The funny thing is if you increase the length (along a side perpendicular to the triangle) of one of the blobs then a^2 + b^2=c^2 doesn't work for their areas anymore. This idea is only considering the increase along the blob side that is parallel to the triangle sides but not the perpendicular one. At perpendicular expansion the areas In my opinion doesn't fit the Pythagorean blob theorem anymore. It will only work if the blobs area always respects Length=Width constraint.
2d fractals usually (but not always) have infinite perimeter, but they only ever have finite area. A 3d fractal usually (but again, not always) has infinite surface area, but only ever has finite volume. And so on for all dimensions.
Obviously, his previous surveyor (may his soul rest in peace) was far more competent then the moron who can't tell the difference between a square and a non-quadrilateral blob who replaced him.
The perfect right triangle is unlikely but possible. First, a straight road is built. Then they build another straight road that intersects it such that the point where the roads meet forms a + sign. Then they build another straight road that connects two different parts of that same road. Then someone claims the land in between those roads. It could happen, though roads are normally not perfectly straight: they're made to fit the landscape. The other three shapes are much less likely of course.
Counsellor: "There you are..." King: _"Where am I?!?"_ lol, *I love this king* XD Story telling and the animation are excellent, thanks for making this!
This was very amusing. I loved it. The narration was simply fantastic, I couldn't stop smiling and giggling. Not only that, but I learned different uses for the Pythagorean Theorem.
There is a Numberphile2 channel you can subscribe to if you are REALLY keen on our stuff!!! This will be extras and stuff that didn't fit here! ua-cam.com/channels/yp1gCHZJU_fGWFf2rtMkCg.html
What if one of the fields is extremely fertile and the others barren? What if one field has better access to water, or to markets. We really need to consider the market value of the lands, not merely their areas, if we want to divide the land fairly.
magister343 You could add a third dimension representing mean soil fertility and then calculate the volumes of the solids. I'm sure they'd all end up with perfectly proportionate volumes thanks to the suspiciously convenient reports from the surveyor.
I've been teaching the Pythagorean Theorem in high school for a couple of years now. I can't believe I just discovered this video. I'm definitely going to use this in my class. Now I just have to find a translation for 'blob' in spanish. That is the tricky part!
werter260 And explanation would be appreciated. How are they separate? The content of the video is the visuals and the audio... which is just the video itself.
Keppit By video he means the animation+montage etc, and by content he means the story and the lesson it teaches. But I'm really hoping you figured that out already and you're just being a smartass
This is still one of my favourite Numberphile videos. The proof is elegant, the story used to present it is great, Barry Mazur tells it beautifully, and Pete's animations tie it all together.
There were three medieval kingdoms on the shores of a lake. There was an island in the middle of the lake, over which the kingdoms had been fighting for years. Finally, the three kings decided that they would send their knights out to do battle, and the winner would take the island. The night before the battle, the knights and their squires pitched camp and readied themselves for the fight. The first kingdom had 12 knights, and each knight had five squires, all of whom were busily polishing armor, brushing horses, and cooking food. The second kingdom had twenty knights, and each knight had 10 squires. Everyone at that camp was also busy preparing for battle. At the camp of the third kingdom, there was only one knight, with his squire. This squire took a large pot and hung it from a looped rope in a tall tree. He busied himself preparing the meal, while the knight polished his own armor. When the hour of the battle came, the three kingdoms sent their squires out to fight (this was too trivial a matter for the knights to join in). The battle raged, and when the dust had cleared, the only person left was the lone squire from the third kingdom, having defeated the squires from the other two kingdoms, thus proving that the squire of the high pot and noose is equal to the sum of the squires of the other two sides.
The moral is: No matter how ignorant the king is of basic mathematics, if you're his councillor, be sure to answer all his questions patiently and politely.
This was _wonderful!_ I wish you explained all math theorems this way! :D That ending was perfect… "The king says…'ah'." I also love how literally you transcribed Barry's speech in the captions. XD
Amazingly funny animations. At first I wondered why you would have a video about just the pythagorean theorem and why it's eight minutes long, but it turned out very, very interesting. Love it!
Did the audio get really distorted at 2:58 for anyone else? Edit: It seems to happen in some other parts as well. Like the guy tried to eat the mic or something.
It's the first time I see this proof of the Pythagorean Theorem and I find it beautiful! It's simple, short and easy to understand, in a word: elegant.
Hi, Brady, nice video again! I have a little suggestion or demand, depends on the point of view. As you probably know, Barry Mazur is one of the current most prolific mathematicians in the entire world. He made, among others, a seminal contribution to the theory that lead to the Wiles' proof of Fermat last thm. The relevant area of study is called Elliptic curves. I think you and prof. Mazur should make series on elliptic curves; provided he's such a good teacher, I believe, he could approach that subject in an elementary and motivated way, that would suit your style, Brady. Recently, you've featured videos on Ricci flow - a rich tool of modern mathematics. Elliptic curves are similiarly recent and far reaching. Please, continue with this awesome challenge of popularizing modern math. :) greetings from czech rep.
