Pssst… Wanna see something cool like this? Another golden era CZcams video (with water) visually demonstrating the relationship between P=VA power volts and amps. Search for this, he uses water-bags and weights in his sink, it’s on the video thumbnail. 👍
@@acanofbeans6798 It's a reference to a funny animation where Perry keeps putting on both Fedoras and platypus hats, as well as 2 Norm hats. From this, Doof keeps chaining more words together. I reccomend checking it out
Back in 2017, when our math teacher introduced the Pythagorean theorem, the first thing he did was showing us this video. That was one of the best things he could do because this made (and still does) so much sense to me to understand this theorem.
Materials used were 1/2 inch gypsum board for the circle. 2x4 inch pine segments to support the back, as well as make the stand for it. Used a short half inch bolt, washers and nut to bolt the gypsum to the stand so it would turn easily. Used the “pencil on a string” trick with a tack in the middle of the gypsum board to create the circle. Used a gypsum knife to cut the circle, though any saw would probably do. Painted the gypsum white. Purchased plexiglass sheets from Home Depot, and had the squares (fronts and backs) as well as the square edges all cut with a table saw. Needed 18 pieces of plexiglass cut. It was key that they all that all of the edges be the same width, so we stacked up several pieces of plexiglass and cut them into strips all at once. It worked great. We used an arbitrary 1 inch width for all square edges. Drilled small holes in the gypsum then screwed the first three squares to the gypsum board, Screwing them in with screws, then dabbing them with silicone caulk so it wouldn’t leak. Then glued all pieces together with superglue, cutting and drilling as needed as a we went along. We added blue food coloring to the water to make it easier to see. All material was purchased from Home Depot. Lowes would have the same thing.
Correction: where it states “Drilled small holes in the gypsum then screwed the first three squares to the gypsum board” should say “Drilled small holes in the PLEXIGLASS then screwed the first three squares to the gypsum board.”
Also, if you dropped a perpendicular from the right angle vertex to the far side of the large square, it would cut the large square into two compartments equal in area to the two smaller squares. You could then use two colors of water to show this. This would be closer to a demonstration of Euclid's proof from the Elements.
6/10 the dialogue wasn't very rich and I feel like the main character didn't have enough lines. And the special effects were mediocre at best, and can somebody explain the plot to me its very confusing.
Pythagorean theorem a^2+b^2=c^2. Euclid proved this in his book Elements. We can think of a^2 as the area of a square of side a. The areas of two smaller squares in the video represent a^2+b^2, and the larger square on the top is c^2.
***** The thing is, this is not a proof. It is merely a demonstration. Sure, I can do demonstrations of mathematical concepts all day long but it doesn't hold up in serious study.
***** This demonstration showed the meaning of a² + b² = c² -- or rather a demonstration for a specific (a,b,c)-triplet. It did not demonstrate that it holds for any other triangle and certainly not that it holds in general. And does it really make anything easier? We already knew it was about two areas that should add up to be equal to another area -- so why introduce volumes? Why, in fact, introduce an extra step just to prove that this example about volumes of water is equivalent to an example about areas, which is what we started out being interested in? Furthermore, we have good empirical evidence from the didactics of physics and chemistry to show us that demonstrations usually /hinder/ learning, at least if they are performed by the teacher. An alternative to this demonstration is to have the student measure areas (by counting squares on graph paper, for example) which is not as "cool" but something we should expect to work better.
Peter Lund I thought for a long time how to answer since clearly my mathematical skills and some english isn't very good. You said: '' It did not demonstrate that it holds for any other triangle and certainly not that it holds in general.'' /So the same demonstration works for other angles that arent right angles, too? Im sorry for my english, maybe i didnt understand you right, please let me know./ But i guess you are right about the fact that extra volumes can actually make it more confusing - i did not even think about it. I guess i really was amazed by the fact that it just looked ''cool''. Although let me say this: It should not be a big problem if it was explained why and how volumes also work on this. (/although you just said that this demonstration works for every triangle? Please let me know if i misunderstood you/) It may add confusion or extra knowledge, depends how well it is explained. And also the ''coolness' adds ''interest'' which could help a lot in the progress of learning. But of course, getting down to the core of it by - lets use your example - counting squares on graph paper, would definitely be the real experience understanding it.
