okay so now what's my morale can you guess Kings ask a lot of questions well in fact yeah that that the initial question of the King asked about scale basically is what this particular proof of the Pythagorean theorem sort of highlights it sheds a certain light on it and it depends very much from it it's an old proof it's probably from heaven I know it was known in France in the late 1900s but the historians would probably be able to bring it who knows all the way back yes that that the initial questions sort of frame the larger issues that you have to have in mind in order to have though in order to ingest the proof very often you're after one thing and in the background let's say in the grounding of that thing will be some very large foundational element that gets practiced in your attempt to understand the specific thing for example well the many examples counter discovered or fell upon his set theory initially working on issue in it's a rather delicate issue and analysis or more contemporary the mathematician Grundig in trying to understand some conjectures of they Andre they about numbers of solutions of equations felt that he had to in fact certainly had to understand the nature of on neighborhoods in topological spaces if you have a point so to speak our neighborhood is some sort of region some of the synergy of it now usually we think of our neighborhood in a fairly naive way but Grubnic in order to understand questions of number theory how to revisionist a neighbor what is a neighborhood in a topological space so this story you've taught this fable you've just shared now it's not about Pythagorean theorem is it's not about Pythagoras well yes and no I mean it is certainly a valid proof of the Pythagorean theorem but I didn't tell it to you for that reason what reason did you tell us what do you prefer exactly what I just described that it's saying that there are always background issues which get highlighted in in proof and I just wanted to emphasize that there's no there many other reasons for giving this there's something striking about the economy of the councillors construction he drew a single line and that totally changed one's vision of of the the geometry involved very often there's a simple simple introduction of something that's not logically within the framework of the question and it could be very simple and it changes your view of what the question really is about and what its framework is

Before watching this video, I attempted to recreate the problem's diagram using a compass and straight edge, as the Greeks would have done. Initially, I cheated and used a protractor to find the point on the hypotenuse to draw the perpendicular line to the right-angled corner. Then I decided to draw some similar blobs using the compass – each blob was a semi-circle. I then found that if I extended the two smaller circles to the hypotenuse that they met at that point I initially used my protractor to find. I was surprised at this, but then gave it some thought and now it seems totally logical.

I'd rather have the single piece of land, because it would save me a lot of fence maintenance. Moral: absolute justice or fairness does not exist.

@0:40: "I know that in France it was known in the late 1900s" … wait … didn't the USA go to the moon in the late 1900's … or at least to a remote location in Utah?

0:9

The moral I got is that a square is a very special kind of blob.

Wow. It's impressive how easy that is to follow. And we got a mathematician's favorite, the general answer instead of the specific.

When he said, "What is the moral of this story?" I immediately thought of education. In the first, however many, days, the king gets that it works, but doesn't actually get why. On the final day, because he'd been trying to understand it, and because it was explained a different way, the king finally actually understood the concept. This is a huge deal in education, because memorization is absolutely useless, if you want to actually use something. Otherwise, you're just a crappy calculator, and you still have still have to put in work to keep that stuff accessible, as long as you need it.

Huh?

I think I might have been less confused not knowing the moral, since I followed it fine up through the whole thing, but then I had the thought: If the surveyor didn't know they weren't squares the first time, how does he know the 3 blobs are all of similar shape?

Or does this matter?

I think the moral is that you can find (sometimes) a way to proof a solution if you put the question at hand in a larger context (or extent the question in such a way that it becomes evident to answer) in stead of pinpointing on what you don't know about the (primitive) smaller question.

And this is still more wonderful.

to me the moral was that the pythagorean theorem is actually a special case of the more generalized pythagoreal blob theorem. who knew

The real moral of the story is that the King's surveyor should be fired.

barry mazur! brady always gets some of the most interesting mathematicians for interviews

sorry to bother, but i don't really understand the point of a second numberphile channel.

The moral I took out of it is a programming moral. Depending on the program, it can take a genius to write it, but a simpleton could come along and break it. So you should always check your solutions with simpletons, and with people who are not experts in your field. The initiated intuitively know how you want your program used; the uninitiated do not.

I think it is just a fun and simple way of proving the pythagorean theorem.

The pythagorean theorem has to be on par with the second law of thermodynamics.. I agree this proof really is brilliant, the philosophical or metamatematics of it having such a broad scale reminded me of Godel and the Vienna circle.

