Prove that this is wrong.
>>16827327Take a 4 inch string and wrap it around a 1 inch diameter pipe. If there's overlap then pi is less than 4.
>>16827327Slide thread, but it isn't wrong for a pixelated circle. It is wrong for a polygonized one or one constructed using a compass. Perimeter describes the distance required to optimally traverse a shape using a series of infinitesimal steps. In the example given, you're unnecessarily constraining yourself to movements of +dx, -dx, +dy, -dy, while the space of 2d shapes in general allows traversal using line segments that can be oriented at an angle. Physically, the stroke of a compass is perpendicular to the line between the needle and the pencil, so having that angular degree of freedom is necessary to match those of the tools used to construct circles geometrically.
This is a classic paradox you'll learn in post-multi var calculus (or you can find yourself if you're trying to understand length and approx. of geometrical shapes), the the function "length of a curve" isn't always continuous when extend your iterations to infinite.The TL;DR is related to the derivative, to not 'break' the length function the derivative of your curve should still exists when you extrapolate to inf iterations (that example works with derivable functions like a sinusoidal curve).
>>16827330I shan't be doing that. Fuck off idiot
>>16827330>>16827364it works in base 11
>>16827330The virgin numerical approximation vs the chad physical approximation
>>16827336>post-multi var calculusWhen was that developed?Are you saying mathematicians prior to its development would have seen the proof in OP or something like it and concluded pi=4 etc? (maybe not for this particular example, because you can physically measure a real-world circle with some string and get a better value, but for some other shape or related concept) Because the line gets closer and closer to the circle, just like mathematicians do with polygons in circles to find the true value of Pi, or with integration for the area under a curve.In fact, this looks a lot like the area under a curve, except that it is length rather than area.Are there examples of simple "proofs" that were widely held, later to be shown false? And is the "post-multi var calculus" explanation applied "organically", as in it would crop up as a natural explanation for why OP's proof does not work, or is it applicable because we know OP is wrong ex post facto?
>>16827419Or maybe not conclude that pi=4 (or similar), but conclude that the concept of a proof is dead, because apparently sound reasoning can be used to show pi=4, which it is not.
>>16827327Circles have no corners. You can't make corners go away by making them infinite.
>>16827419>the line gets closer and closer to the circle, just like mathematicians do with polygons in circlesSee >>16827425The polygon cheat actually makes the corners go away.
>>16827425I would actually take on corners like this.- Let's say we on any iteration of an OP proof.- Now cut any number of corners, without touching the circle.- Perimeter now is < 4, but the resulting shape closer to the circle. This means the approximation doe not converge to the circle but to a different made-up shape (? need help here)
>>16827450>the resulting shape closer to the circle. This means the approximation doe not converge to the circleAt most, that would prove that one approximation converges faster than the other. But the simple fact of the matter is that a circle has no corners.
>>16827327Because circles are defined by points, not sides. This shape would have infinite sides and a circle has none, just points from it's radius.Whoever made it tried to be clever but you would have to redefine what a circle is in order for this to work. It's like... 3rd grade math.
>>16827459>Because circles are defined by pointsBut all the points in OP's pic do end up at the same distance from the center.
>>16827459Reading this thread is making me incredibly sad. People saying this is a paradox and a bunch of other retarded shit don't even know what a circle is. Like, this guy >>16827336 He clearly knows a bunch of math shit but not what a point is.
>>16827462He's right and you're a brainlet.
>>16827456>But the simple fact of the matter is that a circle has no cornersBut fitting polygons with more and more... cornersJust werks?
>>16827461literally impossible if there are sides.>>16827463Look up the definition of a circle you retard. They aren't defined by sides. There is no paradox. How are you people so fucking stupid that you don't even know what a fucking circle is?
>>16827466>>16827467>80 IQ and brown
>>16827468t. 105 IQ thinks he is 120 IQ
>>16827470>80 IQ>brown>seethingName a more iconic trio.
>>16827468>>16827470Are you guys trolling or are you genuinely retarded? Do you even know how you get pi? Do you know what a point is? Circumference?I'm surrounded by idiots. This world is over.
>>16827472>t. tar-black gorilla nigger
>>16827471>>16827470>>16827468>>16827468>A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the center.>all points
>>16827474>all pointsYeah, all the points end up the same distance from the circle at the limit. Imagine being so brown you get filtered by the premise of the meme and never even get to a position from where you can start analyzing what actually went wrong.
