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Calculating the surface area of a sphere (i.imgur.com)

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トップ新着論争中古い順Q&A

[–]Joey_Tulo 13.8k ポイント13.8k ポイント  (555子コメント)

I feel like I just learned something, but in my heart, I know I haven't.

[–]seven3true 1505 ポイント1506 ポイント  (31子コメント)

I feel like I did the opposite of learning and had resorted to "whaaa?"

[–]unvaluablespace 594 ポイント595 ポイント  (21子コメント)

So you turned into Wario?

[–]catechlism9854[🍰] 23 ポイント24 ポイント  (1子コメント)

https://youtu.be/RlbARlVyRAc

[–]youtubefactsbot 12 ポイント13 ポイント  (0子コメント)

Professor Farnsworth: Eh wha? [0:02]

Eloquent as always, professor.

MisterCellaneous in Film & Animation

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    [–]StubbornPotato 884 ポイント885 ポイント  (389子コメント)

    Honestly Calculus is far simpler and intuitive than most people are led to believe.

    [–]itsbull1 364 ポイント365 ポイント  (129子コメント)

    I was intimidated by math for a very long time and placed Calculus on this pedestal as some form of god like math. After actually taking Calc I actually found it easier and more enjoyable than my pre-calculus classes. For me the learning curve in pre-calculus was steep as my foundation was poor and there are so many topics included in the curriculum.

    [–]prestology 128 ポイント129 ポイント  (85子コメント)

    How steep was the learning curve though?

    [–]1-_-7 160 ポイント161 ポイント  (69子コメント)

    80°

    [–]YummyMellow 318 ポイント319 ポイント  (57子コメント)

    NOT RADIANS? Hisssssssss

    [–]Sgtcockboner 303 ポイント304 ポイント  (37子コメント)

    Tfw you finished your physics exam only to realize your calculator was still in radians

    [–]maoxingren 191 ポイント192 ポイント  (4子コメント)

    Just reading that gave me a small panic attack

    [–]portatoes 60 ポイント61 ポイント  (5子コメント)

    That test was easy as pi.

    ... oh fuck.

    [–]psychic_mudkip 30 ポイント31 ポイント  (3子コメント)

    Talk about a complete 180!

    [–]ryry1237 11 ポイント12 ポイント  (0子コメント)

    180 radians = 10313.24 degrees = 28.65 rotations

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      [–]clubba 20 ポイント21 ポイント  (0子コメント)

      r2 , Brutus?

      [–]TheDiplo 38 ポイント39 ポイント  (18子コメント)

      I wish I understood this but I'm an uneducated peasant

      [–]Spartanobeana 29 ポイント30 ポイント  (1子コメント)

      Your calculator can give you the answer to some problems in either radians or degrees since they are proportional so if you have the wrong one selected then your answers will be way off.

      [–]prestology 16 ポイント17 ポイント  (5子コメント)

      To add to other response, radians are just another unit of angle. Just like inches and centimetres. Look at the wikipedia page for radians and you will see that for maths, radians are a much more intuitive way to measure angles.

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          [–]AtomicSteve21 12 ポイント13 ポイント  (11子コメント)

          4/9 pi. rad.

          I think I'll take the degrees on this one.

          Edit: That's 1.396 rad = 80 degrees I have methodology below

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            [–]monkeyfett8 8 ポイント9 ポイント  (1子コメント)

            Which itself is only a point on the curve

            d/dT learning(T)

            [–]P0sitive_Outlook 23 ポイント24 ポイント  (8子コメント)

            Sorry, Brit here.

            We talking Fahrenheit or what?

            [–]boogiemanspud 33 ポイント34 ポイント  (4子コメント)

            Sorry, Brit here. We talking Fahrenheit Freedom Units or what?

            FTFY

            [–]hydrospanner 14 ポイント15 ポイント  (0子コメント)

            I think with the whole Brexit thing they get to start using occasional Freedom Units here and there. That's fair.

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                [–]AtomicSteve21 22 ポイント23 ポイント  (2子コメント)

                I found it somewhat derivative.

                [–]beitasitbe 12 ポイント13 ポイント  (1子コメント)

                If the learning curve is a 2D differentiable function on the x-y plane defined by the function f(x), then it could be found using (d/dx)f(x)

                [–]znnydp 10 ポイント11 ポイント  (4子コメント)

                You need to know algebra, a little bit of geometry and trigonometry, and the rest is a lot of math homework and practice.

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                  [–]PiousLiar 46 ポイント47 ポイント  (23子コメント)

                  Then Calc 2 in college steps up to the plate, and sends a line drive straight to your groin

                  [–]yalittleweirdy2 18 ポイント19 ポイント  (6子コメント)

                  Yeah I just found out that I got a D+ in Calc 2. I'm equally disappointed in and proud of myself.

                  [–]GummyKibble 10 ポイント11 ポイント  (3子コメント)

                  I'm finding that's the universal weed-out course. We lost a lot of my fellow CompSci majors that semester.

