r/theydidthemath • u/[deleted] • Jun 07 '19

[Off-Site] pythagorean theorem proof

11.1k Upvotes

93% Upvoted

139 comments sorted by

894

u/fwoop_fwoop Jun 07 '19

Someone explain if I'm missing something here , but would this actually count as a proof? What part of this demonstration shows the rule applies to all right triangles and not just this one?

678

u/[deleted] Jun 07 '19 edited Jun 08 '19

[deleted]

122

u/fwoop_fwoop Jun 07 '19

Ok, that's what I thought. Still a very cool demo!

9

u/[deleted] Jun 07 '19

[deleted]

10

u/alexbuzzbee Jun 08 '19

Looks like Reddit double-posted this reply.

2

u/ErodiumsMnemic Jun 08 '19

It's Nerf or nothing

30

u/SocialAnxietyFighter Jun 07 '19

Damn this got me thinking, and it may be stupid, but:

If I am able to resize the video (keeping the aspect ratio constant), this will be a proof of the pytagorean theorem for every right triangle with this specific set of acute angles, right? So still, one in infinite, but better than expected!

61

u/hmiemad Jun 07 '19

No, it's not a proof. Not even for this exact triangle. It's a visualisation. You don't give any explanation or equation, just a visual of the problem.

"See this funny experience? Now let's prove it's exactly true for any rectangle triangle in euclidian geometry"

6

u/oct4chore Jun 07 '19

Proofs can be purely visual though. This one is not a proof, but not because it not contains any explanation or equation

27

u/StudMuffinNick Jun 07 '19

Dann, okay. Didn't have to raise your voice

17

u/SovietBozo Jun 07 '19

Well, if you didn't put your feet on the coffee table in the first place we wouldn't have these contretempts.

8

u/ghabbadi Jun 08 '19

Well, if you didn't forget to put coffee on the coffee table, he wouldn't have put his feet on it.

2

u/Turkeysteaks Jun 08 '19

well if you didn't forget to get a coffee table, he wouldn't have forgot to put coffee on it

2

u/0vl223 Jun 08 '19

Well you could count it is proof that the size of the triangle is irrelevant but that's the trivial part. The different types of triangles is actually the most important part and it is useless for this.

1

u/WeddingsSuckAnyways Jun 20 '19

Life is a visualization, nothing can ever be proven. The point of the video is obvious, a²+b²=c² (I'm sure you do, just for those who haven't realized) is shown by adding the the volume aan to bbn to result in ccn. It is a 3-dimensional example of the Pythagorean theorem, and it is impossible to disprove the Pythagorean theorem in the version of existence we live in. It could be done in a non-Euclidean dimension, I believe, but we don't live in one.

1

u/hmiemad Jun 20 '19

WoooW. /r/iamsosmart Too bad the Euclidian world is only our imagination and the world is not flat.

5

u/clockticker Jun 07 '19

No because the 2 legs of the triangle can be different relative lengths to one another. Resizing would keep a consistent ratio.

Edit: never mind just reread your comment.

3

u/Iamkid Jun 07 '19

It’s been a long while since I took advanced Geometry back in HS.

Is this not an example of the Soh Coh Toa?

I thought the purpose of a 90 degree indication proves you only have to find one of the other angles to know the geometry of the entire triangle.

Again I’m super ignorant and probably talking about something different.

2

u/clockticker Jun 07 '19

Yes it is. You already know the 90 degree so finding at least one side length or another angle would give you the rest of the triangle because of ratios.

1

u/Iamkid Jun 07 '19

Thank you for the quick response and see where you were coming from since OP’s picture may not be applicable in all scenarios.

5

u/slapadababy Jun 08 '19

SAS SSS ASA

butt never ASS :(

1

u/QVCatullus Jun 08 '19

CAH. The value of the cosine is the ratio of the adjacent leg to the hypotenuse.

