The simpler quadratic formula | Ep. 1 Lockdown live math

Рет қаралды 1,343,727

Күн бұрын

Another view on the quadratic formula.
Full playlist: • Lockdown math
Home page: www.3blue1brown.com
Brought to you by you: 3b1b.co/ldm-thanks
Beautiful pictorial summary by @ThuyNganVu:
/ 1258217451323416577
Po Shen Loh on quadratics:
• A Different Way to Sol...
Welch Labs on imaginary numbers:
• Imaginary Numbers are ...
Mistakes (there will always be mistakes):
At minute 22, I write "b' / 2" instead of "-b' / 2".
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
------------------
0:00 - Introduction
2:56 - "How often am I going to use this?" + ray tracing example
5:38 - Mental math tricks (factoring numbers, differences of squares)
13:36 - Properties of quadratic functions
18:40 - Deriving the variant quadratic formula
23:07 - Practice problems (ft. complex numbers!)
34:10 - Deriving the traditional quadratic formula from the variant
41:07 - Conclusion (key takeaways)
43:21 - Fun with joke poll questions
------------------
Music by Vincent Rubinetti.
Download the music on Bandcamp:
vincerubinetti.bandcamp.com/a...
Stream the music on Spotify:
open.spotify.com/album/1dVyjw...
If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people.
------------------
3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with KZfaq, if you want to stay posted on new videos, subscribe: 3b1b.co/subscribe
Various social media stuffs:
Website: www.3blue1brown.com
Twitter: / 3blue1brown
Reddit: / 3blue1brown
Instagram: / 3blue1brown_animations
Patreon: / 3blue1brown
Facebook: / 3blue1brown

Пікірлер: 2 200

@Galenus1234 4 жыл бұрын

This human sounds like the talking animated pi on youtube. How curious...

@replacekebab7669 4 жыл бұрын

Galenus1234 once again, it is fair to say that the fact that this is not in fact a talking pi symbol is a shock to us all

@karolakkolo123 4 жыл бұрын

@@replacekebab7669 yeah, probably a hacker or something..

@poulanthrope 4 жыл бұрын

It's an elaborate deepfake.

@akshatsaxena1431 4 жыл бұрын

Lip sync

@technoultimategaming2999 4 жыл бұрын

@@karolakkolo123 Or that pi has a mask.

@hLofA14 4 жыл бұрын

"We all forget a variable here or there" He's like the arithmetic Bob Ross

@DH-be4ur 4 жыл бұрын

"And that remainder can just be our little secret"

@marylenableile4769 4 жыл бұрын

Or the math version of Andrew Ng's "if you don't understand, don't worry about it"

@Carlobergh 4 жыл бұрын

I wonder what part of the quadratic function he'll beat the devil out of?

@math4life95 4 жыл бұрын

@@Carlobergh LOL!!

@pongangelo2048 3 жыл бұрын

I want to see his version "beating the devil out of it".

@michaelscofield4524 4 жыл бұрын

How does he sound so perfect even though it's live, he doesn't stutter at all

@enormousmaggot 4 жыл бұрын

His IQ Is 7000

@johnimusic12 4 жыл бұрын

His oratory skill is flawless

@astrolonim2032 4 жыл бұрын

Skitter cool to be proud of these things, although they aren’t particularly impressive and you do sound like a douche. That said, if you don’t just not stutter but also don’t use pause words (like Grant, who practically never says uh/um/like/etc), did you practice it or did it happen naturally? (I want to learn to do this as well)

@Cryptocurrency_Universe 4 жыл бұрын

lmao 69 likes!

@cbx7415 4 жыл бұрын

Skitter Ok.

@bowtangey6830 4 жыл бұрын

After 30+ years of university teaching I see that I haven't thought deeply enough about the multiplying of two numbers. Fantastic!

@lordbloeckchen332 2 жыл бұрын

The fact that professors(?) Watch 3b1b videos and learn something, Show how insanely good they are.

@romaindautricourt4890 Жыл бұрын

@@lordbloeckchen332 We never stop learning. Even if we are professors.

@calencrawford2195 11 ай бұрын

you're insanely ____!@@lordbloeckchen332

@erikhalvorseth3950 9 ай бұрын

Bless You, Sir. Grant is a gift to the mathematical community, pure joy to listen to him

@ezra6094 4 жыл бұрын

The Bob Ross of math

@kmit9191 4 жыл бұрын

some happy little products here

@ramizchili8024 4 жыл бұрын

Yeah....

