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Cool Pythagorean Theorem Demo [x-post from r/gifs] (i.imgur.com)

submitted ago by b3n

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[–]voteforlee 103 points104 points ago

I showed this to my students this year. Its called the water proof

[–]Deltaway 44 points45 points ago

You can create an anti-proof by putting water in one of the small tanks and ethanol in the other. They don't mix additively, so the mixture won't fill up the big tank!

[–]tripzilch 26 points27 points ago

ha! or you know, make the squares different thickness.

[–]IamaRead 5 points6 points ago

Then you turn it around again and...?

[–]Deltaway 1 point2 points ago

Magic!

[–]scottfarrar 2 points3 points ago

haha thats great

[–]CaressWithAChainsaw 45 points46 points ago

Unfortunately, unlike the geometric proofs by rearrangements, this method only "proves" the theorem for the specific dimensions of the 3 tanks, and not for all such right-angle triangular tanks. Someone please tell me if you think that this can be generalised to the actual theorem though.

[–]squakmix 2 points3 points ago

It seems as if this would work for any three tanks with the same depth (and of course sides that are the length of each component of the triangle).

[–]daroons 1 point2 points ago

Well yeah of course, based on the Pythagorean Theorem. But he's just asking if this demonstration on it's own is enough to prove the general case.

Which I would have to say no, a single example is not enough to prove the general case.

[–]mangodrunk -2 points-1 points ago

Does it really prove anything? The largest tank looks to be longer than the smallest tank.

[–]sakattack 31 points32 points ago

It's simply a visualization of the general theorem. No, it doesn't explicitly prove it, but it shows kids in a very easy way that it's true.

[–]CaressWithAChainsaw 1 point2 points ago

Sorry, I'm not quite sure what you mean.

[–]mangodrunk 1 point2 points ago

I guess my point was that it's hard to tell if they're squares.

[–]CaressWithAChainsaw 13 points14 points ago

Well since the volume just about fills up correctly, if at least two of them are squares then the second one must also be a square.

[–]daroons 1 point2 points ago

Unless they have different thicknesses... but yeah you're right.

[–]IamaRead 0 points1 point ago

You could just measure (which would be necessary anyhow).

[–]xanduba 29 points30 points ago

wouldn't it make them confused about the difference between area and volume?

as a math tutor, I like to use paper to demonstrate area properties, and liquid for volume properties

[–]TheRainbowSheep 27 points28 points ago

If you just state that one dimension (depth) is constant at every single point, it should be fine ;)

[–]xanduba 24 points25 points ago

yeah, but Idk if people learning pythagorean theorem would understand and be confortable with this kind of information

[–]TheRainbowSheep 3 points4 points ago

True enough ;)

[–]onipos 20 points21 points ago

why do you keep winking?

[–]TheRainbowSheep 12 points13 points ago

I'm not winking. I have serious mental disease that makes me think i have to blink with my right eye every time i post on reddit ;)

[–]therndoby 2 points3 points ago

That sounds awful. How is your day going?

[–]TheRainbowSheep 0 points1 point ago

You know those days when life gives you lemons, and as you try to make lemonade of them, some of the juice gets in your eye? One of those days ;)

[–]iGotChubs4You 6 points7 points ago

He is a rainbow sheep for fuck suck

[–]shillbert 4 points5 points ago

Fuck suck? How exactly does one suck a fuck?

[–]RompeElAlba 2 points3 points ago

Was that a reference to Donnie Darko or just a coincidence?

[–]shillbert 0 points1 point ago

I’ve been seeing stuff. Like, a lot of really messed up stuff. And there are chapters in that book that describe the stuff I’ve been seeing. And it can’t just be a coincidence.

[–]iGotChubs4You 0 points1 point ago

Sake.

[–]thang1thang2 0 points1 point ago

Carefully.

[–]not_a_troll_for_real 1 point2 points ago

*comfortable

[–]xanduba 1 point2 points ago

thank you

[–]Techrocket9 4 points5 points ago

It's the same reason you can use surface integrals to find area of arbitrary surfaces in 3 space by using the scalar field f(x,y,z) = 1

[–]tripzilch 27 points28 points ago

I keep telling that to the kids, but they just look at me funny?

[–]Bromskloss 13 points14 points ago

Is this a question!

[–]tehclanijoski 1 point2 points ago

No?

[–]sakattack 2 points3 points ago

Yeah, you can obviously do it very easily mathematically, but we are talking about a result that is often taught to middle schoolers. You won't even find a high school class that covers multiple integration in most places.