I believe this experiment is flawed because the depth of each compartment of water is diffrent and there seems to be no correlation between side length and depth of the water reservoir so this experiment is not showing the Pythagorean theorem it just show's two areas equal one larger area. Which of course is subject to the changing of the volumes of each compartment. This may be incorrect and please correct me if I am wrong, without any measurements of the compartment volumes I have to say it is wrong.
I never understood this video until I looked up the meaning. The Pythagorean Theorem says that you can take the square of the two leg lengths and they will be equal to the square of the length of the hypotenuse. Thats the same thing as finding area of a square (squaring one side length). For this reason, the space that two of those smaller squares takes up should be the same as the space that the larger square takes up. a^2 + b^2 = c^2 OR area of square 1 + area of square 2 = area of square 3.
Captivating truely. The special effects really brought this piece together. There would need to be more dialogue however from the budget and the materials in which the director was given this truely was a film for the ages. Overall the filming and decision to have the camera slightly off centred showed true emotion of all the characters. While the plot was confusing to start with the subtle hints throughout made it clear to the viewer the main characters true intentions and reasons for their actions. This film got very inappropriate towards the end and I would not recommend watching it with younger audiences however if you wish to see a very well thought out and beautiful piece of art I highly recommend this video. We truely did learn the true meaning of friendship and the ups and downs of high school football. Thank you so much for producing this film that admittedly did make me shed a few tears.
I cannot explain why, but this makes me happy. I think it's just because I had never thought about Puthagorean Theorem this way before, but this makes total sense.
It's also assumed that the depth and width of the containers are the same so the volumes are proportional by a factor of c^2 / (a^2+b^2) = 1 which actually proves pythagoras's theorem (assuming c is the hypotenuse etc. )
I’m 4 years into engineering university and now is that I understand the intuition behind this. I always just took it as a fact, but now I understand the concept more clearly.
Thank you! The Pythagorean theorem is actually one of the things I still remember from high school, however I wish I had watched this demonstration back then. How easily would it be to understand.
As stated above, it's not a proof but it's empirical evidence of the Pythagorean theorem for that specific right triangle. Even saying that isn't completely accurate if one wants to be pedantic since the demonstration is based on equivalent volumes and not areas.
For the confused people: 1. Get a piece of paper and a ruler to make straight lines and to exemplify the techniques I will list. 2. Squaring/by common name, Squared: Squaring is symbolized by a little 2 to the top right of your number. Squared means 2x2 or and other number multiplied by itself. For example: 2²/2 x 2. 3. The Pythagorean theorem trick: is too (on a calculator or in head) square both legs (two sides the make the right angle) and combine them. After doing so, square the hypotenuse (the one that slants to connect the 2 ends of the right angle) and find the square root. If the two answers (one from the combined legs are equivalent and the hypotenuse's square root) are equivalent the the triangle is a right triangle. You're welcome. 4. Confusion on the squares: you can break down a triangle easily...there are 3 sides (which are in measurements) and each one needs to be squared, for example: 2 inches TIMES 2 inches, take one of those 2 inches and put it into the height of the square, take the other and make it into the length of the square. BOOM! that's how they got squares. You're welcome. 5. The legs of a right triangle are the ones connect to the little square in the corner, this represents that there is a 90 degree angle from leg to leg. 6. The hypotenuse is the slanting line that connects the two ends of the right angle, this will also be the longest side of the right triangle. 7. The Water Demo represents the trick, the squares are just the measurements of the lines squared. So if those L squares (the squares representing the legs) are filled with water than we can see if they are equal (when combined) to the hypotenuse by transferring the water. Now you have Squaring, Right triangles, Mathematically Creating a Square, and Pythagorean theorem trick consolidated into 7 short paragraphs. You're welcome.
Bodhayan Sulba-Sutra that predates Pythagoras by several hundred years (if not thousands), writes exactly this: दीर्घचतुरश्रस्य अक्ष्णयारज्जुः पार्श्र्वमानी तिर्यङ्गमनि च् यत् पृथग्भूते कुरूतः तदुभयं करोति। - बोधायन सुल्ब-सूत्र (१.१२) The rope corresponding to the diagonal of a rectangle, make whatever is made by the lateral and perpendicular sides, individually. - Bodhayan Sulba-Sutra (1.12)
This works because each area is equal to the squared length of each side of the triangle. Wheres the hypotenuse is the equal to root of the sum of the squares when doing a triangle, this demonstration is actually just the sum of the squares because the root is squared and is thus cancled out.