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                    [–]RyGuy997 5 ポイント6 ポイント  (5子コメント)

                    And then Calc 3 comes from behind it with the bat

                    [–]Austiz 3 ポイント4 ポイント  (4子コメント)

                    Just got a B in calc 2, I was so fucking happy.

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                      [–]Cody6781 9 ポイント10 ポイント  (1子コメント)

                      They take you through the creation of calculus rather than just straight teaching it to you. This has some benefits, but TBH just learning it probably would be better for most majors

                      [–]HasTwoCats 8 ポイント9 ポイント  (0子コメント)

                      I actually felt the same way, and ended up getting a degree in mathematics because I enjoyed calc so much.

                      [–]TheMaybeN00b 24 ポイント25 ポイント  (3子コメント)

                      Calculus is easy, its the Algebra that fucks you over

                      [–]itsbull1 20 ポイント21 ポイント  (2子コメント)

                      Yeah, there were times while learning Calculus I would forget essential algebra concepts.

                      [–]Oomeegoolies 21 ポイント22 ポイント  (1子コメント)

                      Nothing worse than forgetting trig functions, especially to simplify.

                      It's like, I've been doing that for years, but somehow when I saw it in the middle of an exam question I'd blank and keep doing the working out in the more complex form. I'd end up with the same answer in the end but I wouldn't simplify until the very end and I'd be like "Ohhhh, yeah, sin(x)/cos(x) is tan(x). I'm an idiot."

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                        [–]Kalentrine 224 ポイント225 ポイント  (114子コメント)

                        It's the Algebra that gets you.

                        [–]schwooples 118 ポイント119 ポイント  (96子コメント)

                        Oh man, algebra is insanely hard. I'm fine with calculus and real analysis, but groups and fields and stuff are way over my head.

                        [–]Kalentrine 134 ポイント135 ポイント  (24子コメント)

                        I just hated going "Awesome! Look at this cool shit I'm doing with Math." To be followed immediately by "Fuck, now I have to do all of that Algebra..."

                        [–]MizchiefKilz 40 ポイント41 ポイント  (23子コメント)

                        For me it was the time limits on tests that killed me. If I could work out all the algebra using the basic shit I could do it, it was remembering all the damned rules and shortcuts.

                        [–]oddstorms 21 ポイント22 ポイント  (19子コメント)

                        Wow, you all give me hope. I never had a hard time with algebra and I've always wanted to learn advanced math and chemistry.

                        [–]lightedd333 16 ポイント17 ポイント  (10子コメント)

                        From my experience, people who are good at calculus and advanced math are bad with algebra. And people who like algebra, dont get advanced math. Don't let that stop you though!

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                            [–]china999 39 ポイント40 ポイント  (6子コメント)

                            I think they're probably talking about elementary algebra, factoring, inequalities etc... Whereas what you're talking about is often called Abstract algebra (depending on the person really).

                            Without proper foundations it's all pretty brutal though, and why education is so important early on

                            [–]COLDSIEMENS 13 ポイント14 ポイント  (5子コメント)

                            College algebra is basically algebra 1 & 2 from highschool. Abstract algebra is a different course.

                            [–]csbrandon 14 ポイント15 ポイント  (2子コメント)

                            I did that and failed. 'Mathematics for Cryptography' they called it. "It'll be fun", I told myself enthusiastically, thinking I was going to be the next Alan Turing.

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                              [–]StubbornPotato 29 ポイント30 ポイント  (18子コメント)

                              Yeah I'm not a fan of proof and theory courses. The Hardest class I've ever taken was Complex analysis, where all those non-real solutions that were ignored in Algebra and Calculus had to be accounted for and solved. Quadratics became a real pain in the ass and any trig function doubled in complexity. (pun intended)

                              [–]raguirre1 27 ポイント28 ポイント  (39子コメント)

                              I was one college credit away from a degree. I couldn't pass college algebra. I'm embarrassed. Sad thing is, I even had a tutor the last go around and still couldn't get it to click. I took it 3 times.

                              [–]StubbornPotato 19 ポイント20 ポイント  (4子コメント)

                              Hey man, I had to take multiple math course several times. I called it "beating my head against the wall." You did what needed to be done, and did like the potato and got stubborn

                              [–]randomburner23 24 ポイント25 ポイント  (14子コメント)

                              If it makes you feel better, my friend failed linear algebra 3x before passing it. He's a c++ programmer working on counter strike now.

                              [–]turtlemenace 54 ポイント55 ポイント  (3子コメント)

                              Can you ask him to fix hitreg /s

                              [–]DreadedDreadnought 6 ポイント7 ポイント  (2子コメント)

                              LinAlg still haunts me in my nightmares.

                              [–]MizchiefKilz 11 ポイント12 ポイント  (0子コメント)

                              Depending on what he is doing exactly, most programmers use little math and almost no algebra. It's all logic and then just plugging shit into math functions other people made when we need it.

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                                    [–]kmacdowell 23 ポイント24 ポイント  (2子コメント)

                                    In my experience, the way precalculus is taught is often very poor.

                                    Learning 5 formulae for each conic sections so you can identify foci, vertices, directrices, axes of symmetry, asymptotes, major axes, minor axes, covertices, etc. is simply not taught in a compelling way.

