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
>>16139872science bro
>>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
>>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
>>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
>>16148265wtf is wrong with her chin
>>16148265
>>16123714C O P E holy shit you faggots love to cope hard.
>>16123455there'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.
>>16148265Is there a scientific term to describe that kind of chin deformity? Does science know what causes it?
>>16123455
>>16123745/thread
>>16124893>Not one counter argumentSo no one can refute this?
>>16158814Already countered by a dub >>16125188
>>16123455Proof 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.
>>16158730that doesn't prove anything
>>16158835the picrel you referenced doesn't mean anything. plane geometry is for brainlets, its useless. there is nowhere in this universe that plane geometry is legitmate, this pic in >>16124893 is just a right triangle as seen in one of the many, many planar geometries which do exist in irl life
>>16160200why not? i find it convincing
>>16162926only because you're low IQ
>>16123455I'll just Google an existing proof like they did
>>16124893I'll allow it.
>>16163708It's amazing how hard you retards have to cope with every black achievement. I love watching you squirm.
>>16162746>t. IQlet
>>16163758I don't think the 6 millionth redundant Pythagorean proof is much of an accomplishment, but go off.
>>16152315Provide me a true triangle where the theorem doesn't hold
>>16162746
>>161312218/10
>>16164449There is nowhere in this universe where your flat space cartesian fantasyland is reality.
fags
>>161668971. Your argument only holds for large scales2. The universe itself is infinitely flat, without external influence parallel lines in space will never converge or diverge
>>16123455Tell us which part of the girls' proof requires that the Pythagorean theorem holds.
>>16160200It proves it alright. More than that, that's how Pythagoras himself is told to have proven it>>16163561NO U
>>16169669Doesn't matter if it's non-euclidean when it appears completely identical to euclidean
i've read their proof. It's obviously legit and pretty brilliant. I think no one did it before because they simply thought its impossible
>>16169761post the proof (at this point I suspect it doesn't exist)
>>16169771if you're too stupid to use google, you're too stupid to understand it
>>16169779chud moment
>>16158835>the pythagorean theorem is true if you change the numbers
>>16169779Africans and their descendants have come up with pretty much every "new" idea
>>16170209That's because our species originated in Africa.
>>16170223After they revealed that mummies in egyptian and chinese pyramids have european appearance, it became clear, that whites were pushed further and further north by black hordes, and now they opened the gate again.
>>16170236the most gay proof possible, and they teach exactly that proof all over the world, instead of teaching kids the one with triangles within a+b square. Hands down, their task is not to ignite your interest in science, au contraire.
>>16170236>word word wordNerd.At least I try to bully dead people. Pour a bag of beans on his grave, Office Space style.
>>16170392> circles> some other triangleHow does it prove anything?
>>16170373They have to teach what a triangle is and what a square is first, this includes the pons asinorum, you only think it's retarded because the pons asinorum filters you, this is why prop 47 is best
>>16170223no it didn't
>>16170781I thought they taught what triangle and square are in kindergartens. Either way you're not supposed to filter anybody in the common and pretty much compulsory education.
>>16170392Could you give us an explanation for this proof?
>>16170901Lol you can't comprehend mathematics outside of school or work
>>16171427That's also true for most people, sadly.
>>16123465>Can you come up with your own proof?There is no need to re-discover America.
>>16170364source
>>16172590It's pretty much all over the internet now.Picrelated is an egyptian mummy, and here's for the chinese: https://en.wikipedia.org/wiki/Tarim_mummies
>>16172874Whites built the great wall of China in hopes of keeping the chinky baboon people out of the white part of eurasia. Later on Chinks rewrote history and claimed credit for building the wall.
>>16173488The great wall was built over thousands of years in multiple stages
>>16170937No, deduce it.Thats how I was initiated, shown something "strange" and figured it out when everyone else said "Tss nuh uh."
>>16170617>How does it prove anything?Another retard sees information and responds with "THIS DOESNT SAY ANYTHING AT ALL. NO U DUM."Your family should ashamed of you...wake the fuck up, dipshit.....seriously....WAKE THE FUCK UP.STOP TALKING LIKE YOURE THE SMART ONE, RETARD........DID YOU FORGET YOURE NOT A GENIUS?HUH KATHY NEWMAN? FORGOT YOURE NOT A NEUROCHEMIST? JUST [[[FORGOT]]]?
>>16173881>>16173886This is why."The People" are worthy, thats why Bible Codes exist, these soulless pieces of shit are nice until they believe they wield power, then they become some child like vision of a super villian, but since the normally cant their evil sprouts in things like work/politics etc.
>>16173902>arent* worthylol damnit...maybe the "Youth", but theyre no in power at all.
