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Mon Mar 1, 2021, 12:37 PM

Pythagorean Theorem Demonstrated with Fluids.


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Jennifer Taub
@jentaub
😎 This is so cool #Math

Tech Burrito
@TechAmazing
Pythagorean Theorem Demonstrated with Fluids.

15 replies, 1010 views

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Arrow 15 replies Author Time Post
Reply Pythagorean Theorem Demonstrated with Fluids. (Original post)
soothsayer Mar 2021 OP
keithbvadu2 Mar 2021 #1
Clash City Rocker Mar 2021 #2
eppur_se_muova Mar 2021 #3
intrepidity Mar 2021 #4
eppur_se_muova Mar 2021 #5
intrepidity Mar 2021 #6
muriel_volestrangler Mar 2021 #7
intrepidity Mar 2021 #8
muriel_volestrangler Mar 2021 #9
intrepidity Mar 2021 #10
muriel_volestrangler Mar 2021 #11
intrepidity Mar 2021 #12
muriel_volestrangler Mar 2021 #13
intrepidity Mar 2021 #14
Dr. Strange Mar 2021 #15

Response to soothsayer (Original post)

Mon Mar 1, 2021, 12:39 PM

1. 1+

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Response to soothsayer (Original post)

Mon Mar 1, 2021, 01:26 PM

2. Brilliant in its simplicity

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Response to soothsayer (Original post)

Mon Mar 1, 2021, 02:24 PM

3. Well, it works with that *particular* example ... does that necessarily mean it works with others ?

That's the problem with physical examples -- they're specific cases. Actual proofs are general.

I could set up one which shows the fluid in a circle filling up a square, but that would just be the result of very careful measurement for that case. Couldn't give a general rule, and neither can anyone else.

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Response to eppur_se_muova (Reply #3)

Mon Mar 1, 2021, 02:47 PM

4. a2+b2 equals c2

that's exactly, literally what is being shown

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Response to intrepidity (Reply #4)

Mon Mar 1, 2021, 02:51 PM

5. Literally, for that particular case, and no other, except by building other demonstrations.

That is the difference between a demonstration and a proof. The OP says demonstration, which is literally correct. It is not a proof -- literally or otherwise, and the OP doesn't claim it is. Just pointing out the dangers of using such demonstrations to educate.

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Response to eppur_se_muova (Reply #5)

Mon Mar 1, 2021, 02:54 PM

6. Pythagorean applies to right triangle only

so there is no other version.

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Response to intrepidity (Reply #6)

Tue Mar 2, 2021, 06:23 PM

7. There are an infinite number of right angled triangles

Just to take the ones with integer sides: 8,15,17; 3,4,5; 5,12,13; 7,24,25; 9,40,41 ...

Their sides are all in different ratios. A demonstration with one of them doesn't prove it for all of them.

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Response to muriel_volestrangler (Reply #7)

Tue Mar 2, 2021, 08:17 PM

8. Yes, it does

The liquid measures volume. Assume the depth/height of all figures is 1 (H=1).

Now their volumes (LxWxH) are

a2+b2=c2

Unless I'm really missing something and need to relearn geometry...

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Response to intrepidity (Reply #8)

Tue Mar 2, 2021, 08:53 PM

9. It shows it for that specific right-angled triangle, not for all of them

so it's not a general proof of Pythagoras' Theorem, only a demonstration for specific values of a, b, and c.

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Response to muriel_volestrangler (Reply #9)

Tue Mar 2, 2021, 09:50 PM

10. Which one does it not apply to? nt

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Response to intrepidity (Reply #10)

Wed Mar 3, 2021, 06:46 AM

11. It doesn't *show* it for any other.

It doesn't tell you whether it applies to any other.

If I found that the diagonal of a rectangle was equal to the sum of the 2 shorter sides, that would not prove it as a general property of rectangles.

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Response to muriel_volestrangler (Reply #11)

Wed Mar 3, 2021, 01:47 PM

12. Are you disputing the Pythagorean Theorem, in general?

Are you also a flat earther??? I'm being serious, this is mind-blowing.

I thought you were disputing the demonstration using liquid, but it seems not.

Wtaf is going on?

Do you agree that, for right triangles: a(squared) + b(squared) = c(squared)?

Is there a semantic nuance I'm missing??

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Response to intrepidity (Reply #12)

Wed Mar 3, 2021, 02:06 PM

13. No, I'm not disputing the theorem; you are missing the difference between one example

and proving the theorem in general. I don't think that's "semantic nuance"; I think it's the idea of "proof of a general theorem". A proof needs to apply to all cases, not just one.

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Response to muriel_volestrangler (Reply #13)

Wed Mar 3, 2021, 02:11 PM

14. Yes, I truly am missing your point nt

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Response to intrepidity (Reply #14)

Thu Mar 4, 2021, 08:17 PM

15. The point is proving a specific case doesn't prove the generality.

If I claim that every prime can be written as a sum of two squares of integers, and then "prove" it by saying: 13 = 2^2 + 3^2
does that really work?

No, it just shows that 13 is the sum of two squares. But if you try 7, you get an example that doesn't work.

The demonstration above shows that a particular right triangle satisfies the equation in Pythagoras' Theorem, but the Theorem claims that the result will hold for ANY right triangle.

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