for context.

@iancheung3587

3 жыл бұрын

@@GreylanderTV Hey Scott, genuine question, what are the 4 additional big insights to get to calculus?

@branthebrave

3 жыл бұрын

@@iancheung3587 using equations for one, they used shapes. Then I'd guess limits, then perhaps derivatives, also just more knowledge on graphs (rectangular, not graph theory). It'd be possible without our ways of equations and variables, but much harder

Crazy to imagine how brilliant Arhimedes must've been at a time when he had nothing to start from. He had to think of this all by himself, with no previous knowledge from the past. We are truly blessed to have all the information we have today. He had nothing, but still managed to create the base of mathematics. Astonishing.

@patrickadu-amankwah1660

Жыл бұрын

He had a lot of previous knowledge as stated by the video i.e levers and the center of mass of a triangle. 3:03 Still very brilliant, thought of the world and mathematics in a way that wouldn’t be grasped fully for another 2000 or so years

Honestly, sounds like the Richard Attenborough of Mathematics.

It is so difficult for me to imagine mathematics without the technology commonly called graphing.

@EebstertheGreat

3 жыл бұрын

Or paper for that matter

@fallen0851

3 жыл бұрын

Thanks Descartes!

@Triantalex

5 ай бұрын

??.

Archimedes was just about to invent calculus... and then realized he needed a bath.

@IamtheMan1111

3 ай бұрын

If only he didn't born at war at the time....

I wouldn't be surprised if the Library of Alexandria had contained bits and pieces of Calculus invented by mathematicians all over the ancient world before it burned down.

As somebody whose brain is just not made for arithmetic, it is amazing how fond my memories of Think of a Number and its follow up shows are. He's one of the people who showed me that mathematics is a kind of wonderful magic and despite my lack of arithmetic skills, I have been in love with maths ever since. Thank you, Johnny!

This man needs a math series on Netflix, I am always enthralled by his videos, the way he weaves stories with math along with his David Attenborough like voice and enthusiasm gets me everytime.

What an amazing video. Men like Archimedes, Gauss, Euler and Pascal were so important for our evolution as a species.

Imagine how far human civilization could have gone further if calculus was invented back then

@ravindrawiguna8681

3 жыл бұрын

Yes dudd, newton, gauss, euler and etc could've then make a whole new discovery/invention more brilliant than calculus

@lock_ray

3 жыл бұрын

I wouldn't be surprised in this scenario if it was lost during the middle ages and not rediscovered again until the time of Newton, or something like that

@MusicFanatical1

3 жыл бұрын

Genghis Khan could've had a nuke.

@pdreo

3 жыл бұрын

@@lock_ray yeah, in the "middle ages" when universities first started

@z-beeblebrox

3 жыл бұрын

It's really wild how much of modern mathematics existed thousands of years ago, but all scattered around the world in isolated disconnected pieces. If only we got along better and had fewer language barriers...

How do you know that the "weight" of the parabola would balance out the "weight" of the triangle? There's no basis (in this video) for that conclusion.

@willjohnston2959

3 жыл бұрын

Read Archimedes' "Method" Proposition 1, and his "Quadrature of the Parabola" Proposition 5. Key idea is he can prove MO/OP = CF/FN = HF/FN. So arbitrary triangle line MO placed distance FN from fulcrum balances with parabolic section line PO placed distance FH from fulcrum.

@maheshprabhu

2 жыл бұрын

@@willjohnston2959 thanks for the explanation. Not sure why this key part of the proof is overlooked in the video.

More Johnny please! I occasionally teach middle school children and the way he teaches is very inspiring.

Nice to see a childhood hero still knocking about :)

@numberphile

3 жыл бұрын

More Numberphile videos with Johnny Ball: bit.ly/Johnny_Ball

The genius of Archimedes is astonishing, not just an incredible matematician but probably the first scientist before science itself existed as we now know it: as far as I now his Principle of buoyancy is the oldest principle of physics which stands exactly as it was formulated more than 2200 years ago

@asicdathens

3 жыл бұрын

Archimedes papers of mathematical physics, the law of the lever and the floating bodies are the first true papers in physics.