@onemanenclave 4 жыл бұрын

@karolakkolo123 4 жыл бұрын

No, that would be Tibees. Look her channel up lol

@miaclarkwebb 4 жыл бұрын

@@karolakkolo123 I would probably say they are both like that

@thelunes6549 4 жыл бұрын

As a 27 year old grad student, I am not the intended audience for this, but I'd be lying if I said I hadn't been looking forward to the lecture.

@GWAIHIRKV 4 жыл бұрын

At 67 and not that good at math, I’ve still looked forward and enjoyed this. I want to get better. . . .

@michaelz6555 4 жыл бұрын

55yo Ph.D. physicist here, 25 years post-graduate. I watch 3b1b all the time, and I never tire of it. Grant's descriptions of math are beyond compare. I expected nothing less of his lesson on the quadratic formula. I was not disappointed.

@tarioyou9180 4 жыл бұрын

I am 13 and I still learned a lot from it and enjoyed it.

@calebgindelberger3046 4 жыл бұрын

17 year old high school junior, looking into going into computer science. I love the way that he explains things in different ways to help build intuitions

@PeterJansen 4 жыл бұрын

25 yr old vfx artist, so the correlation with ray tracing was kinda interesting to me. Always wondered how renderers algorithmically solve intersections with spheres as opposed to triangles made of three vertexes.

@dsfridley 4 жыл бұрын

0:00 - Introduction 2:56 - "How often am I going to use this?" + ray tracing example 5:38 - Mental math tricks (factoring numbers, differences of squares) 13:36 - Properties of quadratic functions 18:40 - Deriving the variant quadratic formula 23:07 - Practice problems (ft. complex numbers!) 34:10 - Deriving the traditional quadratic formula from the variant 41:07 - Conclusion (key takeaways) 43:21 - Fun with joke poll questions

@UjjwalRane 4 жыл бұрын

Thank you! That's pretty helpful!

@1.4142 4 жыл бұрын

pinned!

@jasonenns5076 4 жыл бұрын

69 the response

@stupidtreehugger 4 жыл бұрын

This is brilliant! I didn't know they had this in the 80s :) I especially like the writing on the notepad bits. Excellent sound quality as well. The what? The maths? (yeah, I'm from the UK :-) That, well, went whoosh above my head :-) Still. I shall return :-)

@VinayKumar-og9zj 4 жыл бұрын

To get roots we also have shri dharacharya formula you can google it

@thasyashetty3797 4 жыл бұрын

I still can't get over your explanation for the second most popular integer chosen as 69. That is why i love this channel!

@pranavmoghe3192 4 жыл бұрын

47:39 Yup, totally that's exactly the reason. You are right Grant.

@lordbloeckchen332 2 жыл бұрын

Don't break his world

@Thor_the_Doge 2 жыл бұрын

i didn't know the *_funny number_* had *_funny properties._* Looks like the *_funny number_* is *_funnier_* than expected

@eskilwadsholt4289 4 жыл бұрын

m ± √(m² - p) is such a meaningful way to put it. Leibniz stressed the importance of choosing meaningful symbols to serve as a vehicle for thought. That is exactly what that is! All that a, b, c, D stuff brings no mental image to my mind, which is now officially blown. Having taught maths for so long, even using that factoring trick, but the dots were still not connected until now. Thank you!

@pieters286 4 жыл бұрын

m,p only valid for germanic/latin languages?

@eskilwadsholt4289 4 жыл бұрын

@@pieters286 Possibly. I am not that versed in non-germanic languages, but I would suggest writing it as mean +- sqrt(mean^2 - product) and translating those words to the desired language and abbreviate to single letters. The point is that the letters signify some easy-to-understand property of the problem.

@talkingstreet3686 4 жыл бұрын

@@eskilwadsholt4289 You can write ± in Windows when you hold down Alt and press 0177 on the Num Pad.

@eskilwadsholt4289 4 жыл бұрын

@@talkingstreet3686 MathJaX should be standard on youtube, but thanks!

@JivanPal 4 жыл бұрын

@@eskilwadsholt4289, oof, no thank you, people would abuse the hell out of that. You can open Character Map and search for particular Unicode characters by name, too.