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This is called "waterproof" :)
Cooling down...
Genius 😅
Next up... FIREPROOF
Good one, but it's not a proof though.
😂😂😂
This is the coolest demonstration of Pythagoreon Theorem I have ever seen!
The fact it was posted 15 year ago too😭
Pssst…
Wanna see something cool like this?
Another golden era CZcams video (with water) visually demonstrating the relationship between P=VA power volts and amps.
Search for this, he uses water-bags and weights in his sink, it’s on the video thumbnail. 👍
And yet, it ages well.
Yeah I mean, it’s not like water is a new technology
@@Indoraptoad but hey, at least it could give some proof that the pythagorean theorem is true (for people that are dum enough to think it's not true).
What an elegantly simple way to visualize this! I love it!
There are easier ways.
What is the 74th..
A demonstration of the pythagorean theorem?
*Brown*
Perry the demonstration of the pythagorean theorem!
Perry the Perry the platypus!
The platypus the Perry the Perry the platypus!
@@50Steaks68 are u having a stroke?
@@acanofbeans6798 It's a reference to a funny animation where Perry keeps putting on both Fedoras and platypus hats, as well as 2 Norm hats. From this, Doof keeps chaining more words together. I reccomend checking it out
@@isaiaholaru5013 sounds like a funny meme. What's the video and maybe it's channel called, so i can find it?
@@arkasha6649 “Perry the Perry the Platypus” by CoolGuy
was only supposed to watch this twice in math class. had it going all day
nah math ain't even over yet
Back in 2017, when our math teacher introduced the Pythagorean theorem, the first thing he did was showing us this video. That was one of the best things he could do because this made (and still does) so much sense to me to understand this theorem.
Incredible, brought tears to my eyes!
I literally cried a river that became the Nile lmaooooooooooooooooooooooooooooooooo XDXD lol rofl xD
What???!
I cried like a baby.
@@quakeev334 I'll cry a river over you.
@@kostasbr51
is that a threat?
Materials used were 1/2 inch gypsum board for the circle. 2x4 inch pine segments to support the back, as well as make the stand for it. Used a short half inch bolt, washers and nut to bolt the gypsum to the stand so it would turn easily. Used the “pencil on a string” trick with a tack in the middle of the gypsum board to create the circle. Used a gypsum knife to cut the circle, though any saw would probably do. Painted the gypsum white. Purchased plexiglass sheets from Home Depot, and had the squares (fronts and backs) as well as the square edges all cut with a table saw. Needed 18 pieces of plexiglass cut. It was key that they all that all of the edges be the same width, so we stacked up several pieces of plexiglass and cut them into strips all at once. It worked great. We used an arbitrary 1 inch width for all square edges. Drilled small holes in the gypsum then screwed the first three squares to the gypsum board, Screwing them in with screws, then dabbing them with silicone caulk so it wouldn’t leak. Then glued all pieces together with superglue, cutting and drilling as needed as a we went along. We added blue food coloring to the water to make it easier to see. All material was purchased from Home Depot. Lowes would have the same thing.
Correction: where it states “Drilled small holes in the gypsum then screwed the first three squares to the gypsum board” should say “Drilled small holes in the PLEXIGLASS then screwed the first three squares to the gypsum board.”
Genius.
@@simranjeetkaur1173 drill two holes and then close them with screws?
@@victorteeter1853 CZcams lets you edit comments.
I love the sound the water makes.
8 years ago omg
@@sourserenity2796 this comment is older than you wow
@@ipenutbrudda8823 by channel age or age age 🤔
Awesome
Are you alive?
cant wait till this is in cinemas
Also, if you dropped a perpendicular from the right angle vertex to the far side of the large square, it would cut the large square into two compartments equal in area to the two smaller squares. You could then use two colors of water to show this. This would be closer to a demonstration of Euclid's proof from the Elements.
woah this deserves to be known more
😮😮😮😮😮
6/10 the dialogue wasn't very rich and I feel like the main character didn't have enough lines. And the special effects were mediocre at best, and can somebody explain the plot to me its very confusing.
instrucions unclear, got dick stuck in the plot
Pythagorean theorem a^2+b^2=c^2. Euclid proved this in his book Elements. We can think of a^2 as the area of a square of side a. The areas of two smaller squares in the video represent a^2+b^2, and the larger square on the top is c^2.