6:38 - there's a massive, unexplained leap of logic around here. Why would putting all the POs at that location balance? Why that distance? What's special about parabola vs random squiggly shape that is also inscribed by the original triangle? If Archimedes determined it with a physical piece of cardboard/wood/marble/etc, that's worth mentioning, but it's not. If it was determined through some insight, that was not mentioned either.

@willjohnston2959

3 жыл бұрын

Read Archimedes' "Method" Proposition 1, and his "Quadrature of the Parabola" Proposition 5. Key idea is he can prove MO/OP = CF/FN = HF/FN. So arbitrary triangle line MO placed distance FN from fulcrum balances with parabolic section line PO placed distance FH from fulcrum.

Johnny Ball!! My hero as a kid. MORE JOHNNY BALL PLEASE!!!!!!!

I grew up with stories about Archimedes and other coll mathematician and science stories., My grandfather past away last year. I'll never forget all those amazing stories he told me about him, some probably hyperbole. He would've loved this video.

The legend Johnny Ball...his calming voice and amazing way of explaining things, any other 40 somethings here remembering their youth and watching him on tv after school or a saturday morning?

Lovely to see you again, Johnny! You were a feature of my adolescent education!

It’s so impressive what the Greeks were doing, well done those guys

@steliostoulis1875

3 жыл бұрын

Its mostly Archimedes by himself tbh

@PHDnHorribleness

3 жыл бұрын

@@steliostoulis1875 Eratosthenes was pretty great.

@Zzzz-lg3iw

3 жыл бұрын

@@steliostoulis1875 Euclid

@Zzzz-lg3iw

3 жыл бұрын

@@steliostoulis1875 Euclid also played a major role in mathematics

@Zzzz-lg3iw

3 жыл бұрын

@@steliostoulis1875 and ofcourse the father of algebra , Al - Khwarizmi is very important too ( he wasn’t Greek tho but still )

"there's only one true parabola"

@Icenri

3 жыл бұрын

The Parker Parabola

@thethirdjegs

3 жыл бұрын

I miss numberphile Matt.

@quacking.duck.3243

3 жыл бұрын

Gloria in x-squaris!

@ngiorgos

3 жыл бұрын

(sees parabolas measured with triangles) Parabolati confirmed!

Started watching without reading the caption and a few seconds in the voice made me say “That’s Johnny Ball!” To people my age (mid forties) in the UK this guy is an iconic part of our childhood!

Still listening to Johnny Ball all these years later. What a legend.

The moment I saw this episode was about parabolas, my mind flashed back to Johnny Ball teaching me about them as a kid on the brilliant Think of a Number. Couldn’t believe it when this one turned out to be him again. Fantastic stuff!

OMG Johnny Ball!!!!! Johnny is the only reason I can count!

More Johnny Ball please, my childhood just came back to me. Still one of the best teachers ever!

So happy to find this channel, I missed Mr Ball, so much positivity made my childhood bareable. We lack such sincere educational presenters.

I wish I could sit and converse with this man. Many stories, experiences, lessons and things to learn from him.👏

what proof did archemides use to prove that it should balance?

@Yobleck

3 жыл бұрын

idk about a mathematical proof but he could have just cut shapes out a material and weighed them on a lever.

@dikenmhrz3902

3 жыл бұрын

What do you mean?

@Nnm26

3 жыл бұрын

Method of exhaustion, you can find them online. It's basically old calculus.

@seanscon

3 жыл бұрын

@@Nnm26 ok, i see. thanks. I know the method, I will check out the implementation of Archimedes later. thanks again.

@RodelIturalde

2 жыл бұрын

Probably exist a more rigorous proof in one of his books

Grew up with Johnny Ball explaining stuff to me as a kid on British TV 30 years ago. He's maths' answer to David Attenborough: an absolute legend. So pleased to see him still educating: and educating *me* no less(!) all these years later!