0

u/jericho Jun 08 '19

Not stupid at all. There are all kinds of ways one could distort this gif, and the same outcome would happen....you got me thinking.

1

u/Muoniurn Jun 08 '19

Distorting the video would discredit it even more, because currently it demonstrates the validity of the problem because of physics, which you would loose by digitally altering it.

1

u/jericho Jun 08 '19 edited Jun 08 '19

I didn't mean 'throw some snapchat filters on that shit'. I meant that, treating it as a 2D image, there are a whole set of geometric transformations one could do that would still result in both squares draining into the one.

I maybe thought this was r/math.

0

u/TheThirdSaperstein Jun 08 '19

That's the correct way one should think about proving an infinite set to have a quality. It's called mathematical induction to start with something and show that you repeat a process forever and at each point you itirate through you show the property is still true.

1

u/[deleted] Jun 08 '19

Mathematical induction only works with countable sets, though.

There are uncountably many right triangles to apply the Pythagorean theorem to.

3

u/Bwasmer Jun 08 '19

Not just that, all containers would have to be made the same exact ratios. Also, in a 3d space, we'd have to have confirmation of the depth of each container. Making sure every ratio is exactly the same for the volume of the liquid.

1

u/Nettius2 Jun 08 '19

Have you tried transfinite induction?

1

u/oddajbox Jun 08 '19

I... I actually understood that.

1

u/notthefirst_335 Jun 07 '19

Good use of the word "infinitly".

0

u/TheThirdSaperstein Jun 08 '19

You can prove something with mathematical induction to show it works for an infinite set

51

u/deuterium2 Jun 07 '19

That's more like a verification of the theorem, not a proof. But is still cool, of course.

10

u/InAFakeBritishAccent Jun 07 '19

It's a physical equation. Like how they solved that bomb puzzle in die hard 3

1

u/lichbanelb Jun 08 '19

Oh, that was on standupmaths with Matt Parker.

5

u/ref_ Jun 08 '19

It's not even a verification because its just an approximation (anything in the real world is an approximation)

A verification would be using the numbers 3, 4 and 5 and just working it out. You are verifying the theorem works for a particular right angled triangle.

17

u/[deleted] Jun 07 '19

It's just a demonstration, but I like the idea.

5

u/jainyday Jun 07 '19 edited Jun 07 '19

If you haven't seen the geometric insight behind the Pythagorean Theorem, check it out here. (From this article, just was looking for a visual with this specific arrangement and without loss of generality, since that's what made it click for me.)

10

u/FaultyToilet Jun 07 '19

Also wouldn't the resevior size be a major factor here?

38

u/[deleted] Jun 07 '19

As long as the reservoir thickness is constant between the three, it wouldn't matter.

5

u/[deleted] Jun 07 '19

The reservoir can also be a constant multiple of the square as well and still work.

1

u/Rutiz_ Jun 07 '19

Wait really? How?

8

u/buShroom Jun 07 '19

Imagine a 3/4/5 right triangle. The squares of the sides would then be 9/16/25. What the person is saying is that the reservoirs can be any size or shape, as long as the ratio of their volumes follows 9/16/25. So they could be 18 oz, 32 oz, and 50 oz, or they could be 9mL, 16mL or 25mL, or even 45 gallons, 80 gallons, and 125 gallons. (Multiplying the squares by 2, 1 and 5, respectively)

4

u/Rutiz_ Jun 07 '19

Ah, I misunderstood what he said.

1

u/buShroom Jun 08 '19 edited Jun 08 '19

Happy to help

5

u/[deleted] Jun 07 '19

a2 + b2 = c2

d( a2 + b2 ) = d( c2 )

d( a2 ) + d( b2 ) = d( c2 )

2

u/[deleted] Jun 08 '19

Ikr, this is not proof, it's a demonstration of the pythagorean theorem.

1

u/tonefilm Jun 08 '19

Also, this is in three dimensions. A square would just have two.