                                    And all of those points and the ways to find them are in fact interesting and meaningful, but every precalc course I have seen that teaches conic sections just gives huge lists of formulae with little explanation.

                                    Calculus is simple enough that most parts are intuitive, i.e. limits -> derivatives, Riemann sum -> integral, etc.

                                    [–]xnfd 5 ポイント6 ポイント  (1子コメント)

                                    The rest of precalc was pretty useful as a base for further math, but all that conic section stuff seems pretty pointless for most people, even those who will go into applying calc all the time. I don't think all high schools cover it in depth though.

                                    Imaginary numbers weren't taught in a compelling manner, and the applications weren't quite clear, but those turned out to be tremendously important for signal processing.

                                    [–]hfxdke 18 ポイント19 ポイント  (4子コメント)

                                    I think I'd learn it better if teachers showed me visuals on how it's done. Most teachers just list the steps on the worksheets. Like, what the fuck is a box and whiskers?

                                    [–]Kalentrine 7 ポイント8 ポイント  (0子コメント)

                                    Having visual reference for Cal is very helpful. I remember once could see graphing for Integrals, it all just clicked.

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                                        [–]AssholeBot9000 27 ポイント28 ポイント  (0子コメント)

                                        Because so many teachers teach it wrong.

                                        I struggled with some precal and Calc in high school, I got to college and had a professor who did an amazing job. With demonstrations like this it was like, "this is amazing and so easy!"

                                        [–]fishsticks40 32 ポイント33 ポイント  (19子コメント)

                                        I've been telling people this for years. Linear algebra? Black magic. Calculus? Basically fancy addition. I can't think of another mathematical area that's so quietly elegant and intuitive.

                                        [–]StubbornPotato 28 ポイント29 ポイント  (3子コメント)

                                        Yeah. I always sensibly chuckle to myself when I remember the fact that then twenty something Newton hashed Calculus out during a school break due to the outbreak of a plague

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                                          [–]itonlygetsworse 12 ポイント13 ポイント  (1子コメント)

                                          "It is simple calculus" - Dota 2's 9th most used meme

                                          [–]lickmyepididimis 6 ポイント7 ポイント  (1子コメント)

                                          I know what you mean. But i've been intimidated by math eversince i was a small lad, so no can do for me.

                                          [–]rytro2 4 ポイント5 ポイント  (1子コメント)

                                          Its really true and the problem is the way its taught or maybe its always taught too quickly and they never grasp what they are doing. The professors explain a very important key concept in 10 minutes then move on to examples and then to the next topic next week.

                                          [–]antigravitytapes 4 ポイント5 ポイント  (0子コメント)

                                          the Menos and Socrates' teaching of the Pythagorean theorem to that slave was when i realized math is actually intuitive in many many ways.

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                                            [–]Starklet 258 ポイント259 ポイント  (67子コメント)

                                            A sin wave is basically drawing a circle

                                            https://imgur.com/c9P9FPl

                                            [–]_Skylake_ 167 ポイント168 ポイント  (53子コメント)

                                            ok, but what do I do with this information?

                                            [–]ISkipLegDayAMA 190 ポイント191 ポイント  (1子コメント)

                                            make sweet gifs

                                            [–]throwawayzax 42 ポイント43 ポイント  (2子コメント)

                                            A lot of things. for instance, you can model any rotary motion"like that of an electric engine" using a simple Sin function, and that may help an engineer to know exactly how much speed and torque his engine is outputting.

                                            [–]QuinZ33 64 ポイント65 ポイント  (14子コメント)

                                            It helps you understand trigonometry, which helps you with calculus and physics, which are used in the fields of physics, engineering, chemistry, finance, and others.

                                            [–]chokoladeibrunst 16 ポイント17 ポイント  (12子コメント)

                                            How is it used in finance?

                                            [–]UrMumsMyPassword 57 ポイント58 ポイント  (1子コメント)

                                            Wicked pie charts

                                            [–]fukitol- 10 ポイント11 ポイント  (1子コメント)

                                            Prediction algorithms, statistics. Basically if you can plot something over time you can use calculus to draw conclusions about it.

                                            [–]max_adam 5 ポイント6 ポイント  (0子コメント)

                                            You can represent with a sin wave how your money goes off.

                                            [–]QuinZ33 4 ポイント5 ポイント  (0子コメント)

                                            Well, there's the Black-Scholes equation for a really famous example.

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                                                  [–]hombredeoso92 40 ポイント41 ポイント  (5子コメント)

                                                  That's an inverted cos wave though

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                                                    [–]overglance 51 ポイント52 ポイント  (8子コメント)

                                                    I can already see myself trying to explain this. "You crack open the sphere, lay it all out. It's a line of pointy oval things and when you outline them it's another oval. Split that oval in half and bam, a sin wave"

                                                    [–]aarghIforget 32 ポイント33 ポイント  (1子コメント)

                                                    "Here, hand me that orange... and some paper towels."

                                                    [–]down_vote_city__ 10 ポイント11 ポイント  (0子コメント)

                                                    Jesus, take the wheel!

