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Cool Pythagorean Theorem Demo (imgur.com)

submitted ago by Understandably3

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[–]TetraHydroFreeForAll 196 points197 points ago

I watched this at least ten times before I could turn away.

[–]doctorperv 28 points29 points ago

I keep wanting to pause it.

[–]Tendie 5 points6 points ago

Escape pauses; f5 resumes!

[–]doctorperv 0 points1 point ago

SHUT, UP!!!!!

load more comments (6 replies)

    [–]MysticKirby 41 points42 points ago

    Is there somewhere where I can find more of these math gifs? I remember seeing one about graphing tangents showing a turning circle..,

    [–]Ziaxra 111 points112 points ago

    Here is another Pythagoras Theorem gif.

    [–]maddawg579 21 points22 points ago

    I've known the Pythagorean Theorem for years, and this makes me even more confused. Granted, I never got past calculus. After 3 semesters of it with 2 different teachers, I realized it just gets too complicated for me to keep up with.

    [–]Foxtrot56 11 points12 points ago

    Likely your algebra wasn't good enough because most teachers are bad and they will pass you too easily without you learning enough algebra.

    Happened to me too.

    [–]RWE03 3 points4 points ago

    And yet many students will beg to be passed and throw a fit if they don't, even when they don't understand the content.

    The idea of "it hurting you in the long run" doesn't make sense to them. This is also why students copy homework and then are surprised and upset when they fail a test that covers said content. Not to generalize, but many teenagers lack this reasoning ability.

    [–]Foxtrot56 2 points3 points ago

    I am a veteran and I went back to school 2 years ago feeling far older than most other students. I took all the classes leading up to calculus and I get Cs in them and then I took Calc 1 and I was going to be lucky to get a C so I withdrew from it. I feel like schools should require a B or higher in the classes leading up to calculus.

    It was partly my fault but I was so use to the military lifestyle of just get things done that I didn't consider that I wasn't learning, I was just trying to accomplish tasks not learn and understand things. It is a hard habit to break and it made school really hard for me and took me at least a year to realize I was doing it and up until even now to try and fix it.

    [–]maddawg579 0 points1 point ago

    I think it was more my pre-calc class. I passed with a B in high school, but only because my teacher was very lenient. I should not have passed that class, but at 17, all I cared about was getting through.

    [–]ImmatureMaTt -1 points0 points ago

    The gif that Ziaxra posted is very complex and confusing, but the one in the OP makes the Pythagorean theorem easy to understand. If you square one side of a right angled triangle, you get a square. What the gif illustrates is that the squares of the two shorter sides equal the square of the longer.

    [–]craptastico 8 points9 points ago

    Where doesthe blue square come from? Why is that included?

    [–]YouLeDidnt 15 points16 points ago

    because unless it's an isosceles triangle, the c2 will never be exactly 4 times larger than the area of the triangle.

    [–]Rhenor 4 points5 points ago

    If it's an isoceles triangle, the Pythagoras doesn't apply (only right angled triangles).

    Edit: with the one exception of 45, 45, 90 (I am an idiot).

    [–]wellthatsjusthurtful 2 points3 points ago

    it can be both

    [–]Rhenor 0 points1 point ago

    There is one triangle which is both: (90, 45, 45) as the angles.

    [–]YouLeDidnt 1 point2 points ago

    right angled isosceles, that was what is was looking for (like a square cut through its diagonal)

    [–]mars20 6 points7 points ago

    At the beginning of the gif, the triangle is "copied" thre times to build a square where the sides have the length c. A square with length c has the area c². The blue square in the centre is only there to fill the area which was not occupied by copying the triangles.

    [–]PinballBob 0 points1 point ago

    If you choose an arbitrary right angled triangle. If we call the longest side c, b the smaller and finally a, the smallest. a<b<c.

    If you arrange the triangles such that C forms the outside of a square, since these are right angled triangle they will tessellate in such a way to leave the blue shape within the center. Note, if a=b then the the blue square disappears.