7.8/10 too much water
Att ya
Viet Long Le Nguyen
I wish everything in math could be shown in a simple way like this!!!!!!!! :((((((
but no one does
***** The thing is, this is not a proof. It is merely a demonstration. Sure, I can do demonstrations of mathematical concepts all day long but it doesn't hold up in serious study.
I think demonstrations should be shown as much as possible because they make everything easier to understand.
***** This demonstration showed the meaning of a² + b² = c² -- or rather a demonstration for a specific (a,b,c)-triplet. It did not demonstrate that it holds for any other triangle and certainly not that it holds in general.
And does it really make anything easier? We already knew it was about two areas that should add up to be equal to another area -- so why introduce volumes? Why, in fact, introduce an extra step just to prove that this example about volumes of water is equivalent to an example about areas, which is what we started out being interested in?
Furthermore, we have good empirical evidence from the didactics of physics and chemistry to show us that demonstrations usually /hinder/ learning, at least if they are performed by the teacher. An alternative to this demonstration is to have the student measure areas (by counting squares on graph paper, for example) which is not as "cool" but something we should expect to work better.
Peter Lund I thought for a long time how to answer since clearly my mathematical skills and some english isn't very good.
You said:
'' It did not demonstrate that it holds for any other triangle and certainly not that it holds in general.''
/So the same demonstration works for other angles that arent right angles, too? Im sorry for my english, maybe i didnt understand you right, please let me know./
But i guess you are right about the fact that extra volumes can actually make it more confusing - i did not even think about it. I guess i really was amazed by the fact that it just looked ''cool''. Although let me say this:
It should not be a big problem if it was explained why and how volumes also work on this. (/although you just said that this demonstration works for every triangle? Please let me know if i misunderstood you/) It may add confusion or extra knowledge, depends how well it is explained.
And also the ''coolness' adds ''interest'' which could help a lot in the progress of learning. But of course, getting down to the core of it by - lets use your example - counting squares on graph paper, would definitely be the real experience understanding it.
This is a really helpful visual example! Thank you so much!
Brilliant idea to demonstrate this fundamental principle. 👍
This is probably the best way I've ever seen to explain the Pythagorean theorem.
I believe this experiment is flawed because the depth of each compartment of water is diffrent and there seems to be no correlation between side length and depth of the water reservoir so this experiment is not showing the Pythagorean theorem it just show's two areas equal one larger area. Which of course is subject to the changing of the volumes of each compartment. This may be incorrect and please correct me if I am wrong, without any measurements of the compartment volumes I have to say it is wrong.
Instructions unclear, failed Geometry class
Brilliant. No words needed. Well done!
A 43 second video finally put some logic into a thing my teachers couldn't.
THIS ACTUALLY MAKES PERFECT SENSE! COOL!
Anyone else from math class😭
Yes my teacher put it for us and I thought it was satisfying hearing the water 😭
...gunna send it to my class mates. it should help 'em
yeah lmao 😭😭
Kᴀʟᴇᴇ Fʟᴏᴡᴇʀs sup my guy
No
I never understood this video until I looked up the meaning.
The Pythagorean Theorem says that you can take the square of the two leg lengths and they will be equal to the square of the length of the hypotenuse.
Thats the same thing as finding area of a square (squaring one side length). For this reason, the space that two of those smaller squares takes up should be the same as the space that the larger square takes up.
a^2 + b^2 = c^2 OR
area of square 1 + area of square 2 = area of square 3.
Thanks for the explanation
I was about to say why explananation?
Sorry i meant explanation
Thanks for doing my math work for me bud
@Joan Ferreira Yes, only in a right triangle! Thanks
Absolutely awesome!
A very creative way. Appreciate u
this is cool but didn't answer the question my teacher attached to it :')
may I ask what was the question?
Yeah what is the question?