                                                    [–]ExtraPockets 5 ポイント6 ポイント  (3子コメント)

                                                    It's the outline part that feels a bit wrong because it fills in an area that wasn't part of the sphere.

                                                    [–]archifeedes 6 ポイント7 ポイント  (0子コメント)

                                                    I don't think it's tracing the outline, just combining the areas. See how the curvature increases as the sections combine?

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                                                        [–]GobletOfDiarrhea 51 ポイント52 ポイント  (2子コメント)

                                                        http://i.imgur.com/zBL0MZt.jpg

                                                        [–]flappytowel 15 ポイント16 ポイント  (1子コメント)

                                                        well that's math for you

                                                        [–]euripidez 7 ポイント8 ポイント  (0子コメント)

                                                        Higher education more generally

                                                        [–]Invisophil 18 ポイント19 ポイント  (0子コメント)

                                                        Wow if someone showed me this is wouldn't have had to take calc1 one and calc 2 twice. Fuck I graduated already

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                                                          [–]AlonEijk 1726 ポイント1727 ポイント  (180子コメント)

                                                          I never understood what the fuck that graph was referring to, thanks OP

                                                          [–]ArmanDoesStuff 657 ポイント658 ポイント  (132子コメント)

                                                          I always thought it graphed a single point along the edge of a circle

                                                          [–]offoutover 498 ポイント499 ポイント  (95子コメント)

                                                          That's pretty much where the unit circle comes from.

                                                          [–]drinks_antifreeze 50 ポイント51 ポイント  (8子コメント)

                                                          As a math major it pisses me off to no end that high school students are forced to memorize that whole thing, while rarely ever getting a proper explanation on what it actually means. It's just a model to illustrate the trigonometric functions. That's it. It's not a mystical black box source of truth (I'm pretty sure sine, cosine, and tangent are all rigorously defined by their Taylor Series), it's a visual aid.

                                                          It's saying, "Hey, imagine if we had a triangle with a hypotenuse of fixed length 1. If we could drag it around in a circle to give its interior angle angle every value between 0 and 2π, the lengths of the legs would be the same values for sine and cosine of that angle."

                                                          This idea could be conveyed so easily through creative teaching or watching LucasVB gifs, but instead students are just told to shut up and memorize. It really grinds my gears. But that pretty much applies to all high school math, which is probably why so few kids can appreciate it for being interesting in the first place.

                                                          [–]offoutover 5 ポイント6 ポイント  (0子コメント)

                                                          Yeah, only after the fact of learning something like this do I have an axe to grind about how it's taught and I know you mentioned high school but I noticed this in college and heaven forbid you try and shake up a STEM college's system of teaching.

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                                                            [–]4rch 783 ポイント784 ポイント  (71子コメント)

                                                            triggered

                                                            [–]offoutover 212 ポイント213 ポイント  (66子コメント)

                                                            PTSD from too much calc homework? I must say, when I looked up the image I had a wave of dread rush over me as if I had tons of homework due tomorrow in which I hadn't even started yet.

                                                            [–]mkeene19 169 ポイント170 ポイント  (48子コメント)

                                                            please you memorize that shit by the time calc comes

                                                            [–]freeyourthoughts 105 ポイント106 ポイント  (0子コメント)

                                                            Yeah I've been meaning to do that for the last ten years.

                                                            [–]pandamite1 23 ポイント24 ポイント  (6子コメント)

                                                            It's honestly easier than most people think. I memorized it by going sin of 30, 45, 60 is simply 1,2,3 as the numerator while 2 always being the denominator. Following cos to be the exact opposite being 3,2,1.

                                                            [–]drakslayer1 7 ポイント8 ポイント  (0子コメント)

                                                            Yup a friend taught me this and I was like HOLY SHIT IT'S SO EASY TO REMEMBER NOW. With just the 1,2,3 and 3,2,1 you figure out the entire unit circle and all the values by reflecting them across the axis appropriately.

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                                                              [–]Orange134 61 ポイント62 ポイント  (30子コメント)

                                                              If you're trying to memorize this, then you're doing math wrong. You should be learning the relationship between the angles, pi, and the points.

                                                              [–]Ahten_Xevious 47 ポイント48 ポイント  (10子コメント)

                                                              You just need to remember sqrt(3)/2, sqrt(2)/2, and 1/2, and where they go for 30, 45, and 60 degrees, then the rest writes itself. You know that sqrt(3)/2 is larger than 1/2, so if the x is larger, it's (sqrt(3)/2, 1/2) and vice versa. I have an absolutely awful time memorizing things, but this was kinda easy for me.

                                                              [–]skuchoochum 40 ポイント41 ポイント  (1子コメント)

                                                              Why are you squirting on everything?

                                                              [–]PmMePicsOfYourDog 10 ポイント11 ポイント  (1子コメント)

                                                              skrt skrt

                                                              [–]inverterx 4 ポイント5 ポイント  (0子コメント)

                                                              Because it's a pretty easy and intuitive pattern, you memorize those three values, and you have the whole unit circle.