Ive shown critically import shit to people over and over, the #1 response "Tssss NuH Uh."Literal national security secrets or shit gets "lmao larp"'d back. Its funny and sad...you could try to give people important and they trash it with pride."I prefer eating feces."Yes...human tend to.
>>16173908>"I prefer eating feces."Oh...and this is the make themselves look smarter as a front to me...but Im the doctor, dipshits...you literally fucking idiots literally walk into a doctors office and try to usurp "doctoral authority" in the room with zero quakifications, its funny and sad.To see someone so out of touch with themselves and the world around them.
I love eating my own poopy
>>16173886I asked you a question, redtard.Also I am a genius, and you're a boring clown from reddirt.
>>16131221That is not how you measure distances, you stupid idiot.
>>16173880where did you read that? wikipedia?
>>16174432You may hate Reddit, but that's what the rest of the Internet thinks about 4chan.
>>16174900who cares what the rest of the Internet thinks?
Waffle cone? More like waffle STOMP!!
>>16174905People on the rest of the Internet.
>>16174920And where you should return, also because you are not even able to follow the conversation. The question was not what you're thinking of anything, but how do those circles prove the theorem.
>>16174900you should go somewhere else if you hate 4chan, you're clearly not here to be a good contributor to the site
>>16146504does she date transbians?
>>161764134chan is packed to the gills with "activists" from other websites who come here to try and ruin this site and jannys do nothing about it
>>16178950Well, jannies are not supposed to do anything about them, it's our job. It's one of the main principles of this comfy platform.
>>16178950so is krautchan
>>16123463euclid's elements isn't rigorous. it has logical fallacies.
>>16178950>can post about anything except stuff i don't like
>>16179786you're the one who is complaining about other people posting things you dislike
>>16123455why are white liberals so patronizing?>LOOK ALL, THE BLACK MACAQUES FROM NOUVELLE-FRANCE ACTUALLY MADE MATHEMATICS. HOW FASCINATING. PLEASE, COME IN, WATCH THIS FREAK SHOW OF CURIOSITY!
>>16124893That's not a right triangle.
>>16123455given the recent rash of fraud and plagiarism committed by negroes, why should anyone believe that their claimed achievement is legitimate?
>>16185023Looks like one to me
It's obvious
>>16185788you're replying to one of those 2+2=4 chuds, they're too low IQ to understand decolonized mathematics
>>16187023>why should anyone believe that their claimed achievement is legitimate?Low IQ, its common, most people have it.
>>16123455It's on Wikipedia so it's must be true faggot
>>16158730right image looks like ukraine and upa flag
>>16123455i could prove it in one word, but that word is banned on /sci/ because it is the n word
>>16181580they're like that because they have low iq
>>16131221>>16133144btw it works from both sides on the real number line
>>16123745Proof of the additive properties of areas?
>>16193354
imagine being a 3 dimensional creature and living in a 3 dimensional universe and thinking plane geometry is real or has any bearing on reality
If I go one way, I don’t go the other.
>>16193645Self evident
>>16123455>Prove the Pythagorean theorem without using a circular argument.Use a ruler to measure the triangle.
>>16195353proof that its self evident?
>>16196495the fact that there is no proof that its self evidence is proof that its not self evident
>>16197318Proof that the fact that there is no proof that its self evidence is proof that its not self evident?
>>16198315Godel's completeness theorem
>>16145427They just are, that's the proof, and it satisfies the OP's challenge.But to answer your question, the Pythagoras theorem works only in flat space. In curved geometric space, like on a sphere, the shapes distort and the relationship is not true anymore.So to answer your question, at our scale, space is locally flat, so that relationship holds. If you tried to do that on a cosmological scale, it would not hold anymore since spacetime is all distorted throughout.
>>16199437why do you consider 2d flat space real and everything else "distorted" when there is nowhere in this universe that flat space exists outside of your imagination?
>>16199437So Pythagoras' "theorem" is a postulate equivalent to Euclid's fifth postulate.OP's question is bait and he is a faggot.
>>16123455Just draw a rectangular triangular into a piece of paper and measure the sides, and see if they fit into the theorem. Simple.Theoretical retards get fucked.
>>16199531I didn't say 2D space is real or not, I said the relationship between those areas is what it is.>there is nowhere in this universe that flat space exists outside of your imagination?That is true, well said, but for practical purposes, at our scale the curvature is negligible, and only detectable with the most sensitive of apparatuses to measure it, like atomic clocks and laser interferometers, etc.
>>16199554It's a property of flat space, yes. Just like the number 3.14159... is.