    So immediately we have the area of the square; c2. But the area of the square is also the sum of area of each triangle and the center blue square. We have are of each of the four triangles ab/2 and finally the center square (a-b)2 . Therefore;

    c2 = 4*(ab/2)+(a-b)2 = 2ab + a2 + b2 -2ab = a2 + b2

    [–]craptastico 0 points1 point ago

    Thank you. I couldn't understand how the blue square was involved and why. Your equation makes it make so much more sense. Thanks math person!

    load more comments (1 reply)

      [–]curlyben 0 points1 point ago

      http://en.wikipedia.org/wiki/File:Pythagoras-2a.gif

      I like this one a bit better.

      http://www.billthelizard.com/2009/07/six-visual-proofs_25.html http://www.math.uga.edu/~clint/2008/geomF08/addition.htm

      These are good, too.

      I taught a seminar with a bunch of these. I'll dig more up.

      [–]scrash -1 points0 points ago

      what's the area of the blue shape? pls

      [–]Gillo_ 3 points4 points ago

      The specific area of the blue shape doesn't matter. It's just used to fill everything up.

      [–]canopener 2 points3 points ago

      (b-a) squared

      [–]PalermoJohn 16 points17 points ago

      I like this one on pi:

      http://en.wikipedia.org/wiki/File:Pi-unrolled-720.gif

      Or this on trigonometry:

      http://inventwithpython.com/images/Sin_drawing_process.gif

      [–]Mayor_Goldie_Wilson 2 points3 points ago

      holy shit. That second gif. This.. this makes so much sense. My mind is actually blown. My teacher badly explained something along these lines, so I just accepted that sine values existed, but I feel like everything just FITS now.

      [–]MysticKirby 1 point2 points ago

      Thanks!

      [–]venefb 36 points37 points ago

      Thank you for calling it 'demo' and not 'proof'.

      This really makes me wanna do a fake one where the thickness of the boxes is not the same, like a 3d version of that old trick 'where is the missing square'.

      [–]PKCarwash 31 points32 points ago

      My geometry teacher did a similar demo to show us that a cone with the same base and height as a cylinder has 1/3rd the volume. Blew my 7th grade mind. Everyone in my class was convinced that you could only fit two cones in there.

      [–]JamesGold 8 points9 points ago

      That's some great teaching!

      load more comments (4 replies)

        [–]zerulia 10 points11 points ago

        Can't...stop...watching...

        I'm trying to find the video of this Indian lecturer explaining the magic behind quadratic functions using just a few boxes. As an engineering grad, nothing ever made more sense than that.

        [–]pieltd 4 points5 points ago

        this sounds interesting! please deliver.

        [–]zerulia 4 points5 points ago

        okay guys I was wrong - it wasn't about quadratic functions per se, but about the logic behind expansion of (a+b)2.

        Behold, the long-haired mathematician who could have been raised in an ashram.

        [–]Shock_Hazzard 3 points4 points ago

        /r/tipofmytongue might help.

        [–]MrKei 1 point2 points ago

        interested as well! please find it!

        [–]zerulia -1 points0 points ago

        okay guys I was wrong - it wasn't about quadratic functions per se, but about the logic behind expansion of (a+b)2.

        Behold, the long-haired mathematician who could have been raised in an ashram.

        [–]Rndom_Gy_159 1 point2 points ago

        Damn. It is so simple. It... It MUST be wrong. There is no way that that could have been explained in a min, what took me a month to understand and memorize.

        [–]TracyEid 1 point2 points ago

        Are you talking about khanacademy.org?

        [–]YouLeDidnt 7 points8 points ago

        I scrolled through all the comments, and couldn't find any source.

        Could anyone provide it please?

        [–]unlimit-ed 2 points3 points ago

        Here.

        [–]kameleon_Walrus 67 points68 points ago

        why did my teacher not have this in geometry?!?!? My life would have been so much easier

        [–]Damadawf 95 points96 points ago

        While this helps demonstrate that the maths is indeed true, it doesn't really help you learn it any better.