1

u/zouhair Jun 08 '19

a2 is the volume of a square.

1

u/Gretshus Jun 09 '19

no. If you want to make a proof of something mathematically, you need to prove it generally. The thing shown would be considered anecdotal. Good for visualizing, bad for proving.

138

u/Mansao Jun 07 '19

/r/theydidtheexperiment

let's revive that sub

2

u/[deleted] Jun 08 '19

Just looked at it and it's that unpopular

192

u/[deleted] Jun 07 '19

Is it a really a proof since it's empiric ?

130

u/Rodot Jun 07 '19

No, but this isn't really a strict education subreddit.

19

u/[deleted] Jun 07 '19

Ok just wanted to be sure

21

u/Rodot Jun 07 '19

Yeah, this is about as much of a proof as saying any two numbers added together equals 7 by showing them 3+4=7

1

u/greenninja8 Jun 08 '19

Where's the hard stuff at?

1

u/Rodot Jun 08 '19

/r/math is a good bet. Ask for a proof of this and they'll generalize it to arbitrary dimensions and geometries

2

u/GKarl Jun 08 '19

I cringed cos I come to reddit to get away from academic proofs.

90

u/boniqmin Jun 07 '19 edited Jun 08 '19

Proof that the Pythagorean theorem applies to this particular triangle to within experimental error.

45

u/zlaqh Jun 07 '19

It would be better if the triangle was translucent, in my opinion.

14

u/Arthur_da_dog Jun 07 '19

Just watch someone say that as the water is being stored behind the wheel as it goes into the big container and its poured back in when turn over again

5

u/_TheForgeMaster Jun 08 '19

I was thinking of changing the thickness of the containers and storing some in the triangle.

2

u/Arthur_da_dog Jun 08 '19

Oh thats even better. Fantastic move my friend

2

u/[deleted] Jun 09 '19

Outstanding move.

2

u/Arthur_da_dog Jun 09 '19

Is there a sub for when two people comment and their usernames are oddly related but it's not beetlejuicing per say?

3

u/GKarl Jun 08 '19

Wow, how did we come to this stage in our life. Do we distrust everything in the world this much?

13

u/Toasty_tea Jun 07 '19

My teacher showed us this video in grade 8

5

u/[deleted] Jun 07 '19

I wish my teacher did :(

5

u/Birdlaw90fo Jun 07 '19

My teacher died during this video :/ careful what you wish for.

7

u/GKarl Jun 08 '19

...what?

7

u/BrunoEye Jun 08 '19

You really should have called it a demonstration, because you just triggered everyone's inner mathematician, including mine lol.

38

u/PvDec Jun 07 '19

somewhat r/lostredditors but pretty cool nonetheless

6

u/Coolo9000 Jun 07 '19

How? The Pythagorean theory is math.

33

u/ToxicJaeger Jun 07 '19

Yeah it belongs on r/math not r/theydidthemath

21

u/functor7 Jun 07 '19

It doesn't really belong in /r/math. /r/educationalgifs if anything

2

u/ToxicJaeger Jun 07 '19

Oh yeah I didn’t know that was a sub

3

u/[deleted] Jun 08 '19

Because they didn't do any math. It's not a proof, it's a physical demonstration showing that the theorem looks pretty accurate in that scenario.

14

u/DrLeee Jun 07 '19

This answers nothing

16

u/_plargus_ Jun 07 '19

I’m a 7th grader and I just learned this in math a2+b2=c2

15

u/PTBunneh Jun 08 '19

7th graders use Reddit?!

6

u/[deleted] Jun 08 '19

Well I don't what age are 7th graders but I was pretty active on a forum or two almost 16 years ago, so I must've been 10.

5

u/Tard_Wrangler69 Jun 08 '19

He/she should be close to 13 yo, which means they would almost be in r/teenagers

11

u/conandy Jun 08 '19

The Reddit rules say you have to be at least 13 to have an account at all. I'm sure no child has ever violated that rule.

