Creative Demonstration Of The Pythagorean Theorem

Submitted by: Tiredofnicks 4 years ago in
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Is it any clearer to you now?
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Male 2,516
@MacGuffin: I`m a physicist, in case you`ve missed the thousands of posts where I`ve made that obvious.

Draw a square in a piece of paper. Bend that piece of paper. OMFG a 2D figure projected in 3D curved space! Holy sh*t that must be the work of the devil for you.

Your picture only demonstrates that it is true in 2D Euclidean space. Good luck demonstrating that the areas remain the same when the square lives in curved space, here`s a hint: they don`t. Ergo, your drawing doesn`t say WHY, by any chance, the sum of the areas MUST be unequivocally the same. Believe it or not, questions like that keep us mathematicians up at night. No meds necessary though.
Female 2,602
[quote] Why it`s true is still a subject of research, as is my understanding, since it doesn`t have to be true (and in fact it isn`t in all kinds of spaces, it is only true in flat/euclidean space)[/quote]

Stay off those drugs, dude. Hint: a *square* (which Pythagoras` Theorem makes heavy use of) is a two-dimensional shape. It only exists in Euclidean space. Otherwise it`d be a cube. Or a tesseract. Or an n-dimensional hypercube. The diagram below demonstrates exactly why Pythagoras` Theorem works - namely that exactly the same amount of space is left over when you surround a square of side length equal to the hypotenuse or two squares with side lengths equal to the lengths of the opposite and ajacent sides laid corner to corner with a larger square of the same size in each case. It is not a "matter of research", it`s a mathematical proof that`s been fully understood for thousands of years.
Male 296
Looks like common sense to me
Male 7,774
Male 2,516
@MacGuffin: That doesn`t demonstrate why either, that only demonstrates that it is.

Why it`s true is still a subject of research, as is my understanding, since it doesn`t have to be true (and in fact it isn`t in all kinds of spaces, it is only true in flat/euclidean space)
Female 2,602
The video demonstrates *that* the theorem is true. This diagram demonstrates *why* it`s true:

Male 8,526
If you need THIS to understand the Pythagorean Theorem, you have not business understanding the Pythagorean Theorem.
Male 2,516
@Draculya: Yes a proof, provided the height of each chamber is the same (and it seems like it is in that video, as I`ve seen this demonstration in person before). It actually doesn`t get more "proofy" than physically putting it in evidence.

@Big61AL: Sure, what you have to measure is the area though, so you have to cut it up in squares and fit them all in the areas of the other two squares. Or you could just flow the area from one to the other two and let fluid mechanics do the arranging.

@carmium: it`s actually geometry, but it`s slightly more complicated than just squaring the sides. It`s not immediately obvious that the area of the bigger square is exactly the sum of the area of the other two squares. Just like it`s not obvious that the internal angles all add up to 180 degrees (in Euclidean spaces)
Female 6,381
OH-oh. Now I get it.

(A lot of work just for people who don`t trust arithmetic.)
Male 3,445
Why are you making me think about something I`ve deliberately suppressed for at least 12 years?
Male 2,552
Why is (a^2)+(b^2)=(c^2) so hard to understand?
Male 59
So what`s the point? shouldn`t a simple measurement of the two squares show the same result?
Male 15,259
Not a `proof` though
Male 5,163
cool.
Male 5,094
Link: Creative Demonstration Of The Pythagorean Theorem [Rate Link] - Is it any clearer to you now?