        [–]SubtleMockery 29 points30 points ago

        Of course it does. just memorizing "a2+b2=c2" is meaningless. This explains what and why.

        [–]matsunoki 150 points151 points ago

        it doesn't explain why at all, just shows that it's true in a more graphical way

        [–]Rawem 35 points36 points ago

        Yes, and people like me (zero mathematical insight) go like "Oooooh, so that's why!"

        Edit: grammar.

        [–]PeterPorty 14 points15 points ago

        http://britton.disted.camosun.bc.ca/Pi_unrolled.gif

        This made me go "WOAHHHHH" harder than I should've; I finally understood Pi is not some random number that works, it's a relationship between the circle's diameter and it's circumference.

        2 x Pi x r == d x Pi, and this gives the perimeter of the circle.

        Yeah, I didn't have good math teachers...

        [–]cynognathus 15 points16 points ago

        Also, sine wave.

        [–]Garrett-R 2 points3 points ago

        Damn, never knew that one before, thanks!

        [–]LarryBlueberry 1 point2 points ago

        Make it go again! Make it go again!

        [–][deleted] ago

        [deleted]

        [–]PeterPorty 0 points1 point ago

        Not from the US; but yeah, I haven't had a decent math teacher since 7th grade.

        [–]Zippy5454 1 point2 points ago

        It helps visual learners understand that it works, and the formula has graphical meaning. Now when they have to remember the formula they'll just see this demonstration of three squares and they will recall the formula.

        [–]SubtleMockery -2 points-1 points ago

        Some people don't think in math very well. What is intuitive to you may just be gibberish to someone else.

        [–]ThSGM 5 points6 points ago

        It was said:

        While this helps demonstrate that the maths is indeed true, it doesn't really help you learn it any better.

        Then you said:

        Of course it does. just memorizing "a2+b2=c2" is meaningless. This explains what and why.

        The problem with this visualization (the flowing water) is that while it is quite pretty, it doesn't lead to much in the way of mathematical intuition. The magic of Pythagoras is left as magic, with the students wondering why it happens that a2 + b2 = c2. The flowing water serves only as a memory device for the formula but not for the proof or the reason.

        On the other hand, this visualization is almost a visual proof of Pythagoras. A smart student can work out the proof just by looking at this picture.

        I think that when people here complain about this demo, they are complaining because the demo does not lead to any intuition about why a2 + b2 = c2; it simply reaffirms what we know from the formula.

        [–]shortyjacobs 4 points5 points ago

        Now that's kind of cool.

        For those trying to prove they are "smart students"...

        The area of the pink square is equal to the area of the bigger square minus the area of the four blue triangles.

        That is to say, c2 = (a+b)2 - 4*(1/2*a*b)

        If you don't remember that the area of a triangle is 1/2*a*b, you can think of the four triangles as two squares, and you get the same thing, since 4*(1/2*a*b) = 2*a*b

        So c2 = (a+b)2 - 2ab

        c2 = (a2 + b2 + 2ab) - 2ab

        c2 = a2 + b2

        [–]SubtleMockery 2 points3 points ago

        A smart student can work out the proof just by looking at this picture

        Yes. Some people learn better with visual representations. Or kinetic representations.

        Dumb people like me have trouble with representations using numbers and language. I couldn't tell you how your proof shows the theorem. I understand the concept of it, now, because I learned it years ago, but something like what you showed me wouldn't have helped.

        [–]ThSGM 2 points3 points ago

        I understand the concept of it, now, because I learned it years ago, but something like what you showed me wouldn't have helped.

        That's fine. It's not meant to be 'obvious' from the picture, and you do need to work to get from the picture to the proof. If I was teaching Pythagoras in a class, I wouldn't just put up the picture and expect the students to fill in the blanks.

        However, the point is that the water demo isn't such a great visualization of Pythagoras because it doesn't offer any deeper educational insight beyond a confirmation of the formula.

        Don't get me wrong. I love visualizations and how visualization can really help students to understand a subject. However, beyond the fact that it's 'cool', the demo is somewhat vacuous. It's akin to a mnemonic.