>>16827476ok you are genuinely retarded.
>>16827477You will never increase your fluid intelligence but you can at least get your mental illness treated.
>>16827479What's your goal here chief?
>>16827327Easy, (cos(1)/2, sin(1)/2) is a point on that circle but no corner can ever map to it because they always map to algebraic coordinates. Therefore your map is bullshit.
>>16827480To convince you to take your anti-psychotic meds so that you snap out of your delusional episode making you think you belong on a "Science & Math" board.
>>16827483I honestly just feel bad for you people. You have no idea the hurt that is coming your way. You've been given every opportunity to turn things around but you just choose not to.I just don't understand how you got this way. What happened in your life to make you like this? Like, you're clearly not ok but why do you let greed control your life? What makes you want to hurt people? Do you get sexual gratification from this or what? Did they promise you a mail ordered bride? Does loneliness cause people to do things this desperate?I really need to understand people like you. Just... there is no humanity in you. There is no intelligence. Your eyes are hollow and empty. There's nothing going on in there. You just think of pussy and money and that's it.Also before you tards go off about the mental illness thing... who do you think is reading this? We all know you tards are retarded here. No one in my "real life" is going to be reading anything I post online. There is no goal here, you're not achieving anything but this is how you choose to spend your time. There are no consequences here but you still put in the effort. You are following the orders of some incredibly stupid people. It's all just really sad.
>>16827327when you have a lim f(x) while x is approaching something, the f(x) has to change tooall that pic "proves" is that p =< 4
>>16827487I'm not reading this. Take your actual, prescribed medications.
>>16827462It's not that complex, some curves will not approximate others doesn't matter how many iterations you make to get close to "infinite", if you try to extrapolate the length of your approximations to infinite (the exact geometric curve) then the result will be different, fractals have the same "problem", you would be wasting time if you expect a good behavior by using segments to measure them.Even if "visually" (for your eyes) the approximation looks similar to a circle it will never be a circle, even if it tends to a circle. You just have to compare the tangents of the approximation vs the circle and it'll be obvious there's a problem, the tangents of your approximation never tends to something circle-like (very smooth).
>>16827523>Even if "visually" (for your eyes) the approximation looks similar to a circle it will never be a circle>t. 80 IQ and brownThe limit of what OP depicts IS the circle.
>>16827526NTA but (cos(1)/2, sin(1)/2) is a point on that circle and is found nowhere in the limit of what OP depicts.
>>16827540>(cos(1)/2, sin(1)/2) is a point on that circle and is found nowhere in the limit of what OP depicts.Prove it.
>>16827526>muh IQThat pic shows an approximation of a curve with another one, approximation that fails to have a continuous length function because of the way it is built, the example is right before the last 2 rows, the last one is wrong because it assumes the length function will be continuous even if you use a curve that breaks in the "step" to infinite.
>>16827547That approximation is the circle at the limit. What doesn't follow is that the length you associate with that approximation will approach the perimeter of a circle.
>>16827544>>16827482
>>16827584Do the points that touch the circle always map to algebraic coordinates?
>>16827425isn't that the whole idea of limits and integrals?
>>16827555Basically that.
>>16827588Not sure what you mean.
>>16827330Me with my 3 inch string. );
>>16827327you are implicitly assuming that your error approaches zero, this is false.What I think is happening is as the length of your mistake approaches zero, the number of times you make that mistake approaches infinite, and it cancels out.
>>16827334>Perimeter describes the distance required to optimally traverse a shape using a series of infinitesimal steps.That is not how teacher defined perimeter in school.
>>16827613>Not sure what you mean.Look at OP's pic. The approximation touches the circle at some points. Then think about my question.
>>16827627That's literally what >>16827482 says. Your question seems to be a precursor, not a follow up, which is why it doesn't make sense. Can you clarify what you mean or are you just confused somehow?
>>16827327Take a square of perimeter 4. The top left corner. The perimeter is still 4. Remove additional corners. Perimeter is still four. In this limit you end up with something that looks like a triangle, but with a perimeter of 4 instead of the expected perimeter of a right triangle with sides unity of 2 + sqrt(2), and it's trivial to see why - drawing a step function between two points and drawing a straight line between two points is not equivalent.