[–]Techrocket9 4 points5 points ago

I think it is a sufficiently subtle detail to fly over the heads of middle schoolers. They will not be thinking in 3D for this model; they will load a much simpler 2D fluid model that explains the demonstration quite well.

[–]sakattack 2 points3 points ago

What? You were talking about surface integrals in multiple integration, now I have no idea what you're trying to say.

[–]Techrocket9 1 point2 points ago

Apologies for the ambiguity. I was referring to the issue raised further up the thread, the issue that the demonstration of the Pythagorean Theorem with liquid would confuse its target audience because the containers have depth, and the problem involves volumes.

My point is that middle and high schoolers will miss this nuance and see it as a 2D problem, which is the desired effect.

[–]IamaRead 0 points1 point ago

I think the volume in this case is quite nice, you could also use very little balls to show it. Kids are quite good at understanding how much fits into a thing and most so called geometric proofs are asuming missing some bits (like rotation symmetry).

[–]zhecks 11 points12 points ago

This is technically a special-case proof, for special-case whatever that triangle is. It's a bad idea to teach that if something works in one case, that it works in all cases.

However, as a demonstration of what the Pythagorean Theorem means, this is great. It introduces the idea in a concrete way.

[–]Bromskloss 4 points5 points ago

Just pull this machine out when the kids say "Teacher! I understand for all other cases, but does the Pythagorean theorem really hold when the sides are 3, 4 and 5, respectively?".

(It's really a demonstration, rather than a proof. It's there to be fun, which is the point of studying mathematics in the first place, I think.)

[–]Furrier 8 points9 points ago

/r/mathpics

[–]_delirium 4 points5 points ago

Nice! It's in a way a version of the classic geometric proofs by rearrangement, except instead of cutting up the squares into discrete subparts and rearranging them, the squares are liquified and allowed to rearrange themselves via fluid flow.

[–]Ph0X 22 points23 points ago

Mods are sleeping, let's post GIFs for the Pythagorean Theorem. This subreddit really needs an overhaul.

[–]mechman39 11 points12 points ago

What's wrong with the gif? Although not a proof in itself, it's a great tool for visualization.

[–]Ph0X 6 points7 points ago

Nothing wrong with the gif per-se, it's just that I've seen so many Pytharoean proof gifs in the years.

http://www.reddit.com/r/math/comments/fr0jq/very_easy_funny_way_to_prove_pythagorean_theorem/

http://www.reddit.com/r/math/comments/tzk5x/thought_id_make_a_gif_proof_of_the_pythagorean/

And quite a few of trigonometric functions too

http://www.reddit.com/r/math/comments/g15ei/tan_demystified_gif/

http://www.reddit.com/r/math/comments/cls4l/in_case_you_werent_sure_cosine_is_definitely_the/

Not that these aren't neat, the argument here is more along the lines of, should we allow cool little visualizations in this subreddit. I personally think these belong more in either /r/mathpics or /r/CasualMath , but that's my own personal opinion.

[–]shmortisborg 15 points16 points ago

Nothing wrong with math being more approachable to the average person, whom is much more likely to visit /r/math and not something called /r/mapics or /r/casualmath. If anything, it would make more sense to have a subreddit called /r/mathsnob that you could go to.

As far as reposts on reddit in general, Ive never understood why people get so worked up about it, most times its brought up Ive never seen the content before, and Im sure Im not in the minority. Its completely normal for things to be reposted on the friggin internet, and I wouldnt want it any other way. If you are browsing online for so long that you see everything the first time, well thats your problem, very easy to deal with.

[–]Ph0X 4 points5 points ago

First off, I didn't say anything about reposts, that's an entirely other issue.

As for your first point, it has nothing to do with being a snob, it's about knowing what you want your subreddit to be. If the people who created this subreddit truly want it to be a place where you post GIFs, then sure, it's not my subreddit, I'm not going to complain.

To me, a perfect example is /r/Science. It could've very easily become a subreddit where people post memes and gifs about science, but the founders decided that they wanted a serious subreddit about scientific discoveries, and that's what they turned it into.

I'm not saying that one is better than the other, that's entirely subjective, what I'm saying is, they should make it clear and stick to it. If I know that this subreddit is going to be about content X, and I don't like content X, and I'll just leave. As simple as that.