        I don't mean to be a downer; my original reply was meant to clarify why some people did not think that the demo was particularly great. I also think that too many of these visualizations can work in a negative sense, convincing students that maths is like magic.

        [–]debman3 0 points1 point ago

        It doesn't explain why, but it gives me a new point of view to memorize it. But seriously, who had trouble memorizing this formula? Try memorizing Bell number (actually not that bad)

        [–]SubtleMockery 0 points1 point ago

        It does explain it. That gif made perfect sense to me. The area of a2 + the area of b2 is the same as the area of c2 when taken from a right triangle.

        [–]Foxtrot56 0 points1 point ago

        This shows nothing though, why is this true? Because two boxes full of blue liquid can probably fill a third box with that same liquid? This isn't really a proof it is just a rough representation of one of the proofs and proofs aren't always the best ways to teach concepts anyways.

        Many proofs require a thorough understanding of the theorem before you can even approach the proof.

        [–]Meathe 0 points1 point ago

        I always thought this was a simple proof.

        [–]10weight 0 points1 point ago

        Couldn't agree more.

        Finally.

        I have seen the light...

        [–]Damadawf -1 points0 points ago

        I never said that having something show you an example which encourages you to understand what you've learned is pointless... but picture the following scenario:

        Teacher: "a2 + b2 = c2 . Now here's a video"

        The video shows that the area* of the two non-hypotenuse sides equals the said hypotenuse, but I don't see how that helps you "learn" it any better. In the comment I was replying to, the user implied that the video (well.. gif) would somehow magically give them genius-level maths skills.

        • Technically it is a volume of liquid that inhabits a 3-dimensional plane. Obviously this doesn't affect the outcome, but Pythagoras theorem in it's most simplistic notation is concerned with 2 dimensions, not 3.

        [–]JamesGold 19 points20 points ago

        Some people learn better with visual aids. I think it's just cool to see confirmation of mathematical formulas in the real world.

        Technically it is a volume of liquid that inhabits a 3-dimensional plane. Obviously this doesn't affect the outcome, but Pythagoras theorem in it's most simplistic notation is concerned with 2 dimensions, not 3.

        We're still using the regular old Pythagorean Theorem. As you noted, in the demonstration the squares have a third dimension: depth. But when all the squares have the same depth, d, it cancels out to give you the plain old Pythagorean Theorem.

        da2 + db2 = dc2

        a2 + b2 = c2

        [–]canopener 0 points1 point ago

        Then for this to be a demo, you'd have to be dividing out the d.

        This demo has no more probative value than showing that in a 3-4-5 right triangle, 25 squares can make the square on the hypotenuse or on the other 2 sides. The fact that it's water doesn't add anything. And that's only one right triangle: the theorem applies to any right triangle. It's anti-helpful, because you shouldn't be convinced by it.

        [–]Mx7f -1 points0 points ago

        It doesn't have to be a proof to be useful. Some people have trouble remembering what the pythagorean theorem states, never mind how to prove it. This is a helpful visual aid in helping some such people remember what the pythagorean theorem is.

        And yes, for some people, remembering this demonstration is orders of magnitude easier than remembering "the square of the hypotenuse is the sum of the squares of the other two sides", or "a2 + b2 = c2 , where c is the hypotenuse".

        Edit: formatting.

        [–]rasatm 0 points1 point ago

        Brains, how do they work? And why is everyone's not connected the exact same way?

        [–]canopener 0 points1 point ago

        This thread is full of people saying that this demo shows why the theorem is true. So the fact that you can't change the dimensions of the triangle makes it misleading. I don't like it.

        I used to teach math and one day I was in a workshop where he leader asked us to devise a way to demonstrate a proof of the Pythagorean theorem without using words. This is not so hard: there are many demos that work strictly graphically. But what I saw when he showed his own version was that he thought that a demonstration of the equality of areas for a given triangle was a proof even if it could not be generalized to other triangles. I pointed this out in a break, and he was very annoyed, because he was a teacher after all, and he didn't know that he didn't know what a proof was. So you really have to be careful about these things. The water demo would work for other triangles, but there's no way you could know that. And to me, that's a fatal flaw. But if it helps people to understand what it means for areas to be equal, who am I to argue.