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                                                                    [–]StaticTransit 12 ポイント13 ポイント  (8子コメント)

                                                                    This is basic trig stuff yo

                                                                    [–]HillaryShitsInDiaper 7 ポイント8 ポイント  (0子コメント)

                                                                    Yeah, but you don't start really caring until you need to know all of it to solve calc problems.

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                                                                        [–]HillaryShitsInDiaper 37 ポイント38 ポイント  (0子コメント)

                                                                        Triggernometry

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                                                                          [–]marcxvi 4 ポイント5 ポイント  (6子コメント)

                                                                          oh god i had to memorize that shit

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                                                                            [–]Lmaobox_TF2_scruby 39 ポイント40 ポイント  (16子コメント)

                                                                            This makes a lot more sense.

                                                                            [–]thatisnothow 104 ポイント105 ポイント  (15子コメント)

                                                                            http://i.imgur.com/zhAXFUo.gif

                                                                            [–]em_square_root_-1_ly 27 ポイント28 ポイント  (0子コメント)

                                                                            That is beautiful!

                                                                            [–]aarghIforget 53 ポイント54 ポイント  (1子コメント)

                                                                            Oh my god that is terrifying.

                                                                            [–]tiger8255 13 ポイント14 ポイント  (0子コメント)

                                                                            Probably because it has all of them at once. If you had one or two graphed, it would likely not be quite as scary.

                                                                            [–]auCoffeebreak 17 ポイント18 ポイント  (2子コメント)

                                                                            Yes, yes, I see. Everything makes perfect sense now.

                                                                            [–]lagvvagon 11 ポイント12 ポイント  (1子コメント)

                                                                            I love the first 2 comments to this.

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                                                                              [–]briandoescode 9 ポイント10 ポイント  (3子コメント)

                                                                              Yes, that's what it's actually defined as.

                                                                              Source: calc student

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                                                                                [–]DMPDrugs 47 ポイント48 ポイント  (10子コメント)

                                                                                That isn't what the graph is referring to. The just smoothed the pieces into the shape of the graph. Might as well have made a square, and measured that.

                                                                                [–]v12a12 22 ポイント23 ポイント  (6子コメント)

                                                                                Actually though, this post appears to have appealed to many people's misunderstanding of calculus. A sine curve is not based on the transformation of a sphere at all, it is the ratio of two lengths of a right triangle for a given angle.

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                                                                                  [–]kluvin 141 ポイント142 ポイント  (21子コメント)

                                                                                  I can't possibly understand why this isn't demonstrated or shown more in school, it would've made so much more sense so much faster.

                                                                                  [–]jeremiah406 43 ポイント44 ポイント  (4子コメント)

                                                                                  I was about write that. It's like I just opened my eyes for the first. I get it now!

                                                                                  [–]kluvin 31 ポイント32 ポイント  (3子コメント)

                                                                                  I was recently told the sine wave is a flattened circle, it didn't really click. I just don't get why no one demonstrates it :/ Also, the square wave makes a lot more sense now I guess.

                                                                                  EDIT: no>mo

                                                                                  [–]i_like_tube_amps 24 ポイント25 ポイント  (8子コメント)

                                                                                  It probably was, it was when I was in school, in a lot of classes.

                                                                                  It's easier to take information in once you've already known it.

                                                                                  That's why you always feel like you found the perfect resource after you spent ages on all those other ones.

                                                                                  That sensation is "revision" as opposed to "study".

                                                                                  [–]kluvin 7 ポイント8 ポイント  (6子コメント)

                                                                                  Well, I'm still in high school, so this has only been glossed over let alone covered. Though now that you mention it, there is indeed a difference between revision and learning, especially when more than a week has passed.

                                                                                  [–]i_like_tube_amps 11 ポイント12 ポイント  (5子コメント)

                                                                                  It's a shame cause these days teachers could literally just show you a perfect youtube video to get the ball rolling.

                                                                                  I think the GIF OP linked is high quality but not very good content, it's just some squidiness. And is like alakazam sine!

                                                                                  This one is quite good: https://en.wikipedia.org/wiki/Sine#/media/File:Circle_cos_sin.gif

                                                                                  [–]kluvin 7 ポイント8 ポイント  (2子コメント)

                                                                                  Definitely, but most of my teachers (being over 50) are a bit technologically inept, but that's how it is I guess.

                                                                                  Oh and; what tube amps do you like? Assuming it is for headphones, because I am on the look for one ;)

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                                                                                        [–]babobudd 12 ポイント13 ポイント  (0子コメント)

                                                                                        FYI, this gif is an inaccurate representation and if you think you have a better understanding of math after watching it, you are wrong.

                                                                                        There is a nice way to visualize the transformation of a sphere into a 1d sine function, but this is not it.

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                                                                                          [–]XkF21WNJ 421 ポイント422 ポイント  (17子コメント)

                                                                                          /r/restofthefuckingowl.

                                                                                          [–]MrVandalous 140 ポイント141 ポイント  (5子コメント)

                                                                                          How to calculate the surface area of a sphere:

                                                                                          Step one, gather a basic understanding of 3d modeling and rendering.

                                                                                          Step two, make a sphere.

                                                                                          Step three, lay a wireframe on the sphere.