Absolutely amazing. Thanks for making me really understand the theorem today! Real genius! 🙏
This is awesome. You are a genius. Thanks you
Cannot be misunderstood... multilingual... not one word wasted! BRILLIANT!! 😊
This is Awesome!
this pleases my grade 11 maths class very much, many thanks :)
uwow, my grade 9 class also loves it. Kind regards, Vicksaa, Bowen737, LiamHems, JamesBon, Empty, (drakeand)Josh, Zach, Farras, Luseal, Lillas, JB-Brown, Lindsoy, Zakattack, Sha-when?, Charlean, MarkDaisey, Krees, Chorly, Cypress Pine, Roarrr, Polo, Raysawn, Nickname, Moreham. Nam, Dav. Tahnks
Amazing, never would of thought of it!
That was really ingenious. Good basic ideas that help the student into geometry ❤
Captivating truely. The special effects really brought this piece together. There would need to be more dialogue however from the budget and the materials in which the director was given this truely was a film for the ages. Overall the filming and decision to have the camera slightly off centred showed true emotion of all the characters. While the plot was confusing to start with the subtle hints throughout made it clear to the viewer the main characters true intentions and reasons for their actions. This film got very inappropriate towards the end and I would not recommend watching it with younger audiences however if you wish to see a very well thought out and beautiful piece of art I highly recommend this video. We truely did learn the true meaning of friendship and the ups and downs of high school football. Thank you so much for producing this film that admittedly did make me shed a few tears.
agreed omg
haha
that was actually quite beautiful.
Cool demo. And love the channel name.
A lot of thanks! It helped me a lot :)
I cannot explain why, but this makes me happy.
I think it's just because I had never thought about Puthagorean Theorem this way before, but this makes total sense.
I came here because of math class, now it's time for me to go back to work
It's also assumed that the depth and width of the containers are the same so the volumes are proportional by a factor of c^2 / (a^2+b^2) = 1 which actually proves pythagoras's theorem (assuming c is the hypotenuse etc. )
Awesomely explained.
Shoutout to mr.crouse who sent this to all the grade eights
My eighth grade teacher sent me this 😳
Same
One of the best ways of demonstrating this idea that I have seen, well done.
Ok this is honestly pretty cool
Thank you very much 👍👍
I am going to use this video in the presentation in the class to prove the pythagors theory
Instructions unclear - completed stereo madness
instructions unclear - electrocuted me and made my muscles spasm to the way of bloodbath
Very nice. Simple, yet elegant
I’m 4 years into engineering university and now is that I understand the intuition behind this. I always just took it as a fact, but now I understand the concept more clearly.
Brilliant! Every math teacher should use this video when presenting the Pythagorean theorem to students.
Pythagoras smiled from heaven.
damn and now I have to go to the bathroom
JudgeBee lol
I know the reference hahahahah BBC
😂
This is perfect, it’s a great explanation of Pythagorean theorem, this 15 year old classic is a masterpiece 💖
Beautiful.
Very satisfying explanation!
This very well answered the question i gave my teacher of "Why do we multiply each side with times 2 instead of just multiplying each side as it is?"
You're not multiplying any side by 2, you're multiplying each side against itself to form a square, hence, "squared"
this is pretty hecking cool :0
Beautiful!
is there one of these for taylor series
Thank you! The Pythagorean theorem is actually one of the things I still remember from high school, however I wish I had watched this demonstration back then. How easily would it be to understand.
its not a demonstration though
you learned it in high school? 😂😂😂
@@yakkoroblox7456 I don't remember tbh
@@alexandreaamaral4155 says "demo" on the title
Waterproof analogy
Fun fact, the 3 squares can be any shape as long as they're identical except for scale, and this still works.
Amazing proof of Pythagorean theorem. Good teaching resource.
This isn't a proof though, this only proves one special case, in which A B and C are the dimensions of those containers.
It is not a proof, it is merely a demonstration. It shows that it IS, but not WHY it is.
As stated above, it's not a proof but it's empirical evidence of the Pythagorean theorem for that specific right triangle. Even saying that isn't completely accurate if one wants to be pedantic since the demonstration is based on equivalent volumes and not areas.
IMO, Bhaskara's proof of the Pythagorean theorem is the simplest to understand for those who do not have experience dealing with proofs.
I'm going to be a math teacher and this demonstrates the pythagorean theorem so well, where can I get one of these?!
nobody helped them
This is a magic trick actually. There’s extra water hidden behind the orange triangle.
