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jendrian Male, 1829, Canada 2493 Posts

Thursday, December 20, 2012 10:29:11 PM @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. 

MacGuffin Female, 3039, Europe 2596 Posts

Tuesday, December 18, 2012 3:01:44 PM 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) Stay off those drugs, dude. Hint: a *square* (which Pythagoras' Theorem makes heavy use of) is a twodimensional shape. It only exists in Euclidean space. Otherwise it'd be a cube. Or a tesseract. Or an ndimensional 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. 

andybme Male, 5059, Western US 296 Posts

Tuesday, December 18, 2012 6:49:31 AM Looks like common sense to me 

drawman61 Male, 5059, Europe 6559 Posts

Tuesday, December 18, 2012 4:45:51 AM Now I'm just confused about something I didn't care about 

jendrian Male, 1829, Canada 2493 Posts

Monday, December 17, 2012 9:56:38 PM @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) 

MacGuffin Female, 3039, Europe 2596 Posts

Monday, December 17, 2012 2:47:25 PM The video demonstrates *that* the theorem is true. This diagram demonstrates *why* it's true:


MeGrendel Male, 4049, Southern US 5126 Posts

Monday, December 17, 2012 10:53:13 AM If you need THIS to understand the Pythagorean Theorem, you have not business understanding the Pythagorean Theorem. 

jendrian Male, 1829, Canada 2493 Posts

Monday, December 17, 2012 10:26:45 AM @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) 

carmium Female, 5059, Canada 6406 Posts

Monday, December 17, 2012 8:47:27 AM OHoh. Now I get it. (A lot of work just for people who don't trust arithmetic.) 

FoolsPrussia Male, 3039, Western US 3403 Posts

Monday, December 17, 2012 8:39:36 AM Why are you making me think about something I've deliberately suppressed for at least 12 years? 

TruTenrMan Male, 3039, Southern US 2565 Posts

Monday, December 17, 2012 8:24:54 AM Why is (a^2)+(b^2)=(c^2) so hard to understand? 

Big61AL Male, 4049, Midwest US 59 Posts

Monday, December 17, 2012 8:15:07 AM So what's the point? shouldn't a simple measurement of the two squares show the same result? 

Draculya Male, 4049, Asia 13408 Posts

Monday, December 17, 2012 7:41:07 AM Not a 'proof' though 

piperfawn Male, 3039, Europe 3960 Posts

Monday, December 17, 2012 7:40:47 AM cool. 

Tiredofnicks Male, 3039, Europe 5010 Posts

Monday, December 17, 2012 7:33:01 AM Link: Creative Demonstration Of The Pythagorean Theorem [Rate Link]  Is it any clearer to you now? 