@XoIoRouge 4 жыл бұрын

In class with normal teacher: If a negative is in a square root, then we'll just say the roots don't exist. Don't worry about it. 3b1b: **Keeps going**

@drumman22 4 жыл бұрын

This always bothered me in public schooling

@shrankai7285 4 жыл бұрын

I had a super great math teacher last year and explained everything with great detail, and talked about negative square root

@ir-dan8524 3 жыл бұрын

All further math classes go in depth with imaginary numbers.

@XoIoRouge 3 жыл бұрын

@@ir-dan8524 Of course, but then the math class isn't normal. Normal math ends at Calc 1.

@ir-dan8524 3 жыл бұрын

@@XoIoRouge Sorry, I'm in Britain, not sure how maths is handled across the world, my bad

@hariikrishnan 4 жыл бұрын

47:40 Oh so that's why people on the internet keep replying with 69 all the time Ah so silly of me to assume something else!

@piirns 4 жыл бұрын

I don't know why this seems funny to me but, weirdly enough you have 69 likes lol

@nestoreleuteriopaivabendo5415 4 жыл бұрын

Grant, I use the quadratic formula just everyday. It's built in my spreadsheets for computing the steel area needed for reinforced concrete beams. The same thing we (Structural Engineers) use for calculating reinforced concrete slabs. For columns, the coefficients change and the forces applied harden the problem, and the result isn't a parabola, but a revolution elipsoid (yes, I know, fellows, that the exact shape is uncertain and is not an exact elipsoid, but think not of the full problem, with second order effects, but of the basic problem, just first order effect). Quadratic formula is my everyday breakfast, lunch and dinner. Is my drink. I breath it. I bath on it. And yet you have something to teach me! Thanks for the update, Grant. Thanks for all you do.

@TheRandomizerYT 4 жыл бұрын

Wow, continue with the great work, friend... Aslo, congrats, he noticed and hearted your comment... 👍😉

@hulmey676 4 жыл бұрын

Yes, you can also use it to work out the maximum deflection in a beam.

@nestoreleuteriopaivabendo5415 4 жыл бұрын

@@hulmey676 And bending moments diagram for an uniformly loaded beam. And shear forces for an linearly loaded one. The deflections, rigorously, are a 4th grade polynomial for the simplest case. Anyway, quadratics. Quadratics everywhere! 😅

@vinitagupta4760 4 жыл бұрын

Hey could ypu please tell me if I will learn this level of maths in university??

@nestoreleuteriopaivabendo5415 4 жыл бұрын

@@vinitagupta4760 It surely depends. It varies from one to university another. But calculus is way beyond this, I assure you. If there is calculus in your course, you will need to grasp this and much more.

@N0Xa880iUL 4 жыл бұрын

Grant every bit the maths teacher I ever wished for. Dream come true.

@wmaiwald 4 жыл бұрын

Never got an English teacher though!

@raphaeldayan 4 жыл бұрын

Agree

@IvanSal778 4 жыл бұрын

I had a heart attack reading this

@itiscujo 4 жыл бұрын

Goodness people, the poor guy was just being nice. i added this just because I know that lower-case i is driving you nuts.

@mildly_edgy4210 4 жыл бұрын

commas are truly integral to the english language

@themorellonomicon2757 4 жыл бұрын

Left eye: Blue Right eye: Blue Shirt: Blue Hair: Brown Name checks out.

@PlayerMathinson 4 жыл бұрын

Right eye: 3blue1brown

@quanhoang2396 4 жыл бұрын

He always wears a blue shirt to keep this in check.

@cemo475 4 жыл бұрын

The Morellonomicon Actually that’s his channel name because his eyes are 3/4 blue and 1/4 brown if u look closely.

@Shotzdownn 4 жыл бұрын

Well, this hair is blonde but you know better sir

@thebullybuffalo 4 жыл бұрын

I just call his channel blue balls or blue brown balls

@Chiramisudo 4 жыл бұрын

You're ability to make complex mathematical topics easy to understand with excellent visuals is astonishing. I think I speak for the entire Internet when I say how profoundly grateful we are that you're not just some stuffy professor in a university where only a small handful of students get the privilege of learning from you. Instead, you generously share your talents with the world and we have all become your students. I'm tremendously grateful for your videos Grant and they have caused me to fall in love with math again! Also, it's nice to finally see your face.