>>16827644Can one of the points that touch the circle be (cos(1)/2, sin(1)/2)?
>>16827655No, that's literally what >>16827482 (You) says. Literally. You're replying to a post by asking a question that the post is literally an answer to. Like wtf lmao.
>>16827659My bad. I was too charitable in my interpretation of your post. Your statement is simply wrong.
>>16827677More like you're too charitable in your assessment of your own intelligence.
>>16827685>Science & Math>states his "math" without proofBrainlet.
Actually pi=3sqrt(3)
>>16827701>Doesn't realize his post is largely self-referential.Sub-brainlet.
>>16827729I didn't make any mathematical statements without proof ITT. Looks like you're hallucinating.
>>16827745>Your statement is simply wrong.This is well below retarded. The only form of reply you deserve is insult and mockery. So is >Looks like you're hallucinating.You're just a total clown with no redeeming qualities at all lol.
>>16827749Whom are you quoting, brainlet?
>>16827751Total clown show you are>>16827677>Your statement is simply wrong.>>16827745>Looks like you're hallucinating.
>>16827752Did you forget your meds today?
>>16827761>Self-inserts in anonymous dialogue as anon>"Did you forget your meds" subhuman retard quipTotal fucking clown lol.
>>16827765I hinted at your error multiple times but you just kept doubling down due to your mental illness.
>>16827768This isn't a dating app, you irrepressible faggot. I don't give a fuck about whatever flirty "hints" (lmao) you think you're dropping
>>16827770See >>16827701
>>16827771Not typesetting your homework for you. If you can't figure out what points the first three iterations of corners map to and induce your own proof, that's all on you.
>>16827772See >>16827701
>>16827773>>16827773
>>16827775>retard seethes so hard it starts spazzing out
>pi is an algebraic number, i know this because i did 3 iterations of [insert pi approximation]the absolute state of /soi/
>>16827777>>16827777>>16827779Non sequitur using "Indian reply syntax" I believe lol.
>>16827779It's 80 IQ browns from /pol/.
>>16827796>New brahmabot update installed
>>16827801Anally abscessed.
>>16827802Sorry to hear it
>>16827487>CTRL-C + CTRL + V in google>it's not a copypastaholy shit did I just witness the birth of a new pasta?
>>16827482Any interval, no matter how small, contains infinitely many non-algebraic numbers. Pick a point on the circle where the tangent is 45 degrees. Zoom in on its vicinity until it's arbitrarily close to a 45 degree straight line. The jaggies are recursively bisecting it. Focus on one coordinate. The jaggies are recursively bisecting that, too, covering every real number on that interval.
>>16827838Works for a line segment, fails the diagonal argument for coordinate tuples: | {x, y}^N | < | N |
>>16827840*Flip the inequality, you get it.
>>16827840Do it on the diagonal where x=y. "It's a line segment" obviously doesn't help your case. Bisecting the line segment bisects the intervals for both coordinates.
>>16827843You're making a Cantor crank 101 mistake. You can't cover an interval with a countably many steps.
>>16827468>80 IQ and brownYes, let's explain your concept as we all are 80 IQ, brown and 7 year old.Well, circle has no corners by definition, all points are on the same distance from the center. To make a corner you have to put at least one point further than another.
>>16827847Every step doubles the number of points.
>>16827854Yeah, that's what makes it uncountable. It's literally one of the most common Cantor crank arguments.
>>16827857So what's the problem? It's a countable infinity of recursive bisections producing uncountably many points to cover the interval.
>>16827858Equivalent to saying we can use countably many nodes in a binary tree to count R.
>>16827862How many nodes in a full binary tree with infinite levels? :^)
>>16827864How many bisections to cover the circle?
>>16827868I dunno but unless you can name a specific flaw in my argument (besides >Cantor bad) your claim is refuted:>>16827482>they always map to algebraic coordinatesThe recursive bisection will inevitably cover non-algebraic coordinates.
>>16827869>Cantor badYour argument fails due to Cantor's argument. Not because Cantor's argument is "bad" lol what the fuck how did you even come up with that?>The recursive bisection will inevitably cover non-algebraic coordinates.Nope, see >>16827862
>>16827327The perimeter would be spiked instead of smooth which isn't a circle
>>16827880So what's the cardinality of the set of points you get from infinite recursive bisection?
>>16827887Power set of N. What did you think it was?