                                                                                          Step four, animate the sphere.

                                                                                          Step five, ???

                                                                                          Step six, ?....

                                                                                          Step seven, spherical surface area.

                                                                                          [–]v12a12 48 ポイント49 ポイント  (6子コメント)

                                                                                          Honestly this gif is unnecessary. The last step requires integrals, which is calculus. If you have access to integrals, you can just derive the volume of the sphere directly (actually using the Pythagorean theorem in a cool way).

                                                                                          [–]XkF21WNJ 11 ポイント12 ポイント  (3子コメント)

                                                                                          This is a 'calculation' of the surface area though, but yeah in the end it's just integration.

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                                                                                              [–]PastelFlamingo150 284 ポイント285 ポイント  (21子コメント)

                                                                                              When I add up those 2 curves, I get 0

                                                                                              [–]joeyhatesrain 172 ポイント173 ポイント  (15子コメント)

                                                                                              The second half of the curve is below the x-axis, meaning that its integral (the area between the curve and the x-axis) is negative. If you calculate it correctly (from left to right), it should give zero so you did that right. The reason this doesn't work for finding area is that area is always positive, so you have to compensate for the part of the curve that has a negative integral by simply making it positive.

                                                                                              In the GIF, if you notice on the final line, the integral is not set up from left to right (since, as you found out, it adds up to zero because both sides cancel each other). They split the area into two sections. The first integral is taken from the origin to the halfway point and the second is taken from the end of the graph to the middle (or 'backwards' so to speak). Taking the second one backwards simply makes the value negative so it turns the initially negative value positive in the end. The sum of those two (+first half and -second half, which was negative to begin with so it becomes positive) is the surface area.

                                                                                              [–]treefing3rs 62 ポイント63 ポイント  (2子コメント)

                                                                                              I thought he meant that if you take a curve (
                                                                                              And you take another curve )
                                                                                              And you smush them together ()
                                                                                              You get 0
                                                                                              But, you know, your way's probably good too...

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                                                                                                [–]MonkeyCB 5 ポイント6 ポイント  (0子コメント)

                                                                                                If you do regular homework, yes. But notice the second equation has the interval backwards. So we're technically adding the inverse of the second part.

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                                                                                                  [–]berniebrah 775 ポイント776 ポイント  (143子コメント)

                                                                                                  I understand the surface of the sphere unraveled...then it just gets smooshed into a parabola? That part seems tricky to "calculate" as the title suggests

                                                                                                  [–]Deto 698 ポイント699 ポイント  (84子コメント)

                                                                                                  It's a sine wave, not a parabola. Slightly different in shape.

                                                                                                  But yeah, they might as well have just smooshed it into a square.

                                                                                                  [–]Joshtopher_Biggins 308 ポイント309 ポイント  (28子コメント)

                                                                                                  You're a sine wave

                                                                                                  [–]cartechguy 6 ポイント7 ポイント  (16子コメント)

                                                                                                  So is the surface area of a sphere equal to the area of a sine wave for one period?

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                                                                                                    [–]14sierra 76 ポイント77 ポイント  (17子コメント)

                                                                                                    I thought the same, it was great up until that point then it lost me.

                                                                                                    [–]lucasvb 92 ポイント93 ポイント  (13子コメント)

                                                                                                    It's because it's wrong. That step is an invalid transformation, as it's changing the Gaussian curvature from positive (sphere) to zero (flat). Using the flat faces as approximation doesn't help because they won't converge to the area of the sphere unless you also make then thinner, but then the visualization doesn't work.

                                                                                                    You can't flatten those ()-shaped strips from an actual sphere without stretching/compressing them (that is, changing their area - this is Gauss' Theorema Egregium), so by assuming the flat () shapes have the same area as the bent ones you already assumed the result of the calculation.

                                                                                                    The animation is trying to illustrate how to setup an integral, but it's doing it in a roundabout way that's simply misleading. It's unjustified eye candy.

                                                                                                    EDIT: To illustrate, what the animation is doing is approximating the sphere with slices off the side of a cylinder, which can be flattened because the cylinder has zero curvature. This is because the only limit being taken here is in the number of subdivisions on each slice. However, you also need to increase the number of slices if you want to compute the area of the sphere properly, but then each slice would be infinitely thin and all these visuals would be pointless.

                                                                                                    Purely from the visuals, the flattened area shown in the animation is the area of this weird sphere-like thing, which clearly has a larger area than the sphere. The area of the shapes on the paper cannot equal the area of the sphere.

                                                                                                    So you can't simply flatten those slices, stack them and use that to magically show a sine for your integral. You didn't justify that step.

                                                                                                    [–]ArmpitPutty 19 ポイント20 ポイント  (2子コメント)

                                                                                                    That's why all the people in here saying they've "learned something" or "finally get it" are full of it. The only thing this gif teaches is that the area of the sphere is the area of this segment of a sine wave.

                                                                                                    [–]TheVegetaMonologues 11 ポイント12 ポイント  (2子コメント)

                                                                                                    "So, to figure out the area of a sphere, you just cut it into a bunch of pieces and then figure it out."