Johnny Ball did more for my maths ability than school ever did. Some of the best afternoon children’s TV in the UK ever. 👍

Absolutely wonderful mathematician, wonderful explanation, and the reveal at the end!

Yay! The great Johnny Ball! More, please!

Man, Sunday morning science and maths are the best! Coffee, apple fritter, and Johnny and Brady to make my day! Cheers

Johnny Ball! One of my childhood heroes.

Fantastic! the beauty of mathematics lies in the fact that it describes the beauty and harmony of the world

5:22 Why did he double that line? And why put the fulcrum there? Why not triple, or quadruple? I don't understand that part.

@zym6687

3 жыл бұрын

Think back to the ruler, 6 inches on one side of the fulcrum and 6 inches on the other. F being the fulcrum then FH must be the same length as CF to "balance" without any PO or MO (the dominoes)

@andymcl92

3 жыл бұрын

Yeah, it does seem like there's a bit that's glossed over. "I bet this balances at that point." Why? Sure, it balances somewhere, but why does it have to balance there?

@jonnyogood

3 жыл бұрын

The video really skipped over this, and I had to pause at 7:00 and stare at it for 5 minutes to figure out that each PO balances each MO individually, so he could check a few points and after seeing each one that he checked balance, he assumed that they all balance. For example the one at the center of the rectangle is half the distance from F and P is half the height of M.

this type of meaning of calculus was around for maybe 1000s years, the story goes like this, the governor wanted to punish a certain farmer and told him to count every rice grain in a metric ton without a single loss of grain or would forfeit his life, the farmer back and said next day he counted all and it was 10^7 grains, farmer asked the governor to verify if he wanted, but he couldnt so he asked how? the farmer replied, a spoonful of rices had 100 grains, 1 dipper had 1000 spoonfuls of them, 1 ton had 100 dippers, after that the governor never bothered the farmers again

Man the MO and PO part is just pure thinking excellence.

The nice mixture of the history of math and the lovely geometrical interpretation of things!

I always thought Zeno with his arrow and hare paradoxes was on the cusp of inventing calculus as well. But got shut down, and probably body slammed instead.

@annaclarafenyo8185

3 жыл бұрын

Zeno inspired Eudoxus to define real numbers as limits (although they didn't quite use this terminology), and Archimedes came right after Eudoxus.

Holy crud, that is an amazing mathematical intuition, right there. As soon as they showed the sums of all those slices, I literally got a chill. How is this story not more well-known?!

Even if I didn't completely understand, I was still captivated. Pretty sure I saw Johnny Ball in the theatre as a child

AMAZING video. Thank you for producing and sharing this.

Love you Johnny Ball! Loved watching you as a kid.

Where does the 1/3 ratio of the triangle bisectors come from? I understand how it relates to the proof as equal “weights” from the fulcrum but the value itself is pulled from thin air

@therealax6

2 жыл бұрын

I'm pretty sure that was a well-known result even by then.

@timotejbernat462

2 жыл бұрын

@@therealax6 That may well be but it isn't what I asked, how do you derive that result?

i still don't understand, why all POs will balance the triangle ?

@hermannbarbato

3 жыл бұрын

Because the "POs" make up the parabolic section, which has an area of 1/3 the big triangle, so if you give both of them a sort of weight based on their area, they will balance according to that proportion exactly at the center of mass X of the triangle

@wbfaulk

3 жыл бұрын

@@hermannbarbato So you're saying he used the "weight" of the parabola to determine the "weight" of the parabola?

@viliml2763

3 жыл бұрын

@@hermannbarbato But what is the proof that the area is indeed 1/3 the big triangle?

@hermannbarbato

3 жыл бұрын

@@viliml2763 The proof is empirical: he probably made the figures and used some sort of cantilever to determine the proportion. But the point of the video is that the geometrical explanation he used was radical for the time and preceded calculus.