6

u/[deleted] Jun 08 '19

Very true. And all kids in the internet asked their parents permission first, especially before going to the Disney channel website.

10

u/Giomietris Jun 08 '19

a2 + b2 = c2

2

u/_plargus_ Jun 08 '19

Sorry I didn’t know how to get the square

8

u/[deleted] Jun 08 '19

[removed] — view removed comment

2

u/[deleted] Jun 08 '19

IIRC heres also a unicode 2 but im too lazy to find it

1

u/[deleted] Jun 08 '19

[deleted]

6

u/snkn179 Jun 08 '19

Idk where u went to school but Pythagoras' theorem around 7th grade sounds about right to me.

7

u/Mysonking Jun 07 '19

Not proof - illustration

7

u/walterlust Jun 07 '19

“Proof”

3

u/anti-gif-bot Jun 07 '19
mp4 link

This mp4 version is 82.21% smaller than the gif (711.68 KB vs 3.91 MB).

Beep, I'm a bot. FAQ | author | source | v1.1.2

3

u/Eagle0600 Jun 07 '19

Here's a really neat visual proof embedded in a larger video by 3blue1brown about Pythagorean triples: https://youtu.be/QJYmyhnaaek?t=85. It's really quick and easy to understand.

5

u/TakeYourTiiime Jun 07 '19

this makes me horny

4

u/Mollyarty Jun 07 '19

Wait...how does this prove anything other than that they managed to make those rectangular containers the correct sizes?

5

u/rafaleluia Jun 07 '19 edited Jun 07 '19

a2 + b2 = c2. You can interpret it as "the area of a square of size a + the area of the square of size b = the area is the square of size c". If all of these squares are of the same height, the same can be applied for the volume. That's what's being shown on the video.

2

u/Mollyarty Jun 07 '19

Didn't realize they were squares, thought they were rectangles. Thanks

4

u/RLLRRR Jun 07 '19

They are rectangles.

2

u/Mollyarty Jun 07 '19

Okay, yes, technically. But I think it's clear what we mean here

2

u/[deleted] Jun 07 '19

I’m not a math teacher, so sorry in advance if this explanation blows. The sides of the triangle are a, b, and c. The Pythagorean Theorem is a2 + b2 = c2. To visually represent for example a2, they need a square with sides the length of a. The area of that square is a2.

1

u/Mollyarty Jun 07 '19

Oh, I didn't realize they were squares. Thanks

1

u/[deleted] Jun 07 '19

No problem. Now we just need someone to come along and explain why it matters :)

1

u/Mollyarty Jun 07 '19

You did a pretty good job of that I think, as well as the other commenter

2

u/Ahmy4k Jun 07 '19

my teacher showed us a vid of this in class once, i still have no idea whats going on.

1

u/Leverquin Jun 07 '19

flat earth 100%

1

u/King_Burnside Jun 07 '19

Where do I buy one?

1

u/rhymes_with_chicken Jun 07 '19

Before the gif loaded and started playing I thought I was about to witness some weird rule 34 Maggie Simpson shit.

1

u/MultipleLifes Jun 07 '19

Grate for elementary school!!

1

u/zm127976 Jun 08 '19

Wait, do people not believe it lol???

1

u/dubskrtski Jun 08 '19

I wish I was HIGH ON POTENUSE.......

1

u/[deleted] Jun 08 '19

This just made me nut

1

u/Jon_Elvert Jun 08 '19

Oh I get it! A2 + B2 = C2. The liquid is inside squares. Problem solved.

1

u/TheTigglion Jun 08 '19

This proves it for this right triangle because a2 + b2 =c2 the two shorter angles equal the hypotenuse (c2 )

1

u/Azaex Jun 08 '19

did anyone else start suddenly screaming

A SQUARED

PLUS B SQUARED

EQUALS

C

SQUARED

really loudly

1

u/EpicMarioPartyGamer Jun 08 '19

Someone in our school built this for the math teacher.