                                                                                                    [–]frozensun516[🍰] 17 ポイント18 ポイント  (1子コメント)

                                                                                                    You're taking the length of each strip at each position x and adding them together. It is very impractical to calculate that way, but this just serves to show the derivation of the equation for the surface area of a sphere, which is shown at the very end.

                                                                                                    [–]Denziloe 5 ポイント6 ポイント  (0子コメント)

                                                                                                    What they're saying is that it doesn't fully show the derivation, because it doesn't clearly demonstrate that you would get that particular curve by stacking the pieces.

                                                                                                    [–]Jaybleezie 11 ポイント12 ポイント  (1子コメント)

                                                                                                    I think it's just compressing the gaps after it gets laid out flat and that shape is what we're left with. Confused me too and I could be wrong but that's just my guess.

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                                                                                                      [–]Squirtleyngmt 405 ポイント406 ポイント  (17子コメント)

                                                                                                      Was expecting send nudes

                                                                                                      [–]evlbuxmbetty 82 ポイント83 ポイント  (8子コメント)

                                                                                                      Sent this to my husband and all he responded was "wrong" then called to give me a very long and technical explanation of the theory behind whatever fucking formula it is to calculate the surface area of a sphere and fuck now I feel like I know even less than before this gif came into my life.

                                                                                                      [–]thepest97 52 ポイント53 ポイント  (3子コメント)

                                                                                                      Ok. So....magic.

                                                                                                      [–]Yvanko 21 ポイント22 ポイント  (4子コメント)

                                                                                                      Mathematician here: this gif makes 0 sense, even if you slice sphere you cananot flatten it the way shown.

                                                                                                      Pretty much even small pieces of sphere cannot be flatten preserving their internal structure.

                                                                                                      [–]MyNameIsZaxer2 4 ポイント5 ポイント  (0子コメント)

                                                                                                      But what if you slice it... infinity times?

                                                                                                      This gif is just demonstrating a calculus concept in layman's terms. The same way they teach you reimann sums of A=4 before moving on to reimann sums as A approaches infinity.

                                                                                                      This is the "reimann sum" of sorts of a sphere cut into 20 pieces. If we cut the sphere into "infinity" pieces it becomes fully accurate.

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                                                                                                        [–]Redingold 64 ポイント65 ポイント  (10子コメント)

                                                                                                        This is stupid, the final step relies on knowing calculus. If you can do calculus, finding the area of a sphere is not complicated, and if you can't do calculus, then you can't use this to find the area of a sphere. Either way, it's not helpful to anyone.

                                                                                                        Also, it gives us no good reason to assume that the area in these steps is constant. It could well be using trickery to manipulate the areas at each step, like how this gif manipulates the area of its triangles to create chocolate from nothing. It isn't actually doing this, but you couldn't verify that without knowing that it produces the right answer in the end, which defeats the point.

                                                                                                        [–]-but_it_do- 108 ポイント109 ポイント  (21子コメント)

                                                                                                        This teaches you nothing and is just pure graphical bullshit. They don't show how the unraveled sphere equals that region they graphed.

                                                                                                        Anyone who has taken Calc 2 should know how to derive the formula for the surface area of a sphere, though. HINT: It's the sum of all arc lengths (integral) of a circle revolved around an axis. Using polar coordinates makes it ridiculously easy. If you took Calc 3 (a.k.a. multivariable calc), it should be even easier.

                                                                                                        EDIT: I paused it to check out their integral. They don't show how they arrived to that integral (you can sorta guess how, though), they completely glossed over how the fuck they obtained the region to integrate.

                                                                                                        [–]FF1750 32 ポイント33 ポイント  (11子コメント)

                                                                                                        It's kind of sad. But what's sadder is the plethora of people that are like "ohhhh ok I get it now blah blah blah". Yeah... I'm sure you understand the topology behind converting the area of a sphere to a graph...

                                                                                                        [–]hitlerallyliteral 3 ポイント4 ポイント  (0子コメント)

                                                                                                        here's the counter-circlejerk I was looking for... this animation is useless because it doesn't show you why the area's are equivalent, it doesn't even avoid the need for calculus and all the people going 'now I get it, why couldn't the teacher have shown me this', don't get it

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                                                                                                          [–]jsmooth7 5 ポイント6 ポイント  (0子コメント)

                                                                                                          Yeah it is not at all obvious that the deformations they did don't change the area, plus it's not obvious that the final shape would be a sine curve. And then you still have to do calculus at the end anyways. You might as well just start with calculus.

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                                                                                                            [–]pannekakekake 10 ポイント11 ポイント  (1子コメント)

                                                                                                            "draw the rest of the owl"

                                                                                                            [–]Frptwenty 15 ポイント16 ポイント  (0子コメント)

                                                                                                            Is this the final exam in animation school?

                                                                                                            [–]BlueWallBook 6 ポイント7 ポイント  (1子コメント)

                                                                                                            That is not correct you can't just fill in space

                                                                                                            [–]RamsesThePigeonThor 173 ポイント174 ポイント  (78子コメント)

                                                                                                            On my first day learning calculus, I asked my professor how it was actually used.