@PaulPower4

3 жыл бұрын

I guess ultimately Archimedes was an engineer as well as a mathematician, so sometimes his solution to a problem was "let's just try it"

I had no idea he did this - this alone puts him in the Top 3 for sure.

Great video. And always amazing to see what conclusions were made back then with the limited tools they had.

"And that's when he got cheeky." 😁😁 Fascinating episode! Part math(s) lesson, part history lesson. Bonus, his voice is so soothing yet enthusiastic!

Woah, the great Johnny Ball, TV legend and enthusiastic educator extraordinaire!

Think of a Number... got it? Great. Now... Think Again. :) Maybe I’m just a SOG (Soppy Old Git), but as soon as I heard the (unexpected) voice of Johnny Ball, I felt my heart swell and a great sense of peace descended upon me. Thank you Numberphile (and Johnny Ball) for transporting me back 40 odd years.

this is *_absolutely_* wonderful

Johnny Ball. Great to see you back on my screen. A regular on tv when I was young.

@numberphile

3 жыл бұрын

More Numberphile videos with Johnny Ball: bit.ly/Johnny_Ball

Best video so far. It included no hipsters and had great information

I absolutely love how Archimedes is drawn. He’s like a quiet little quaint genius that doesn’t say much XD

Johnny Ball! Love him!! Thanks Numberphile!

Love the sound effects

Wow! This was such a great video! I never would have thought that Archimedes thought about calculus 2000 years ago, way way before Leibniz... with such creativity in his methods too! ♥️

What a joy to see Johnny again!!

Wow. Great explanation! And what a great discovery!

oh what an amazing story! thank you all

Thinking of a number for some reason. I'll never forget growing up learning from Johnny Ball.

This is some heat

This is so calming, I love it

1:25 Whoa, COOL!! I can’t believe I never knew this!

6:10 *Archimedes proceeds to discover integrals and calculus*

This cat's love of mathematics is touching, to say the least.

this was such an exciting video!

A voice from my childhood TV programmes. 😊

Love any vids on ancient greek geometry. Please do more!

Wonderful video. Wonderful Johnny Ball. Wonderful story about Archimedes and integral calculus.

More of Johnny Ball, please!

I rewatched it 5 times and couldn't find an explanation for why the parabolic section at the end of the lever should balance with the triangle.

What a stunning explanation... Fantastic

Getting Johnny Ball on is amazing. 80s kids rejoice!

6:14 bro just discovers calculus back in the classical age. Too bad he got shanked by a Roman soldier in the First Punic War. “…sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare”

@jonathanrichards593

3 жыл бұрын

Well played. There is too little Latin quotation on KZread, I find.

@crsmith6226

3 жыл бұрын

@@jonathanrichards593 those were his last words basically saying “don’t disturb my circles” to the soldier who shanked him

@jonathanrichards593

3 жыл бұрын

@@crsmith6226 Yes, as reported by Valerius Maximus more than 200 years later! I'm interested to see that you wrote 'puluere' instead of 'pulvere' for the word for 'dust'. "Don't disturb my circles" is not a quote from Valerius M., though.

What I keep saying in defence of seeming "idiocy" is: It is very difficult (if not impossible outright) to choose what to seriously think about in depth, mainly, before you have done it, it is very difficult (if not outright impossible) to know if the problem or the results might be interesting. If for Archimedes Calculus was a fire-and-forget kind of tool, that's because he did not need it for any other problem (likely).

he speaks with so much love about this... I wish we were made to prove mathematical concepts at school. I don't like being given stuff and being told it just works in math class... math should be a class with the intent of expanding our critical and analytical thinking

@johnacetable7201

9 ай бұрын

But then you'd have students thinking. And thinking is so powerful, it's basically addictive, so you'd have thinking adults, and well, let's say, populists don't like adults who know how to think and question,- they're an existential threat to their little enterprises, - it's the same reason why books are so boring in schools, - they want to make you hate them.