Prove the Pythagorean theorem without using a circular argument. That means no trigonometry, brainlets.
Euclid's Elements, Prop I.47. c. 300 BC.
>>16123463Can you come up with your own proof? 2 black girls did it, why can't you?
>>16123465I have no idea what you're talking about.
>>16123465Their "proof" was just to apply trigonometry and it hasn't even been validated through peer review, so it doesn't meet OP's standards, its not an accepted formal proof, and it isn't even based entirely on their own work, its just applied trig.
let "a" be triangle base and "b" heightnow, curve of hypotenuse is y=b/a xlength of curve c=integral sqrt(1+(dy/dx)^2) ,x=0...aso c=integral sqrt(1+(b/a)^2) ,x=0...ac=a sqrt(1+(b/a)^2) = sqrt(a^2+b^2)
The pythagorean theorem is disprovable
>>16124893????
>>16124905I know, I was surprised too
>>16124893kek
>>16124893I cannot tell if you are intentionally being stupid or not.
>>16124893Forgot the image.
>>16123455a^2+b^2=c^2>>16123465What proof, the numbers work and give the correct result, there's no need to "prove" anything
>>16124893>The pythagorean theorem is disprovableyou may have missed the point that a, b and c are the actual lengths of the sides, not merely any number written on them.
>>16123455>>>/sci/mpsg
>>16123463This.
>>16123455I measured every single triangle, Pythagoras didn't lie
>>16123455I'm going to draw some lines on a piece of paper.
>>16123455https://www.cut-the-knot.org/pythagoras/index.shtml>That means no trigonometry, brainlets.There are trigonometric identities that can be proven without presupposing the Pythagorean Theorem, and therefore can be used to prove the Pythagorean Theorem. Namely, the sum and difference formulas can be proven with only Ptolemy's Theorem. See:https://www.cut-the-knot.org/pythagoras/TrigProof.shtmlhttps://www.cut-the-knot.org/pythagoras/TrigProof2.shtml
>>16124893white man science btfo!
>>16123455The pythagorean theorem can be shown to be equiv to Euclid's 5th Axiom. So, it is essentially an axiom for flat geometry. Like, it obv aint true for a sphere or hyperbolic plane
>>16123455>without using a circular argument.Prove to me anything without axioms.
The triangle inequality is false
>>16131221>i is perpendicular from reals>1 line is horizontal>i line is vertical>i length is perpendicular to vertical>i length is horizontal>distance from the two ends of the two horizontal lines is 0It works
>>16123455Nothing is gained from from the simplistic.
>>16123455Trangles
>>16131221Idk, man.i+1>01+0>i0+i>1Seems to check out just fine for me.
>>16135247omg lmao
>>16131221hold up... doesnt this work?
>>16131221Yes in monkey magic math the definition had to be changed so that Re^2 + Im^2 = length^2
done
>>16139663how does that prove anything
>>16139872science bro
>>16136442what'd i miss?
>Prove the Pythagorean theorem without using a circular argument.
>>16133177an sheeeeeiiiiiitttt
>>16139663why are they equal tho
>>16145427figure it out why boi
>>16143090I would date this girl if she had a better personality.
>>16139872
>>16145438Twum is a lesbian.
>>16145451>the first two squares become rectangles that fit perfectly into the third square because muh theorem is true thats just more circular reasoning, you don't understand how proofs are supposed to work
>>16123455Ok read to get rekt OP?pythagorean theorem = TrueBooooooom 360 head shot
you can prove trigonometry from complex analysis thoughbeit. you can define sin(z) and cos(z) in terms of exp(iz) and exp(-iz) to prove that sin^2 + cos^2 = 1from there, you can use rotation invariance to prove that distance to the origin is constant on paths parametrized by (r sin(t), r cos(t))
>>16146595Using exponential definition of sin and cos, how do you show these functions are related to triangles?
let x and y be orthogonal vectors. Then (x,y)=0. if z is the vector x+y, then ||z||^2 = (z,z) = (x+y,x+y) = (x,y) + (y,y) = ||x||^2 + ||y||^2if we denote the lengths of x,y,z by a,b,c the result is proved
>>16146769invariance under rotation implies that if [math]y dx + x dy = 0[/math] then [math]d ||(x, y)|| = 0[/math] (the path has a constant distance from the origin)you can show through calculus that the path given by [math](r \cos t, r \sin t)[\math] satisfies this property
>>16125188>unintentionally makes use of the Pythagorean theorem while trying to disprove it
>>16146595Can you build up enough complex analysis to prove that without invoking Euclidean distance or the modulus of a complex number, though? Using Euclidean distance to prove the Pythagorean theorem is circular.
>>16146507>I don't understand how area works
>>16147862That area proof only works in the case that the pythigger theorem is true
>>16148265Right, so its a circular argument. If the theorem were false then the two squares would not add up to the 3rd square
>>16148265The area proof worka because it's directly observable and applicable to reality, 1l is 1l doesn't matter if your container is shorter or taller, you absolute negroid
>>16149167>the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works because the area proof works because the pythigger theorem works becauset. circular argument arguer
>>16123455Just count the triangles in the big square and compare it to the number of triangles in the two lozenges. No need for trigonometry, but you can use your fingers if you need to.
>>16150687I accept your concession
Triangle is half square so its linear fr fr
>>16123455Use a ruler on graph paper with millimeter precision. I draw a sequence of triangles with varying leg lengths,L = {1,2,3,4,5,...}mm and H = {1,2,3,4,5,...} mm all the way up to {L,H} = {10cm,10cm}, yielding hundreds of data points. I tabulate the two columns in Excel. I then use my ruler to measure the hypotenuse of the triangle and tabulate that data in Excel. I then plot the data in a bunch of different ways until a clear trend appears. >t. physicist
>>16124893Based
>>16149167>it's directly observable and applicable to realityIt isn't, there is nowhere in this universe that euclidian geometry is true, euclidian geometry is an abstraction that was invented for midwits who can't figure out real geometry
>>16148265wtf is wrong with her chin
>>16148265
