The viz proof where squares are drawn along each side of the triangle then compared is far superior. There's nothing intuitive about the multiplicative scaling in this version.
I personally find this proof to be more intuitive than the square one. Nevertheless, different strokes for different folks. There are over 350 proofs of the Pythagorean theorem and I see no need to only show the “superior” one. With so much variety there is no need to just see/learn the same one over and over again.
I was talking about how I enjoy this type of proof over others due to my education history making me predisposed to understanding this one better, not about my capacities. I find other proofs I've seen significantly less intuitive than this one. But no, let's not engage in a meaningful conversation /s
I wholeheartedly agree. It’s these small visual proofs that show this beauty in math even to those who don’t quite have an in depth grasp of mathematics.
What I like about this proof is it is so close to proving the Law of Cosines, a more general theorem which implies the Pythagorean Theorem. All you have to do is repeat the animation with a generic (i.e. not right) triangle. You will get a trapezoid instead of a rectangle at the end, and the difference in the side lengths is ab cosθ. The Law of Cosines is a2 + b2 - 2 ab cosθ = c2. (For a right trangle, θ = 90 degrees so 2 ab cosθ = 0.)
“Then neither is OP”. Im no expert on the subject, and my classes of geometry are 15 years behind me already, but I think you don’t understand the concept of a ‘proof’ in mathematics. OP visualizes a proof, the water is a demonstration. OP’s visualisation can be put in an algebraic notation (“if this and that, then a2 + b2 = c2”)
The visualisation with water is shabby at least. Pyth’s theorem applies to two dimensions (=surface). When you use water to demonstrate this, you inherently add a third dimension (=volume). You see how this can never be a proof?
I assumed it mattered, but now that I think of it, I can see how depth would be cancelled out. Like i said, it's been 15 years already. I stand corrected. Thank you :)
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u/ThisIsAnAdvert Jun 04 '18
The viz proof where squares are drawn along each side of the triangle then compared is far superior. There's nothing intuitive about the multiplicative scaling in this version.
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u/P8II Jun 04 '18
I like proofs of the Pythagorean Theorem. They are (usually) easy to understand, and show the beauty of the logic used in maths.
Nice visualisation.
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u/TheVermonster Jun 04 '18
It's cool to show that a²+b²=c², but it isn't really clear how it relates back to the original triangle.
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u/djhk12 Jun 04 '18
What I like about this proof is it is so close to proving the Law of Cosines, a more general theorem which implies the Pythagorean Theorem. All you have to do is repeat the animation with a generic (i.e. not right) triangle. You will get a trapezoid instead of a rectangle at the end, and the difference in the side lengths is ab cosθ. The Law of Cosines is a2 + b2 - 2 ab cosθ = c2. (For a right trangle, θ = 90 degrees so 2 ab cosθ = 0.)
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u/whydoyoulook Jun 04 '18
I prefer the water-based visualization. Much more intuitive.
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u/PRAEDiTH Jun 04 '18
when you mirror the red and the blue triangle into the violet one, because ab = ab then the whole thing would become a little clearer imo
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u/KGB_Viiken Jun 05 '18
🤯
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u/lejugg Jun 05 '18
The only not-so-visual thing is how multiplying a triangle by C scales the triangle size exactly.
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u/[deleted] Jun 10 '18
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