                                                                                                            He replied by saying that we'd cover that as the semester went on.

                                                                                                            It took me several months of rote memorization and repetition before I finally (and independently) realized that our lessons had to do with three-dimensional objects... and I can't help but feel that if I'd just been shown this animation, I would have understood things much more easily.

                                                                                                            [–]i_like_tube_amps 271 ポイント272 ポイント  (34子コメント)

                                                                                                            Hate to break it to ya but calculus isn't "to do with three-dimensional object", anymore than it's to do with the temperature of your bath tub.

                                                                                                            Calculus is the mathematics of change (differentiation) and the accumulation of those changes (integration).

                                                                                                            It's a mathematical tool, just like algebra is to do with relations and operations and no one thing.

                                                                                                            [–]cartechguy 14 ポイント15 ポイント  (15子コメント)

                                                                                                            I've been told from the youtubes it's the math of physics and was even discovered to explain the motion of our planets. I'm just starting to dabble with integral calculus so my understanding of how much application Calc has is limited. I did just learn about optimization with objects. That was actually pretty simple surprisingly.

                                                                                                            Oh, and I can't take the physics class I need for my major until I complete integral calculus so that also affects my perception of the purpose/application of calc.

                                                                                                            [–]Hispanicwhitekid 28 ポイント29 ポイント  (9子コメント)

                                                                                                            Calculus can be used to describe basically anything that changes with time. So the application is extremely wide, but with physics you'll mostly use the equations derived after the calculus operations are already done.

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                                                                                                                [–]w_a_s_d_f 116 ポイント117 ポイント  (8子コメント)

                                                                                                                ...really? like the first thing you should learn after differentiation is the relationship between displacement -> velocity -> acceleration. Sounds like you had a bad teacher.

                                                                                                                Honestly this gif isn't even that great of an example of how calculus is used to evaluate geometric quantities, particularly for a beginner.

                                                                                                                [–]Tall_dark_and_lying 45 ポイント46 ポイント  (7子コメント)

                                                                                                                That is A use, not the use.

                                                                                                                Example, in motion control calculus is used to calculate the position, velocity, accelerarion, jerk, and snap from each other.

                                                                                                                It's also used all over mathematics, I used it quite extensively in finance for instance.

                                                                                                                [–]snowden_le_hero 20 ポイント21 ポイント  (3子コメント)

                                                                                                                Fun fact, Sir Isaac Newton invented Calculus at the age of 23 because he wanted to predict the motion of the planets but the math to do so didn't exist yet.

                                                                                                                Another fun fact: the equations and laws Sir Isaac Newton came up with were so accurate that we used those same equations and principles to put a man on the moon.

                                                                                                                You don't need calculus to figure out sales tax, balance your checkbook, or track your calories for the day. It's when you start trying to figure out the really complicated shit that the more advanced math starts becoming useful.

                                                                                                                [–]-but_it_do- 19 ポイント20 ポイント  (1子コメント)

                                                                                                                It should also be known that A LOT of the stuff we get taught in calculus classes today doesn't come from Issac Newton. A lot of things taught in calculus courses didn't even exist until 1800s, where mathematicians started exploring infinity. I wouldn't get your panties in a bunch if you have trouble in your calculus classes since a lot of stuff that is taught to students today comes from multiple people.

                                                                                                                Also it should be noted that Leibniz and Newton independently invented calculus. Newton gets all the credit due to the mathematical political climate at the time.

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                                                                                                                  [–]Scotch-and-Cigars 6 ポイント7 ポイント  (0子コメント)

                                                                                                                  16 years old. Taking calculus at the junior college in the early eighties. The instructor said this on day one. "Calculus is about change and rates of change, and curves that get spun along an axis to form multi dimensional shapes. Keep that in mid as we go through this course and you won't be lost." It helped a lot. Edit: typo of one word

                                                                                                                  [–]Brother0fSithis 11 ポイント12 ポイント  (7子コメント)

                                                                                                                  Calculus is used for EVERYTHING in physics and engineering. Is essentially the reason our society is where it is.

                                                                                                                  [–]Trillen 10 ポイント11 ポイント  (2子コメント)

                                                                                                                  Well that and 99% of kinematics...

                                                                                                                  [–]Denziloe 6 ポイント7 ポイント  (0子コメント)

                                                                                                                  And areas.

                                                                                                                  And electromagnetism.

                                                                                                                  And the rest of physics.

                                                                                                                  And economics.

                                                                                                                  And...

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                                                                                                                      [–]funkmasterhexbyte 6 ポイント7 ポイント  (0子コメント)

                                                                                                                      It's impossible to draw out the surface of a sphere on paper without stretching pieces out so, yeah, this is wrong.

                                                                                                                      [–]xakare 10 ポイント11 ポイント  (1子コメント)

                                                                                                                      /r/mathgifs

                                                                                                                      [–]turnipheadscarecrow 4 ポイント5 ポイント  (0子コメント)

                                                                                                                      r/math is unimpressed.

                                                                                                                      The problem with this gif is that you can't flatten sphere slices like that. This is begging the question.

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