@JasperRLZ 4 жыл бұрын

Fun fact, there's a re-arrangement of terms of the quadratic formula, known in computer graphics circles as "citardauq" ("quadratic" spelled backwards), which provides better precision on computers with floating-point numbers. Whenever you draw a Bezier curve with the pen tool in Photoshop, root-finding is one of the approaches we use to draw it, and the "citardauq" formula is what's used there.

@leonardodicaterina7675 4 жыл бұрын

cool where can I find more about that?

@DanKaschel 4 жыл бұрын

Leonardo Di Caterina have you tried googling it?

@moshadj 4 жыл бұрын

It's actually hard to find by googling the name. Try looking up "quadratic formula for floating points". There's a good stackexchange post talking about where the quadratic formula is lossy for large floating numbers.

@pkmath12345 4 жыл бұрын

Yes, I agree with your point!

@DanKaschel 4 жыл бұрын

@@moshadj hmm. That's the second result when I Google citardauq.

@1.4142 4 жыл бұрын

That's definitely why 69 is such a popular number

@dimitrispapadakis2122 4 жыл бұрын

ofcourse. Why else?

@ryansajeev123 4 жыл бұрын

I felt like he was so ready for that number to come up😂😂😂

@karolakkolo123 4 жыл бұрын

@@ryansajeev123 yesterday when he was doing a secret test-stream for a small audience, people answered 69 too, but he just laughed at it saying "of course it would be one of the answers" or something. This shows that he expected that and prepared for today's stream lol. Next time let's do 420

@rogerwang21 4 жыл бұрын

Obviously, it's because 69 is the third composite number in the 13-aliquot tree.

@pranavsingla5902 4 жыл бұрын

Lol also 69! is the largest factorial that can be calculated on a scientific calculator.

@ili626 4 жыл бұрын

I love this dude. He's a consummate teacher and an inspiration to us other teachers

@Citius1974 4 жыл бұрын

Grant, I had asked my 14-yr old son to watch this live yesterday (he loved it!), and I came back to enjoy it myself today...truly wonderful. Thank you! So great to see you adding such mathematical beauty into this world, and sharing it with all of us. Your channel is a favorite of mine, and now even more so. By the way, my number would have been 137 for the fine structure constant. Please keep doing these. I will contribute to your Patreon in my appreciation for what you add to this world

@christinosim 2 жыл бұрын

It is crazy how something as notoriously difficult as quadratics can be expressed in a way an 8th or 9th grader can understand. A testament to his skill in explaining mathematical concepts.

@kienthanhle6230 2 жыл бұрын

@@christinosim bro, quadratics is 8th grader stuff.

@unicockboy1666 Жыл бұрын

@@kienthanhle6230 I didn't understand it in 8th grade. You can use it, but most likely you'll not yet understand

@someone0623 Жыл бұрын

@@christinosim ?? I am forced to learn all these is grade 6

@closmasmas9080 4 жыл бұрын

That geometric representation of the difference of squares was so satisfying

@no1ofinterst 3 жыл бұрын

Yes! It’s so much prettier than just learning it algebraicly

@pooppooper4252 4 жыл бұрын

plot twist: the blue blurry PI in the background on the bookshelf is the one talking and controlling this human! Hail to the PI overlord!

@pedronunes3063 4 жыл бұрын

That's not a plot twist, That's the actual truth

@conanichigawa 4 жыл бұрын

Hail!

@vaevictus4637 4 жыл бұрын

Forget about the Raspberry Pi! It's all about the Blueblurry Pi!

@arpitdas4263 4 жыл бұрын

Hail🙌🙌🙌🙌

@camicus-3249 4 жыл бұрын

After all this time... The brown pi teacher was being controlled by one of the students

@veerzara3857 Жыл бұрын

Great ideas from a great teacher: - The best way to expand your understanding about any subject is when you connect it with real life problems. - Try to see the concept by different visions since that lets it sink deep in your mind. As an example: look to the quadratic formula using geometry by changing the variable X by a rectangular and the rest by the suitibale geometrical shapes. - The ultimate way to learn is to practice what you learn immediately. - Do not stop if you find yourself go out of the topic. Math likes making connections. - To go from A to C, look for another point B which will decrease the difficulty.

@deleenstallings3236 7 ай бұрын

It’s been bugging me for a while as a math teacher that the formula for finding the x-coordinate of the vertex and the descriminant are taught separately and then students are taught the quadratic formula as though they are separate ideas. The quadratic formula is this beautiful combination of the two that you explain in a unique way, here. I love how this explanation focuses on that idea by making “m” your “-b/2a” (in a slightly different order). Then you attach meaning to how the desriminant finishes finding your solutions, or zeros. Conceptually this is beautiful on several levels.