        [–]Mx7f 0 points1 point ago

        I agree with you on pretty much all counts.

        [–]OMGorilla 8 points9 points ago

        I think the simple fact of illustrating the theorem with squares juxtaposed to the sides makes it more palatable for some.

        Before watching this gif I never gave much credence to the term "squared." Now it visually makes sense. I never struggled with phthagoras' theorem; but this aptly translates an abstract idea into a concrete one.

        [–]Ender2309 8 points9 points ago

        just since you seem like a semantics guy, when thickness is constant across the boundary, you effectively have only two dimensions to deal with. so there's that.

        [–]eyereport 0 points1 point ago

        Technically it is a volume of liquid that inhabits a 3-dimensional plane. Obviously this doesn't affect the outcome, but Pythagoras theorem in it's most simplistic notation is concerned with 2 dimensions, not 3.

        So did you forget that the GIF uses volumes of liquid inhabiting a 3-dimensional plane? Since the GIF has no sound (obviously), we don't know what the presenter was saying to narrate the demonstration. It's pretty likely, however, that they were explaining the same things about the formula that you're griping about.

        And why are you so concerned with "proofs?" When I was a student, I was TERRIBLE at most trigonometry and calculus because of the heavy reliance on proofs, but I excelled at geometry because I was able to visualize planes, slices, folding, etc. Sometimes, I could even do decent at trig and calc because the problems had a an easily-visualized real-world like rate of acceleration. But if you plunk me down in front of a proof of that same concept, I'm just going to zone out. (I think I may have mild dyscalculia, because numbers tend to jumble together in my head and jam up my ability to process thoughts.)

        Luckily, I don't work in a math-heavy field, so I don't really need to know the proofs. I get that they're important to prove the theories of why these things work, but they're terrible as teaching tools and not important at all for everyday use by non-mathematicians.

        [–]Damadawf 0 points1 point ago

        Dude... I do a heavily maths based study curriculum and the numbers jumble together in my head and everyone elses. That's why maths is so unpopular!

        [–]canopener -1 points0 points ago

        I disagree: the theorem applies to any right triangle, not just one with these proportions. And this isn't a proof!

        [–]SubtleMockery 0 points1 point ago

        The visual display would work with any right triangle though.

        Also, I never said it was a proof.

        [–]canopener 0 points1 point ago

        The display shows only one triangle and provides no reason to believe it would work with any other. So it fails on the what, because it fails to show generality. If there were infinitely many displays, that'd be another story.

        As for the why-that's what a proof is! There's no understanding why a mathematical theorem is except for understanding a proof of it.

        [–]canhazhotness 0 points1 point ago

        But it's not meaningless! That is an essential formula that can be transformed and modified to fit whatever trigonometric need you may have! It's wonderful!

        Edit: I misspoke, not necessarily ANY trigonometric need. You may have to venture out into the Law of Cosines which has part of the Pythagorean theorem in it (c2 = a2 + b2 - 2abCosØ), or into the Pythagorean identities, such as sin2 Ø+cos2 Ø=1

        [–]Eraser1024 -1 points0 points ago

        It helps to memorize the theorem.

        [–]KISSOLOGY 14 points15 points ago

        You needed help memorizing that?

        [–]inoffensive1 6 points7 points ago

        It helps to understand the theorem. Rote memorization of eight characters won't accomplish anything. A demonstration like this can actually help people understand that the square of one side plus the square of the other side equals the square of the hypotenuse. That understanding is a far more powerful intellectual tool than memorization.

        [–]KISSOLOGY 0 points1 point ago

        I agree. Read the comment above mine. It says "It helps to memorize" Its literally... literally as easy as A B C to memorize.

        [–]Eraser1024 0 points1 point ago

        When I was 10? Yes.

        [–]TheSecretMe -1 points0 points ago

        It does, it visualizes the concept, making it easier to understand. Wrapping your head around it is the most difficult part of learning.