Ya know, that young lady is showing this video
to her teenage kids and they LOVE IT ALSO!
Thank you ma'am.
god damn my class is confusing
i had to watch two times to understand the proof.
said being that I'm studying calculus 2 at the moment.
It is weird isn't it. I have the same feeling and i have spent a third of my life studying maths.
WOW qué ingenioso!!! Me encanta!
Very well done!
Nice one :-)
How did you make this?
glass and water
Uploaded 15 years ago, demonstrating a theorem from 3500 years ago... may it live forever!
It will be fun when learning math like this
Poor girl was probably kidnapped
nop
nop
nop
Nop
nop
Someone should point out that the boxes are perfectly square ex: 6X6X1, 8X8X1, 10X10X1 for this to work and be true.
I mean... of course they are, that's what it means to "square" a number.
Thanks this was very useful
Amazing!
I like eating poles made out of trees
Perry the platypus
This is so cool!
That's a nice nice visualization!
very emotional, im touched.
Watched this in class
ATTENTION PLS , it's 15yrs old video
Right ... because of course Pythagoras theorem has evolved in the past 15 years ...
Wow! Great idea!
For the confused people:
1. Get a piece of paper and a ruler to make straight lines and to exemplify the techniques I will list.
2. Squaring/by common name, Squared: Squaring is symbolized by a little 2 to the top right of your number. Squared means 2x2 or and other number multiplied by itself. For example: 2²/2 x 2.
3. The Pythagorean theorem trick: is too (on a calculator or in head) square both legs (two sides the make the right angle) and combine them. After doing so, square the hypotenuse (the one that slants to connect the 2 ends of the right angle) and find the square root. If the two answers (one from the combined legs are equivalent and the hypotenuse's square root) are equivalent the the triangle is a right triangle. You're welcome.
4. Confusion on the squares: you can break down a triangle easily...there are 3 sides (which are in measurements) and each one needs to be squared, for example: 2 inches TIMES 2 inches, take one of those 2 inches and put it into the height of the square, take the other and make it into the length of the square. BOOM! that's how they got squares. You're welcome.
5. The legs of a right triangle are the ones connect to the little square in the corner, this represents that there is a 90 degree angle from leg to leg.
6. The hypotenuse is the slanting line that connects the two ends of the right angle, this will also be the longest side of the right triangle.
7. The Water Demo represents the trick, the squares are just the measurements of the lines squared. So if those L squares (the squares representing the legs) are filled with water than we can see if they are equal (when combined) to the hypotenuse by transferring the water.
Now you have Squaring, Right triangles, Mathematically Creating a Square, and Pythagorean theorem trick consolidated into 7 short paragraphs. You're welcome.
*_a² + b² = c²_*
This is creative!
I vote this for E3 contest. Big ups!
Who else is here from Mr. Tran's class
guys, can share us on how did you construct it? It would be a big help! Thanks.
Three cube glass boxes that satisfy a^2+b^2=c^2, affix to spinning wheeling.
This is actually really clever.
Only works if the squares have exactly the same thickness. Really cool experiment!
wait, i want to pee.
Can you please show how to make this ?!!
This is fantastic!
I agree
this is so cool!
who made this cuz this is cool look how much peeps have watched it
lol
Bodhayan Sulba-Sutra that predates Pythagoras by several hundred years (if not thousands), writes exactly this:
दीर्घचतुरश्रस्य अक्ष्णयारज्जुः पार्श्र्वमानी तिर्यङ्गमनि च् यत् पृथग्भूते कुरूतः तदुभयं करोति।
- बोधायन सुल्ब-सूत्र (१.१२)
The rope corresponding to the diagonal of a rectangle, make whatever is made by the lateral and perpendicular sides, individually.
- Bodhayan Sulba-Sutra (1.12)
well while you guys were too busy shitting in the streets the Arabs came and transferred that knowledge to greece
Greeks had this knowledge before the Arabs.
15 years later we all got this video recommended 😂
This works because each area is equal to the squared length of each side of the triangle. Wheres the hypotenuse is the equal to root of the sum of the squares when doing a triangle, this demonstration is actually just the sum of the squares because the root is squared and is thus cancled out.