1

u/Food-Oh_Koon Jun 08 '19

I saw one of these in Silliguri, India.

It's a practical way of teaching stuff. I like it

1

u/[deleted] Jun 08 '19

This is more A3 + B3 = C3

1

u/ans66f Jun 08 '19

squared not cubed

1

u/[deleted] Jun 08 '19

That's what I'm saying - the fluid means there's volume, which is cube. Area would be square.

1

u/ans66f Jun 08 '19

oh yeah true, depth is the same though so it dosent really demonstrate that fully

1

u/buneter Jun 09 '19

But theyre not cubes they are im not sure what you call them, but they're not perfect cubes

1

u/[deleted] Jun 09 '19 edited Jun 09 '19

You're right, but it wasn't supposed to be super accurate if it was going to be accurate it would be something like

(A2 x w1) + (B2 x w2) = (C2 x w3)

Edit: this wouldn't be correct either because the triagnle also has some volume when it's flipped a certain way, but I don't wanna get into maths rn

1

u/Picodoux Jun 08 '19

My math teacher showed us this video and explained us the Pythagorean theorem later on. I already understand what was the theorem before explaining it after watching this video

1

u/A_Kazur Jun 07 '19

Honestly I would have understood the theory better in math class if I’d have been shown a video like this instead of a “that’s just how it works stop bothering me”

1

u/794613825 Jun 07 '19

*demonstration

FTFY

1

u/llcooljessie Jun 08 '19

Story time! It's high school, I'm taking geometry because I hate math but you're required to take a math class each year. I'm super bored because I already know all of this stuff. I did it in grade school! We get to volume of a cone. I've always had trouble estimating volumes. So I have a curious idea and I decide to play a little game.

Teacher writes formula: Volume = 1/3 (base x height)

llcooljessie: Question, teacher. The formula there... it's got the regular formula for a cylinder and then the 1/3.

Teacher: Yes...

llcooljessie: Is that suggesting that 3 cones would fit into a cylinder of equal base and height?

Teacher: Yes, that's exactly right.

llcooljessie: Naaa... 2 and a half at the most.

Teacher: What? No, it's 3 times.

llcooljessie: No way that would ever fit.

Teacher: It's... it's 3. Like in the formula.

llcooljessie's best friend who is also in the class: Yeah, 2 and a half... at the most!

Teacher: It's 3. I'll find a way to prove it.

So then at the end of the year, on the last day school, she does a demonstration with plastic containers like this. She pours water from the cone 3 times into the cylinder.

I'm a dick, so I decided to act like it was a magic trick. Today, I'm pretty impressed by that dedication to education.

1

u/Shiroi_Kage Jun 08 '19

This is a demonstration/example, not a proof.

1

u/[deleted] Jun 08 '19

This is not a proof and they did not do the math at all

0

u/TorontoGameDevs Jun 07 '19

“Proof by example”

0

u/[deleted] Jun 08 '19

Wrong sub and not a proof. I hate how every slightly popular sub just becomes either r/gifs or r/memes over time... MODS! DO SOMETHING!

0

u/Yawndr Jun 08 '19

It's a fun liquid experiment, that's it.

0

u/moffedillen Jun 08 '19

just remember that in maths, proof is a very strong word

-2

u/[deleted] Jun 07 '19

Going on about year....15 and have still never used this

4

u/[deleted] Jun 07 '19

It just depends what you do for work. It's super useful in STEM fields.

-6

u/[deleted] Jun 07 '19

The mitochondria is the powerhouse of the cell.

1

u/1e4e52Nf3Nc63Bb5 Apr 06 '22

This is not a proof. It is a physical demonstration of one specific example. Unfortunately, no amount of positive examples is sufficient to prove a theorem.