That's unfair from the start ! One of the daughters will have to see her father each time she wants to go from a small blob to the other and the other daughter can just live in her big blob forever and see none of that crazy family.
That is a very illuminating proof. A totally different approach from the typical construction we saw in school involving cutting the large square into 4 pieces...
What a wonderful demonstration of generalization. I've understood the Pythagorean Theorem since High School (more decades than than I'm willing to admit - I'm 63 year old.) But I had never seen the generalization (the Pythagorean Theorem of Similar Blobs) until I saw this video. Thanks.
This was absolutely beautiful. By far the best explanation of the pythagorian theorem I've ever heard or saw. I Wish I had Barry as my maths teacher back in my schooldays.
"Israel and Palestine both claim to occupy the same land!" Exclaims the king. "Ah," says the surveyor, "Well don't worry. I have here what's called a 'Two Blob Solution.'"
On the 4th day the king returs and says that the blob is actually a fractal.
+Darko Simonovic Dude needs to fire that surveyor.
The funny thing is if you increase the length (along a side perpendicular to the triangle) of one of the blobs then a^2 + b^2=c^2 doesn't work for their areas anymore. This idea is only considering the increase along the blob side that is parallel to the triangle sides but not the perpendicular one. At perpendicular expansion the areas In my opinion doesn't fit the Pythagorean blob theorem anymore. It will only work if the blobs area always respects Length=Width constraint.
What kind of fractal?
Some fractals have a finite area, others don't, I believe.
2d fractals usually (but not always) have infinite perimeter, but they only ever have finite area. A 3d fractal usually (but again, not always) has infinite surface area, but only ever has finite volume. And so on for all dimensions.
It’s because of fractal dimension
I think the bigger question is how the King ended up with land that forms a perfect right triangle and three perfectly similar shapes.
Obviously, his previous surveyor (may his soul rest in peace) was far more competent then the moron who can't tell the difference between a square and a non-quadrilateral blob who replaced him.
Politics man, politics.
darkmage07070777 than*
The perfect right triangle is unlikely but possible. First, a straight road is built. Then they build another straight road that intersects it such that the point where the roads meet forms a + sign. Then they build another straight road that connects two different parts of that same road. Then someone claims the land in between those roads. It could happen, though roads are normally not perfectly straight: they're made to fit the landscape.
The other three shapes are much less likely of course.
Maybe his surveor gave him wrong the informacion
That surveyor is crap.
Counsellor: "There you are..."
King: _"Where am I?!?"_
lol, *I love this king* XD
Story telling and the animation are excellent, thanks for making this!
This was very amusing. I loved it. The narration was simply fantastic, I couldn't stop smiling and giggling. Not only that, but I learned different uses for the Pythagorean Theorem.
The king needs to chill out. Counselor's got the situation on lock down.
@JL-CptAtom Said your mom.
Revise your comment
This comment aged badly didn't it
There is a Numberphile2 channel you can subscribe to if you are REALLY keen on our stuff!!! This will be extras and stuff that didn't fit here!
ua-cam.com/channels/yp1gCHZJU_fGWFf2rtMkCg.html
This is great. Majestic. YES.
this man is so amazing:) i love his courage and he looks and sounds so friendly
product placement
This guy's voice is greeeeaaat
Spoiler Alert: The King says 'Ah'...
This video was really fun to watch. The animator did a great job :)
I hope you make more videos like this.
thanks - the animator was Pete McPartlan and the music was by Alan Stewart
This is like something straight off Normalboots
The king says "Ah..." and executes the guy for being a witch... warlock... thingy.
I like how passive-agressive the counsellor is. 4:31
_look_
_look at this_
Fantastic video! Good job to the whole team behind the animation and music!
The story was very well told, too. It was very entertaining to watch.
+blazebluebass +1
What if one of the fields is extremely fertile and the others barren? What if one field has better access to water, or to markets.
We really need to consider the market value of the lands, not merely their areas, if we want to divide the land fairly.
magister343 You could add a third dimension representing mean soil fertility and then calculate the volumes of the solids. I'm sure they'd all end up with perfectly proportionate volumes thanks to the suspiciously convenient reports from the surveyor.
Splitting rent tho
I've been teaching the Pythagorean Theorem in high school for a couple of years now. I can't believe I just discovered this video. I'm definitely going to use this in my class. Now I just have to find a translation for 'blob' in spanish. That is the tricky part!
JanickGers0 ¡"Coso"!
