'Euclid's Elements, Prop I.47. c. 300 BC.';

'>>16123463
Can you come up with your own proof? 2 black girls did it, why can't you?';

'>>16123465
I have no idea what you're talking about.';

'>>16123465
Their "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.';

'undefined';

'let "a" be triangle base and "b" height

now, curve of hypotenuse is y=b/a x
length of curve c=integral sqrt(1+(dy/dx)^2) ,x=0...a

so c=integral sqrt(1+(b/a)^2) ,x=0...a
c=a sqrt(1+(b/a)^2) = sqrt(a^2+b^2)';

'The pythagorean theorem is disprovable';

'>>16124893
????';

'>>16124905
I know, I was surprised too';

'>>16124893
kek';

'>>16124893
I cannot tell if you are intentionally being stupid or not.';

'>>16124893
Forgot the image.';

'>>16123455
a^2+b^2=c^2
>>16123465
What proof, the numbers work and give the correct result, there's no need to "prove" anything';

'>>16124893
>The pythagorean theorem is disprovable
you 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';

'>>16124893
kek';

'>>16123463
This.';

'>>16123455
I measured every single triangle, Pythagoras didn't lie';

'>>16123455
I'm going to draw some lines on a piece of paper.';

'>>16123455
https://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.shtml
https://www.cut-the-knot.org/pythagoras/TrigProof2.shtml';

'>>16124893
white man science btfo!';

'>>16123455
The 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 0
It works';

'>>16123455
Nothing is gained from from the simplistic.';

'>>16123455
Trangles';

'>>16131221
Idk, man.
i+1>0
1+0>i
0+i>1
Seems to check out just fine for me.';

'>>16135247
omg lmao';

'>>16131221
hold up... doesnt this work?';

'>>16131221
Yes in monkey magic math the definition had to be changed so that Re^2 + Im^2 = length^2';

'done';

'>>16139663
how does that prove anything';

'>>16139872
science bro';

'>>16136442
what'd i miss?';

'>Prove the Pythagorean theorem without using a circular argument.';

'>>16133177
an sheeeeeiiiiiitttt';

'>>16139663
why are they equal tho';

'>>16145427
figure it out why boi';

'>>16143090
I would date this girl if she had a better personality
.';

'>>16139872';

'>>16145438
Twum 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';

'>>16123455
Ok read to get rekt OP?

pythagorean theorem = True


Booooooom 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 = 1
from 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))';

'>>16146595
Using 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||^2

if we denote the lengths of x,y,z by a,b,c the result is proved';

'>>16146769
invariance 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';

'>>16146595
Can 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';

'>>16147862
That area proof only works in the case that the pythigger theorem is true';

'>>16148265
Right, so its a circular argument. If the theorem were false then the two squares would not add up to the 3rd square';

'>>16148265
The 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 because
t. circular argument arguer';

'>>16123455
Just 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.';

'>>16150687
I accept your concession';

'Triangle is half square so its linear fr fr';

'>>16123455
Use 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';

'>>16124893
Based';

'>>16149167
>it's directly observable and applicable to reality
It 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';

'>>16148265
wtf is wrong with her chin';

'>>16148265';

'>>16154311
https://www.youtube.com/watch?v=c5AFHu8Xrw4';

'>>16123455
how come all the self proclaimed geniuses of /sci/ got outsmarted by a couple of high school girls?';

'>>16123714
C O P E holy shit you faggots love to cope hard.';

'>>16123455
there's a pretty simple one given in Lang's Basic Mathematics (would recommend btw) that avoid trigonometry. The proof, iirc, is done by connecting four right-triangles such that they form two squares, and then using previously proven properties of squares to prove that the length of the sides of the inner-square is equal to the square root of the outer lengths. it's actually a really fun proof.';

'>>16148265
Is there a scientific term to describe that kind of chin deformity? Does science know what causes it?';

'>>16123455';

'>>16123745
/thread';

'>>16124893
>Not one counter argument

So no one can refute this?';

'>>16158814
Already countered by a dub >>16125188';

'>>16123455
Proof is always circular. A is the case because B is the case. Otherwise an endless chain of questions and answers follows (why B 'cause C why C 'cause D etc. So it must be axiomatic that B is sufficient to prove A or A itself is an axiom. In this case the most fundamental axiom is that the surface area of rectangles with sides A and B is AB and it's axiomatic that a diagonal divides the surface area in halves.';