@duncanw9901 4 жыл бұрын

This represents the difficulty in education: does one define such that the formulas are simple or does one write the formulas in such a way to make the relationships they represent be obvious?

@aathish04 4 жыл бұрын

The best way,in my opinion, is to write them in such a way that the relations are obvious, and lead into the simpler form from that.

@ShadowMario2000 4 жыл бұрын

my friend

@connorhayes2374 4 жыл бұрын

Teachers need to spend more time on one question. It would be cool to do just one day of analyzing the quadratic formula. When you go deep into a question, the beauty of math comes out

@duncanw9901 4 жыл бұрын

@FriedIcecreamIsAReality It is, at the end of the day, always a time constraint, ultimately that imposed by death, that is the difficulty in anything. Heck, some economists even define value that way. Everything in math is a definition; in some sense that's the entire point. If one takes the time to give 3 definitions where one suffices to provide a prerequisite you just made all of math 3 times longer. So instead of being able to contribute to mathematical research at, say, 20, now one has to learn until 60 to write their first published result. This is how we are able to teach what was the cutting-edge 180 years ago to undergraduates today: we've filtered out the redundancies.

@michaelleue7594 4 жыл бұрын

@FriedIcecreamIsAReality The question that matters is what teaching strategy leads to the student's greatest understanding in the most useful (read: smallest) amount of time. Teaching both doesn't *seem* to suit that requirement, although I suppose it might under certain circumstances. In general, my observation has been that you teach with simpler concepts and more involved formulas to begin with, and then gradually simplify the formulas and ramp up the conceptual requirements. Perfect understanding of math would have extremely simple formulas contain entire universes of depth to them, like the Maxwell equations, for example.

@TheFlimTV 4 жыл бұрын

Me: "im on quarentine, I refuse to study for class" Also me: "im going to watch this 1 hour lecture by 3B1B"

@user-rv9vk8by5i 4 жыл бұрын

Same problem here - I'm procrastinating with my maths homework to watch maths. The issue is that this particular homework is tedious, boring, and uses a website that is not at all user friendly. And they've set me ~300 tasks to do on it, with 10-20 questions each :c

@ganaraminukshuk0 4 жыл бұрын

"How many times do you expect to use the quadratic formula?" I just used it yesterday when I was extrapolating the familiar category 1-5 hurricane scale beyond the familiar categories of 1-5 by fitting a quadratic to the minimum windspeeds, plus those for the "proposed" category 6 and 7. The answer I got was a category 17 hurricane. (Sometime afterwards, I realized an exponential would be better, then we'd have a log scale like with earthquakes.) I also remember a^2 - 1 = (a+1)*(a-1) extraordinarily well from high school.

@tomkirbygreen 4 жыл бұрын

Huge, huge thank you for this series of videos. Whilst I’m no longer in school the wonder of these is in the community, spirit of adventure and warmth. Gosh I wish all maths was presented with these elements.

@nanigov4725 4 жыл бұрын

Absolute king can do the job of both a college and high school teacher

@antidote8083 4 жыл бұрын

Omniteacher!

@GajanaNigade 4 жыл бұрын

The math Zeno

@CHOCOLATIONZ 4 жыл бұрын

internet: answered 69 just for fun 3b1b: explained surprising maths fact internet: (surprised pikachu face)

@dannykool-hc3oq 4 жыл бұрын

lol

@immortal3597 4 жыл бұрын

Did anyone understand what he explained?

@CHOCOLATIONZ 4 жыл бұрын

Immortal 3 69^2= 4761 69^3= 328509 4761 and 328509 contains all 0-9 only once

@immortal3597 4 жыл бұрын

@@CHOCOLATIONZ got it,thank you :)

@Crucizer 4 жыл бұрын

People wrote 69 because it's a sexual position, right?

@bigbadbith8422 2 жыл бұрын

I know its been a couple of years, but these live streams were something I looked forward to during lockdown. It was like having someone come over to my house and say, 'hey - want to learn something interesting?'. Thank you for that. It was great and it still is.

@sangitaekka 4 жыл бұрын

I have switched careers and no longer a techie. However I was always condescending about the "put the formula get the answer" approach as lots of questions went unanswered. I wish my generation was taught like this. Keep these videos coming. Subscriber from a long time now. My curiosities are finally getting answered. Thank you so much!