>>16123463Euclid's Elements should only be of interest to the historian of mathematics. The work doesn't hold up to scrutiny and it is a poor way to learn geometry
>>16123455>high school girls are good at mathmore evidence that math is a dumb topic which only idiots could devote their lives to
>>16172874the mummy has more hair than the average white male
>>16199531My imagination is more real than what you measure with your silly instruments. I have access to my imagination directly while you have to rely on your eyes relying on gauges relying on some measurement mechanism.Math is more rigorous than physics. Have you never done any research? In physics we often throw out results because they're unphysical lol
>>16123455>>16123455For the benefit of mathematics, I will not discuss magnitudes that are incommensurate. >>16123463Euclid's 4th was always wrong.-t. hyperbolic geometry >>16124893And Hippasus is a drownable human (at least according to Hebrew translated greek). Not because he was "right", but because he was an insufferable moron who even after divulging the nature of the irrational insisted math could be used to solve it (which was why Pythagoras was shamed). You think that sounds like a dumb reason to drown someone? Look at the all the retards preaching "real numbers" now and pretending it' hot shit that means a bucket of piss. Down them, all of them!These secrets were know long before Pythagoras, it's even why they don't refer to 0 or 1 as "of number". Even Aristotle and Euclid knew 1 wasn't a number. It's the principle of number
>>16123463>Euclid's Elements, Prop I.47. c. 300 BC.This!It only took turds 2300 years to catch up to us.
>>16187023This. OP is as real as picrel
>>16187023
>>16205029>someone who can count to 10 on his fingers insulting the math ability of someone who can only go up to 9
>>16124893Absolutely based Platonists will never recover when forced to contend with the fictionalist chad
>>16206134Everything about plane geometry is fictional. We don't live in a 2d universe
>>16131221yee haw
>>16123455SHOW THE CHILDREN!
https://www.youtube.com/watch?v=KihYpOn32KI
>>16209211https://www.youtube.com/watch?v=2-eitsutpOc
>>16209211lolI wonder if its true that different races have different nutritional needs
>>16162746lol
>>16166897I hope the AIDS kills you slow
>>16200972And it still has more intelligence than a nigger even after being dead for 5000 years
Fags
>>16168737The universe is only locally flat if it is empty, any energy causes curvature and any curvature causes distorted geodesics.
>>16195289Doesn't matter, still can be rigorously defined. Learn what the Riemann tensor is, or at least learn about the Poincare disk/half plane.
>>16212124they definitely do, thats why immigration is so bad, it takes people out of their natural ecosystems
>>16124893I kneel
>>16220225>did someone mention me?
>>16221313>kneel on de grasse tyson
>>16123455its works
>>16199579But how do you know it holds for every right triangle?
>>16193645kill yourself
>>16224785so you're saying you have no proof
>>16218183
Space is a vacuum...which direction do it pull? Light travels through it. Vacuums create planets. Vacuums make round objects. Gravity makes round. Light only can be seen if gravity is present.8 minutes for light to reach earth and how many minutes to reflect on moon?
>>16228011>Space is a vacuum.false premise, it isn't
>>16123455do i get to use the euclidean distance?
>>16124893best bait award
>>16218174
>>16229233it just goes to show that anyone can put lines and worlds on a jpeg, but that doesn't make whats on the jpeg true. The global warming shills use the same trick with all their fake graphs
>>16165263The nazi party being asked about rascism
>>16123455Let v be a 2d vector, so v = ax + bylength is defined by the quadratic form a^2 + b^2this induces a geometric algebrawherein the area of the square is given by v^2(ax+by)^2a^2xx + abxy + bayx + b^2yya^2 + abxy - baxy + b^2a^2 + b^2we're talking about flat euclidean space, hence that particular quadratic formwere talking about lengths, so the basis vectors have unit length, so x^2 = y^2 = 1and we're talking about right angles, so x,y anticommuteyou can verify that this is the correct quadratic form by checking that it's rotationally symmetric, since it's already obviously correct on the axiswe can do this by taking a rotor, given by two unit vectors m,n, and showing the form applied to v is the same as applied to mnvnm(mnvnm)^2mnvnmmnvnmmnvnnvnm since units square to 1mnv^2nmv^2 mnnm scalars are in the centerv^2
>>16232554sorry, phone posting from workthat's the wrong formula for the area of a squareit's the magnitude of the xy component of vxyv(ax+by)xy(ax+by)(-bx+ay)(ax+by)-bax^2 +aby^2 + (a^2+b^2)yx(a^2 + b^2)yxso the magnitude of the component isa^2+b^2
>>16123455Blacks are so good at all aspects of science and math these days. Should all other races be formally excluded? Nobody can compete with African intellects, research and publications by non-blacks is just a big waste of resources
>>16233808Yes, but negroes should be excluded from athletics, they can't compete with the white race
>>16234962Big win for Luka tonight.
>>16231887
>>16233808Perfect time to end affirmative action, they can sustain on their own now
>>16203593