        [–]GuardianReflex 3 points4 points ago

        If only everyone could be taught science and math, in person, by Bill Nye using awesome contraptions and devices like this. That's a world I want to live in.

        [–]Corndawgz 1 point2 points ago

        Or videos with live demos that you can rewind and play at your own discretion, like khan academy.

        [–]colinsteadman 0 points1 point ago

        Why didn't my teacher tell me you could use triangles to measure the distance to stars. They could have even have substituted cm's for light years. I'd have been mad for that instead of completely confused disinterested.

        [–]PalermoJohn 0 points1 point ago

        Real-world application would be a good idea for all of the stuff you learn about in math class. Derivations? I guess most people remember that they were tedious and lame, but not so many could tell you what they are actually used for.

        [–]eyereport 0 points1 point ago

        Derivations? That's...like...finding water underground with wires, right?

        [–]PalermoJohn 0 points1 point ago

        Sorry, differentiations.

        http://en.wikipedia.org/wiki/Differential_calculus

        [–]TheFreeloader -1 points0 points ago

        I think there are easier visual proofs of the Pythagorean theorem (not requiring several of hours of woodwork). Like this one, or this one (which is essentially just the first one in .gif format).

        [–]canopener 0 points1 point ago

        That video is beautiful. And unlike the water thing, it's actually a proof.

        [–]PalermoJohn 1 point2 points ago

        I find this much harder to grasp (harder, not hard). The OP one is immediately clear to me, this one I need to watch a couple times to see what is going on.

        [–]eyereport 0 points1 point ago

        Definitely. I think people are getting too caught up in the idea of "proofs" instead of just "proving" the idea in a simple way. I've never had any trouble with the formula in question, but it the original GIF made it immediately clear what the formula actually does and shows.

        [–]xenoph2 -1 points0 points ago

        If you had actual problems with understanding this, it might wasn't the teacher's fault after all...

        [–]iHeartCoolStuff 6 points7 points ago

        So uh, whats goin on here? Are those perfect squares?

        Can someone give a run down of the math behind this.

        [–]Ivence 19 points20 points ago

        A2 + B2 = C2 is the pythagorean theorem.

        What this does is at the start it has 2 squares with sides that are the length of the 2 shorter sides (side A and side B) of the triangle (each square has the volume of the length of that side squared), when it's flipped the liquid in those 2 smaller squares pours into and fills exactly the larger square attached to the hypotenuse (side C).

        Basically its just a very clear demonstration that A2 + B2 does most certainly equal C2 without using math.

        [–]iHeartCoolStuff 0 points1 point ago

        Awesome, exactly what I needed. Thanks

        [–]PalermoJohn 1 point2 points ago

        May I ask how old you are and how long ago you took math in school?

        [–]iHeartCoolStuff 1 point2 points ago

        1. Been a while since I mathed

        [–]huytn89 2 points3 points ago

        What the hell is a perfect square?

        [–]iGotChubs4You 3 points4 points ago

        He's thinking of numbers.

        A perfect square is a square that is the product of an integer with itself.

        9 is a perfect square. Why? Because 9 is the product of the integer 3 times itself. On the other hand, 1/4 is not because it is the product of 1/2 times itself, 1/2 being a rational and not an integer.

        [–]Ender2309 1 point2 points ago

        or maybe just rectangles. would somebody who understands rationals and integers need a rundown on the pythagorean theorem?

        [–]iGotChubs4You 0 points1 point ago

        What do you mean? Someone can understand rationals and integers without having understanding of pythagoreans theorem.

        [–]Ender2309 0 points1 point ago

        i mean yes, but the likelihood is pretty nil. more likely he meant "are those boxes perfectly square in shape or are they rectangles?" cause the small ones, they look like rectangles.

        [–]iGotChubs4You 0 points1 point ago

        Oh yeah you might correct.

        [–]iHeartCoolStuff 0 points1 point ago

        Touche

        [–]quappucinno 2 points3 points ago

        Is the Pythagorean theorem really that hard that it needs a visual?