Moral of the story (at least from my point of view): Focus on your proof/goal but don't forget about useful byproducts of your aim (in the case of the fable, pythagoras's theorem applicable and more generalized to blobs in some sense).

It's kind of weird that there are "truths" to be discovered in mathematics, when really it's all figments of our imagination.

Translation: In mathematics when you ask a question, the question itself does not highlight everything going on in the issue. Often the answer to the question (the proof) highlights what was really going on in the issue.

If I ask for a proof that the sum of the area of the a square and b square equals the area of the c square on a right triangle, that does not in any way lead to this proof. This proof highlights that the Pythagorean isn't really about the squares but about ratios and what happens to ratios in geometry when you scale things.

Thats a pretty deep moral for something that seems unrelated. Great way to tie it all together

Moral? Your daughters, they have "huge tracts of land."

Does this only applies to blobs smaller than the square that would form?

This video showed up on my "recommended" list…I have no idea what I'm watching.

Will there be a Numberphile channel for every number?

The Moral:

Smart people often end up working for dumb people. because one side realizes its limits, understands things that are real and does not waste time believing in things that aren't real; while the other side not only cannot see limits, they believe in things that aren't real and don't understand things that are.

I noticed the logo for this channel is a 2 on the Numberphile paper. Why not make it the symbol for Tau because Numberphile has the symbol for Pi and Tau is 2 Pi.

So if you deform all the squares equally, Pythagorean theorem still works? That is interesting.

Damn straight. Never stop trying to figure things out, even if those things don't seem very important. You may just stumble upon a lemma that illuminates a huge category you hadn't even thought of before.

Actual moral of the story: review, revision, re-imagine, reframe.

make more videos like this!

The extra bits link leads back to the fable itself. Is that intentional?

I'm just a layperson but it seemed to me he was saying, doing a proof can prove something about proof doing beyond merely the proof at hand. But you have to do a proof to prove as much and even then what you are getting at remains implicit.

7/5-2014 21.33 GMT+1

The discovery of a new channel.

It all becomes clear. These videos are subterfuge for Brady's globe trotting.. He'll be doing History in Manoa, Honolulu next.

When he went from talking about the Pythagorean theorem to talking about the Grothendieck topology, I literally fell out of my chair laughing. Talk about a jump in difficulty xD

NumberphileTau!

More stuff to watch =D

0:39 known in France in the late 1900's? LOL those French are really slow.

So very inspiring… at a time of my life when I need so much inspiration.

I'm absolutely enamored and obsessed with math. It is my absolute favorite thing. I love it a little too much o.o and like… it's just too beautiful. After I graduate high school and during college (I'm in 11th grade now) I'm going to study the mathematics of nature and the cosmos! :3 I have a theorem that could explain the distribution of prime numbers and how phi is presented, but I need programming skills to do what I have in mind, and my computer is also broken. I wish I could get this done before I start applying for colleges so I have something to show them! Ohhhh I love math sooooooo much!

i think the moral is to inquire until you've understood something rather than taking people's word for it, like the king did. Something every kid should learn in their formative years

That's a really cool way to introduce people to the Pythagorean theorem… Didn't know that it can extend to any shapes and not only squares.

I am the 3900th subscriber.

Beautiful. I love stories about historical enlightenment! Tell us more Great Brady!!!

I am officially unsurprised that Brady has this other channel, especially when I listen to the podcast (-_-)

No… don't stop. I love the way he approached his way of explaining, but it feels like he needed to say more. The explanation feels unfinished.

So the moral of the story was ?

Brady was abviously confused to, but he answered, 'what i just told you'

Of course I have my ideas, but am far from certain without a rewatch.

Interested to see any replies.

He could not have used a better example than the Pythagorean Theorem. Initially, it looks like a geometric pattern, then you fiddle around with it and you notice it might in fact be more suited to Arithmetic since it has connection to prime numbers. Then you learn that the equation for the circle uses this theorem, and so on. It might seem like a cute little theorem about triangles at face value, but its meaning is much deeper.

And this convinced me to subscribe. If there's more like that on Num2, then I would be the king's fool not to find out…

Brady are you going to add all extra bits of numberphile in numberphile2 that way you dont have to make them secret and people can find them by browsing youtube randomly?

I always though it was a shame that you have secret videos, from the perspective that people cant find them by mistake when browsing. You probably have your reasons, I assume.

either way, awesome video!

Science!