Juan Garay Jaja, eso puede funcionar!
el blobbo
sólo es una figura
Try “chingadera”
WHERE AM I?! says the king
I'm going to say 'WHERE AM I?' any time someone says 'there you are' to me now
Wonderful job with the illustrations Mr Brady!
there is no way I could have done them!
Simply amazing: both the video and the content.
Are the video and the content not the same thing?
Keppit No.
Keppit Maybe he wanted to say that both the video editing and the content were amazing. :)
werter260 And explanation would be appreciated. How are they separate? The content of the video is the visuals and the audio... which is just the video itself.
Keppit By video he means the animation+montage etc, and by content he means the story and the lesson it teaches. But I'm really hoping you figured that out already and you're just being a smartass
Well that was actually pretty entertaining, both narration and animation worked well together.
This is still one of my favourite Numberphile videos. The proof is elegant, the story used to present it is great, Barry Mazur tells it beautifully, and Pete's animations tie it all together.
finally i understand that Pythagorean theorem.. it only took like 10 years.
Ultra Window Likewise! See, they should teach it this way!
aaaah! The audio!! :D BRAADDYYY!!!!
you got your revenge with all CAAAAPPPPITLS and repeated letters, which annoy me back. :)
Numberphile
The guys voice goes from soft to loud almost randomly. I know it's how he speaks, but at least put some compression :P
There were three medieval kingdoms on the shores of a lake. There was an island in the middle of the lake, over which the kingdoms had been fighting for years. Finally, the three kings decided that they would send their knights out to do battle, and the winner would take the island. The night before the battle, the knights and their squires pitched camp and readied themselves for the fight. The first kingdom had 12 knights, and each knight had five squires, all of whom were busily polishing armor, brushing horses, and cooking food. The second kingdom had twenty knights, and each knight had 10 squires. Everyone at that camp was also busy preparing for battle. At the camp of the third kingdom, there was only one knight, with his squire. This squire took a large pot and hung it from a looped rope in a tall tree. He busied himself preparing the meal, while the knight polished his own armor. When the hour of the battle came, the three kingdoms sent their squires out to fight (this was too trivial a matter for the knights to join in). The battle raged, and when the dust had cleared, the only person left was the lone squire from the third kingdom, having defeated the squires from the other two kingdoms, thus proving that the squire of the high pot and noose is equal to the sum of the squires of the other two sides.
I don't get it.
=the square of the hypotenuse is equal to the sum of the square of the other two sides
+Skizzofonik And...?
Bravo!
I don't know why I commented three years ago that I didn't get it.
Now my comment is: You. Asshole. +1
The captions and illustrations that follow Dr. Mazur's voice and tone exactly are hilarious.
The moral is: No matter how ignorant the king is of basic mathematics, if you're his councillor, be sure to answer all his questions patiently and politely.
This was _wonderful!_ I wish you explained all math theorems this way! :D
That ending was perfect… "The king says…'ah'."
I also love how literally you transcribed Barry's speech in the captions. XD
That last 'Ah' was so anticlimatic!
I was expecting Red Wedding shit or something LOL
That's a beautiful proof.
Not only do I like the animation style, but the story was awesome and the math exercises were interesting to boot! Great stuff today!
The daughters will dispute anyway. At least one of them will claim that the land of the other daughter is more beautiful then theirs
Mr Counsellor!! How should I split my daughter between my lands?
No Problem! Just take your daughter and push her somewhere else!
Patrick Star Replying to your own comment eh?
***** Two can play at that game
***** No.
Amazingly funny animations. At first I wondered why you would have a video about just the pythagorean theorem and why it's eight minutes long, but it turned out very, very interesting. Love it!
cheers
Councillor : "There you are."
The king: "Where am I!"
i think this is my favourite Numberphile video so far.
The animations are great.
thanks - they are by Pete McPartlan who animates a few of my videos....
Numberphile His channel: Pete McPartlan
Gotta love the attitude of that counsellor. "No Problem!". Every king should have a counsellor like that. Patient and pleasant.
Why doesn't the counsellor go "you're a bad messenger, send me the surveyor"
That would make this so much faster
You don't say that to a king!
I'll be sure to read this to my children as a bedtime story.
I'm so glad I waited until it was bedtime for me to watch this video. Such an amazing bed time story.
I hadn't thought about the pythagorean theorem in this way before, as literal squares who's areas are relatable. Really made it click.
"Three squares, one triangle" sounds like a really wild numberphile video.
Did the audio get really distorted at 2:58 for anyone else?
Edit: It seems to happen in some other parts as well. Like the guy tried to eat the mic or something.
This was really nice.
Woah, that is some Shyamalian plot twist, right there!
Those markers scratching the paper always give me goosebumps.
It's the first time I see this proof of the Pythagorean Theorem and I find it beautiful!