        [–]iGotChubs4You 23 points24 points ago

        There is a difference between being told "a2 + b2 = c2" and regurgitating that info and seeing a visual proof of it and actually understanding why it is true.

        [–]OldLeopardSkin 2 points3 points ago

        This isn't a proof. It's a demonstration for a specific triangle. I can't imagine it helping you understand why it is true.

        [–]Tomus 11 points12 points ago

        This would work for any right angled triangle...

        [–]alofons 14 points15 points ago

        His point is that you can't demonstrate the theorem in general by just using examples, because there's an infinite number of right angled triangles, and a finite number of examples you can build in your life.

        "It works for this specific triangle, therefore it works for all right angled triangles" isn't a valid proof of a mathematical theorem, because you're not reasoning why you can go from a finite number of examples to an infinite number of right-angled triangles.

        [–]PalermoJohn 2 points3 points ago

        It's not proof but it helps to give meaning to the jumble of numbers and symbols that some perceive "a2 + b2 = c2" to be.

        [–]canopener 1 point2 points ago

        Quite right.

        [–]iGotChubs4You 0 points1 point ago

        Not a proof in this strictest sense, know, but if you assume the squares are accurately measured and that the water is correctly displaced then yes, it certainly helps one understand it.

        [–]ps7825 4 points5 points ago

        It's a very easy theorem that makes perfect sense without visual, but visual is just cool :)

        [–]JamesGold 1 point2 points ago

        It's not that the Pythagorean Theorem is difficult to understand; it's that it's not immediately obvious. There's a big difference between the two.

        [–]spidy_mds 1 point2 points ago

        Finally, my proudest boner !

        [–]Aerik 0 points1 point ago

        That's nothing. That type of math still goes very far for geometry. Watch videos by UNSW professor wildberger about rational trigonometry and hyperbolic geometry.

        [–]taurentino 0 points1 point ago

        Sauce?

        [–]rljacobson 1 point2 points ago

        http://www.youtube.com/watch?v=CAkMUdeB06o

        [–]vorty59 -1 points0 points ago

        Still don't get it..

        [–]Carps182 0 points1 point ago

        I hope I can remember this to use it as my future kids' science project.

        [–]TriumphantDefeat 1 point2 points ago

        Such a simple, yet completely didactic example. If you do not understand it after seeing this example, you might want to register for a remedial elementary class.

        [–]GetItTogether 0 points1 point ago

        I know a lot of people who would have been really happy to have this during geometry class.

        [–]scorpion990 0 points1 point ago

        I would make the thicknesses different to "prove" the theorem wrong. And then I would watch a bunch of 12 year olds freaking out. Muhahaha

        [–]MasterNyx 0 points1 point ago

        When I see these kinds of demonstrations or diagrams I think of people like Pythagoras, Liebnitz, and Newton and wonder what it must have been like to see numbers like they did.

        [–]Helenius 0 points1 point ago

        How do I know they aren't cheating?

        [–]notalakeitsanocean 0 points1 point ago

        my grade ten socials teacher would sing us a song every week until it was stuck in our head. he said it would be useful for our next year of math. he would sing "the squaaare of the hy-po-tenuse, of a riiiight an-gle triangle, is equal toooo the sum-of-the-squares of the two a-djacent sides!"

        [–]Mr_Ected 0 points1 point ago

        That's what I don't like about many math teachers. They don't really explain WHY, they just come up with cute songs, rhymes, etc that explain how. Once you understand why then you don't have to memorize stupid shit because it just makes sense.

        [–]AquaAvenger 0 points1 point ago

        that's pretty late for that

        [–]iJustmadethis2upvote -1 points0 points ago

        I don't understand what's so hard to understand about this theorem and why people's minds are blown....

        [–]AquaAvenger -1 points0 points ago

        I think you're trying to connect two concepts that no one else was trying to connect.

        This demo being cool is unrelated to anyone being confused or not by the theorem.