[–]iSecks 1 point2 points ago

Well this clearly isn't a meme, but is it not math? Because to me, this looks like math. This seems like the perfect subreddit for this type of thing. Now if someone posts a meme then that's a completely different story.

It seems to me like you're getting upset because people are helping people visualize math that it's you with the problem. As you said, gifs are posted here quite a bit, some reposts some not. If the mods had a problem with it they would have said something.

[–]Ph0X 6 points7 points ago

http://www.reddit.com/r/math/comments/s3ejb/a_disturbing_trend_this_is_not_rcasualmath/c4athn4

They have said things, they've never acted on them though. Again, for the third time, all I'm asking is for them to make it clear what they want this sub to be like, and moderate it accordingly. Is that too much to ask?

[–]TadMC 0 points1 point ago

I agree with both of you. I think that there should be some balance.

[–]bradygilg 1 point2 points ago

It's kind of sad that the simple gifs get 20x the upvotes of actual math is the only thing.

[–]UOLZEMOS 5 points6 points ago

I like this!

[–]Soronume 1 point2 points ago

I want one.

[–]UOLZEMOS 0 points1 point ago

Dude, I may be a little drunk... but I would buy/make one of those, and mount it to my wall, and spin it with multicolor lights on it... fuck yea.

[–]MrBarry 0 points1 point ago

If someone used this to demonstrate a concept to me that I didn't already know was true, I'd say it stinks to high heaven. There could easily be minute differences in volume that could make this appear to work. I can't tell with my naked eye whether the bottom square is exactly the sum of the top two, neither can I tell whether any of the squares are completely full of liquid. There is also the possibility of trickery if one installs reservoirs behind the triangle that hold any extra liquid necessary for this to work.

[–]WDC312 5 points6 points ago

yeah, it's not supposed to be a rigorous proof obviously, it's supposed to be a cool demonstration of the already proven fact.

[–]IamaRead 0 points1 point ago

Tell me about a proof of the pythagorean theorem which works even for sceptics.

[–]MrBarry 0 points1 point ago

If it is a proof, it is immune to skepticism. This gif is similar to "proof by picture" which is no proof at all.

[–]choc_is_back 0 points1 point ago

Aaaah, 'proof by picture' typically means that a rigorous proof will be a bitch to arrive at :)

(Pytaghoras being an obvious exception)

[–]MrBarry 1 point2 points ago

I've seen it used a lot in graph theory, but even there you have to be very careful what exactly you say that picture proves. In this picture, the tanks could not be square; they could be different widths; the plastic could be different thickness; they could not be squares, either by length or by angle; the fluid could be ever so slightly not filling the whole of one of the squares; the triangle itself could not be right. Actually, this would be a compelling demonstration of why proof by picture is usually invalid if they had a second machine which looked identical but produced a different result.

[–]IamaRead -1 points0 points ago

Most proofs contain axioms and often other stuff which is not mentioned. Anyhow please show me a proof which I can accept for the Pythagorean Theorem.

[–]alpha_omicron 1 point2 points ago

Are you just trying to make a point about always being able to deny prior assumptions (like axioms or previously proved theorems) or do you actually want a proof of the Pythagorean theorem? If the latter, I'm sure Wikipedia or MathWorld will serve.

[–]IamaRead -2 points-1 points ago

My point is that no proof you can show in school really proofs a thing. You are ignoring much and especially in geometry the proofs are based on intuition.

For the pythagorean theroem you have to accept that rotation does not change your object, that sacling does not change the area effects, that rearanging parts does not change a thing (which it can be, if done in very small spaces).

To criticise that it is a volume based proof is to criticise it is a proof based on objects in the real world instead of abstract rooms.

[–]MrBarry 0 points1 point ago

This is an example of the sort of shenanigans that can go on when using proof by picture.

[–]MrBarry 0 points1 point ago

Take your pick.

[–]secretly_rational 0 points1 point ago

This demonstration (possibly a simmilar one, also using liquids) can be found at Cite des Sciences in Paris.

[–]two_if_by_sea 0 points1 point ago

This gif is great but it starts too quickly. We need half a second at the beginning to take in the "before" scenario.

[–]bigfig 1 point2 points ago

Bear in mind, its an entertaining illustration and not anything like a proof.

[–]Muirbequ 0 points1 point ago

Isn't the smallest side supposed to be a square as well? It looks like a rectangle.

[–]Marcassin 10 points11 points ago

I think that's just the shadow from the lighting.

[–]redditmeupbaby 0 points1 point ago

Technically that's volume, not area.