It's simple, short and easy to understand, in a word: elegant.
I love the king in these animations. He just looks like he's in a constant state of amazement and wonder. XD
Brilliant video, loved the animation too
thanks
King says "Ah." Lol made my day. Love the video, it was excellent!
This was mind-blobing.
Such a nice video, wonderful animation and wonderful storytelling.
thank you
So...it's the Pythagorean Theorem.
The councillor is Patrick?
No, it´s Professor Patrick!
omfg
- There you are.
- Where am I?
Hilarious!
The way this man speaks by randomly pausing or saying a worldly loudly is so funny! I need more!
Hi, Brady, nice video again! I have a little suggestion or demand, depends on the point of view. As you probably know, Barry Mazur is one of the current most prolific mathematicians in the entire world. He made, among others, a seminal contribution to the theory that lead to the Wiles' proof of Fermat last thm. The relevant area of study is called Elliptic curves. I think you and prof. Mazur should make series on elliptic curves; provided he's such a good teacher, I believe, he could approach that subject in an elementary and motivated way, that would suit your style, Brady. Recently, you've featured videos on Ricci flow - a rich tool of modern mathematics. Elliptic curves are similiarly recent and far reaching. Please, continue with this awesome challenge of popularizing modern math. :) greetings from czech rep.
This video..... was incredibly boss
That's unfair from the start ! One of the daughters will have to see her father each time she wants to go from a small blob to the other and the other daughter can just live in her big blob forever and see none of that crazy family.
WHERE AM I?? -King, circa once upon a time
I laughed so hard @ 2:07 when you strike the wrong "the".
A really enjoyable video. It's nice to see something different from this channel once in while.
That is a very illuminating proof. A totally different approach from the typical construction we saw in school involving cutting the large square into 4 pieces...
Awesome video!
I especially enjoyed the literal subtitles (eg. exact words and sizes), and small touches such as the music pauses. :)
Really enjoyed this! Story, music and animation are great. You could do something similar for the Wheat on Chessboard problem
This is probably the best explanation of the Pythagorean Theorem I've ever seen.
One of your best yet Mr Haran! Also love the brown paper for the animation keeping to the theme =]
What a wonderful demonstration of generalization. I've understood the Pythagorean Theorem since High School (more decades than than I'm willing to admit - I'm 63 year old.) But I had never seen the generalization (the Pythagorean Theorem of Similar Blobs) until I saw this video. Thanks.
I just love how silly the animations are, its brilliant!!!
This was absolutely beautiful. By far the best explanation of the pythagorian theorem I've ever heard or saw. I Wish I had Barry as my maths teacher back in my schooldays.
The kinetic typography going on in this video is hilarious and amazing.
The text makes this even more hilarious.
wow!! My favourite video from any of Brady's channels so far!!!
gosh, thanks
Numberphile It keeps getting harder to choose :)
This is an extreamly good way of proofing a theorem. Nice in so many ways!
I loved the allusion to King Lear at the beginning.
That was just beautiful. I was smiling throughout the whole video :)
Such a nice and informative story! And great animations ofc ;)
Thanks!
The animation in this video is HILARIOUS.
Epic production! :D I love the music!
King: No Wait! My land isn't squares! It's Made Of Blobs!
Counsellor: Don't Worry, Blob Pythagorean Theorem!
How to solve world peace
"Israel and Palestine both claim to occupy the same land!" Exclaims the king.
"Ah," says the surveyor, "Well don't worry. I have here what's called a 'Two Blob Solution.'"
This should be used in schools around the world. :) great way of explaining pythagorean theorem.
Best explanation for Pythagoras' Theorem I've ever seen
I love the fact that the counsellor looks like a wise Patrick Star.
This is my favourite video on the internet.
ta for a charming video. Was the generalisation from squares to blobs known to Pythagoras or did it come later?
Beautiful story, music and animations ^_^
Keep up good work guys!
This is the best numberphile video to date. Even though it was quite simple and basic it was very very entertaining!
Best.
Animation.
Ever!
Do more!
Fantastic animation! I wish my friends were as excited as the king was.
Where am I ? Says the king XD
The moral of the story is; Kings are annoying. And this guys maths is so powerful it distorts the audio.
Very nice video, good job! The background music gives it that extra something, that makes you (at least it made me) pay extra close attention.
Excellent, didnt know the blob theorem until now and the proof is so simple!! Thank you.
Wow. This is actually amazing.
the 'where am I?' Just killed me, It's just me in math classe after lunch..
The king says "ah"
And the moral of the story: Kings ask a lot of questions.
It's my favorite theorem ,explained in different ways. Thank you for this video.
I love the drawings in this video.
Who knew Patrick Star was such a mathematician.
Very interesting stuff! I knew the Pythagorean theorem, but the story and animations are fascinating!