        [–]iJustmadethis2upvote 0 points1 point ago

        I think the reason people think it's cool is because it helps them understand it. I don't imagine anyone thinking it's cool because of the blue water.

        [–]new_to_the_game 0 points1 point ago

        I have to say...it's the blue water

        [–]Mr_Ected 2 points3 points ago

        Because many of us are retarded with maths, and don't really conceptualize things like "squaring". Some people don't really think of squaring as a square, just some abstract idea that exists in maths because magic. To actually see squares helps conceptualize the idea for those of us who had really shitty math teachers.

        [–]iJustmadethis2upvote 0 points1 point ago

        Thanks.

        [–]chreez 0 points1 point ago

        It took me too long to get this. I am losin touch with my math metacolorians

        [–]platypusmusic 0 points1 point ago

        Go home Pythagorean Theorem you're drunk

        [–]splourde 0 points1 point ago

        I hate math and this is awesome.

        [–]XenomorphSB 0 points1 point ago

        http://imgur.com/1iLtF

        [–]slickboarder89 0 points1 point ago

        I fucking love math.

        [–]TheOldBean -2 points-1 points ago

        I appreciate this is a nice way to show it to kids and stuff but it doesn't really show anything if you think about it, the two squares of water on a and b sides could be any size and this demonstration wouldn't work... if you understand what i'm saying?>....

        [–][deleted] 1 point2 points ago

        No, the squares are exactly the size of the side of the triangle. That's the point. And it would work with any right triangle of any size.

        [–]TheOldBean 0 points1 point ago

        No, the a and b squares could be a different depth or length and the example would not work.

        Edit for clarity: They would still be attached to the triangle, with one length being the same but they could hold a much larger volume of water than the c side square meaning the demonstration would not work.

        [–]mafaa 1 point2 points ago

        First of all, if they are different lengths then they are not squares so of course the theorem doesn't work, you made a model of ad+be =c2 not a2 + b2 = c2. Also the theorem is just for two dimensions, obviously different depths make the squares potentially hold as little or as much water as you want.

        [–][deleted] 0 points1 point ago

        They'd be rectangles of they were different lengths, not squares. And the depth always assumes it's the same depth as the triangle.

        [–]mafaa 0 points1 point ago

        I'm either misunderstanding what you are saying or you do not correctly understand the theorem. If a and b are squares formed by side a and b, the water contained (or the area) of the two squares combined is always going to be the same as the area of square formed by side c (assuming standard nomenclature for the sides and the triangle is of a valid type etc)

        [–]bo87 -1 points0 points ago

        My pedantic nature makes me annoyed that she isn't holding it straight.

        [–]ONZERHYS 0 points1 point ago

        OPP 2 + ADJ 2 = HYP 2

        That is probably the easiest thing i did all year.

        [–]QuiteBoringName 0 points1 point ago

        What's the benefit of naming the sides in that? I just remember that the two smaller sides add together to make the bigger one.

        [–]ONZERHYS 0 points1 point ago

        The side closest to the angle you are working with is called the adjacent side and the other one is called the opposite. The hypotenuse is always the larger side. There is no benefit in Pythagorean Theorem but it is impossible to do trigonometry without knowing the sides.

        [–]QuiteBoringName 0 points1 point ago

        Oh yes, I know the names, I was just confused as to why it was overcomplicated as you only use the names when working with angles (bar the hypotenuse).

        [–]ONZERHYS 0 points1 point ago

        Well i guess you don't really need to for Pythagorean, but you may as well to get it ingrained and make other parts of math that little bit easier.

        [–]SuperTurtle -2 points-1 points ago

        Why can't real math be this cool?

        [–]bigjimmyjam -1 points0 points ago

        And why is this cool?

        [–]dafuqdidIwrite -4 points-3 points ago

        That's the way Mathematics should be taught... not cramming up formulae!

        [–]irreverency 0 points1 point ago

        HEY! DO YOU KNOW WHO WROTE THIS?! A PHONY! A GREAT BIG PHONY!

        [–]dafuqdidIwrite 0 points1 point ago

        Well...

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