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Related: About this forumPythagorean Theorem Demonstrated with Fluids.
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Pythagorean Theorem Demonstrated with Fluids.
keithbvadu2
(36,793 posts)Clash City Rocker
(3,396 posts)eppur_se_muova
(36,262 posts)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.
intrepidity
(7,295 posts)that's exactly, literally what is being shown
eppur_se_muova
(36,262 posts)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.
intrepidity
(7,295 posts)so there is no other version.
muriel_volestrangler
(101,312 posts)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.
intrepidity
(7,295 posts)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...
muriel_volestrangler
(101,312 posts)so it's not a general proof of Pythagoras' Theorem, only a demonstration for specific values of a, b, and c.
intrepidity
(7,295 posts)muriel_volestrangler
(101,312 posts)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.
intrepidity
(7,295 posts)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??
muriel_volestrangler
(101,312 posts)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.
intrepidity
(7,295 posts)Dr. Strange
(25,921 posts)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.