>>16827891https://en.wikipedia.org/wiki/Power_set>In particular, Cantor's theorem shows that the power set of a countably infinite set is uncountably infinite. The power set of the set of natural numbers can be put in a one-to-one correspondence with the set of real numbers
>>16827896Doesn't mean it covers the circle lol. Simple counterexample.>https://en.wikipedia.org/wiki/Cantor_setIt's your lucky day, you learned something on 4chan. Rare event.
>>16827899I'm getting pretty bored of your incoherent thrashing. Should've heeded your interactions with other posters and realized you're a retard.
>>16827904>I'm getting bored of being wrongBad habit, leads to failure.
>angles>still beleiving in determinismseriously?>needs help with religionNow isn't that who we really are? As scientists y'know... dimming the sideofyeh phasallity has some pixious verbat set siyndrom in sameness is only inevitable as psychologies Anyone up fore developing the beanstalk with the castle at the top?... fuqn miracle gro everywhere.... fqqqnnnnnn 3G testicalliformiaGlue bell warming... ahsighaights~- <@#>
>>16827910You made a series of false claims, then settled on a "counter-example" to a claim I didn't make. You can get arbitrarily close to any number on an interval using repeated bisections. Since we're talking about every possible infinite sequence of bisections, that indeed covers every point on the interval. Not wasting any more time on obvious retards.
>>16827913Nope. Good luck in your fantasy world I guess.
>Retard having a meltdown because his meme floppedJust ban all non-metric countries.
>>16827623I'm surprised this one got as much attention as it did. If your shape is composed of line segments you can just add up their lengths, which is the high school definition of perimeter. You do need to modify the definition a bit when you don't have line segments.You can make an analog to this slide thread bait question that isn't complicated by curves by rotating the square in the OP 45 degrees and doing a similar construction by inscribing it inside of a larger square of side length sqrt(2). The perimeter of a square with side length 1 obviously isn't 4*sqrt(2) by the typical definition of perimeter, so the construction is problematic in the exact same manner.
>>16827838based>>16827840cringe
>>16827950jeet
>Linearity>1 DimensionalHow many positions? Each step of towards an equation of dimension itself... the serious not only does it exponentiates it makes fractions of beyond inside itself.... 'nows' like.. bullshit. call that shit elementary... fucking hyper suspension ...Go love that shit you jeez...#binaryheartsmithszzz's
>>16827327>Prove that this is wrongJust drill a hole that way.
>Prove that this is wrong.It's not. You just need to do it with a regular polygon with side count approaching infinity. The answer shrinks with the count increasing.
>>16827327>Prove that this is wrong.This construction is only a circle at the limit, but then the side lengths are 0, so it gives you no actual way to calculate the perimeter.
>>16827482Good post, simplest disproof itt.OP construction will never be able to construct a non-algebraic coordinate.
>>16827364
>>16829370Extremely obvious samefagging.
>>16829731>Extremely obvious seethingNope, >>16829370 isn't me. You're just mad you still don't understand why 2^N points almost never covers an interval lol.
>>16829735>same misunderstanding about how to use a coma>same insertion of newlines where they don't belong>same use of made up terms>same nonsensical "argument" repeated>updooting a post that literally no one cares aboutLearn to samefag correctly.
>>16829742comma*
>>16829742You seem to be wrong about everything. Sucks to be you I guess
>>16829743No, coma works better for you lmao. Dumb mf.
>>16829745Learn to samefag correctly.
>>16829747>01:38>02:40Kek. Learn to samefag correctly. Or better yet, just go back to the upvote arrows website.
>>16829748>If I say it enough I'll come out of my comaDoubt
>>16829750Those are both me you absolute ass. Fucking lol.
>>16829731Not samefagging lol, you're bitter
Me>>16829752Not me>>16829757Faggot>>16829750
>>16829752>Those are both meClearly. Also see >>16829742. Closing this retard-tier thread now, but your mental illness will force you to shit out another post that no one will ever read.
>>16829759>Punch bug no returnIndian debate syntax.
>>16827391its base 8 baby in base 11 you cant justify any fractions at all and its not 12 because 12 is already more than 10 and theres no reason anyway 5 is upside down 2 because 10/2 is 5 and 10/5 is 2 which indicates that god would like you to remove numbers 3 and 7 or add numbers before and after 5 and or remove 5 when you do this