@okuno54 4 жыл бұрын

I do math constantly, and yet in the first ten minutes I've realized all my school math was just another one of the top 10 anime betrayals!

@MindcraftMax 4 жыл бұрын

And then, you learn that π isn't the true one, τ is. Then, that power notation is a mess. Later, that sets are not the most fundamentals objects, mult-fuzzysets are way more powerful. And finally, you discover that infinity might be a lie. Good luck! ^^

@lokeshchandak3660 4 жыл бұрын

@@MindcraftMax You forgot to point out the i isn't really imaginary.

@TheOutZZ 4 жыл бұрын

@@lokeshchandak3660 Yeah, it is a bit more complex than that.

@mr.potato8000 4 жыл бұрын

@@TheOutZZ but it remains constant

@user-cy7dx1wh3d 4 жыл бұрын

@@MindcraftMax Honestly pi vs tau is such meaningless and pointless discussion, and power notation is only a problem for high schoolers. Most people get through math fine with sets as the most fundamental object and what do you even mean by 'infinity might be a lie'? I feel this is the problem when people get too much math exposure on YT without really doing math.

@AnonymousAnonymous-ht4cm 4 жыл бұрын

Edit: the start has been fixed. Old comment: Grant starts talking at 10:50

@repker 4 жыл бұрын

kinda misses the point to skip here...

@Moltensheep 4 жыл бұрын

@@repker he hadn't cut off the beginning earlier, there was a section of "starting soon" at the beginning before

@repker 4 жыл бұрын

@@Moltensheep ah, makes sense

@3blue1brown 4 жыл бұрын

Fixed now.

@dhruvpatel4948 4 жыл бұрын

Ah.. I saw this presumably after Grant fixed this and coincidentally now if we hit the time stamp it takes to classic 3B1B animation.. now I get it that Grant starts talking from there..😅

@Crustee0 4 жыл бұрын

19:32 "its often much more helpful to have numbers", this guy truly knows how to teach maths. Some people cant just visualize the general rule without first given an example first

@datsmydab-minecraft-and-mo5666 3 жыл бұрын

I spent two years having memorized the vertex formula, the weird guess and check factoring, and the messy quadradic formula, now I not only know a much neater formula, but I know why things work! THANK YOU SO MUCH!!!!!

@kyriakosphilitas6950 2 жыл бұрын

What about completing the square???

@webentwicklungmitrobinspan6935 4 жыл бұрын

respect for him performing for thousands of students for the first time. i enjoyed the stream ty so much!

@beyondcatastrophe_ 4 жыл бұрын

Here in Austria, this modified quadratic formula is the only one we learn ("small quadratic formula"), the original ("big quadratic formula") is mostly just listed in formula books. x^2 + px + q = 0 ==> x1,2 = .-p/2 +- sqrt((p/2)^2-q) ("p-q-formula")

@lamme4049 3 жыл бұрын

In Sweden too!

@jabunapg1387 3 жыл бұрын

In Germany too

@osleff 3 жыл бұрын

I was looking for this comment. Very good. Still, students struggle with it and don't get it.

@SoWe1 3 жыл бұрын

@@jabunapg1387 keine "Mitternachtsformel" mehr in Deutschland? Oder hast du op falsch gelesen?

@maxp3141 3 жыл бұрын

I don’t get why one would use this instead of the simpler one you get if you scale to x^2/2 + bx + c = 0 which gets rid of those half factors that are pretty ugly in the p-q one.

@iamlikemex 4 жыл бұрын

This video is both amazing and so calming. I really wish I'd a) been taught quadratic equations like this (so I could actually see what they're doing!), and b) had you to lead my lessons because you've just got such a calm and affirming persona!

@zamf 4 жыл бұрын

I actually also wrote a ray-tracing graphics engine and the first formula I used was the quadratic formula. I also used the formula for finding the intersection between a line and a plane. So, lots of these algebraic formulas are found in geometry, as well. It was my most favourite activity in maths - solving complex geometric relationships by simplifying them down to simple algebraic formulas. Great lesson. Thanks for the video.

@davidm.johnston8994 4 жыл бұрын

39:12 "It's like code that hasn't been refractored properly." You blew my mind there! Yeah, math should have layers of abstraction, just like code.

@davidm.johnston8994 4 жыл бұрын

Wow I never thought about it this way. This phrase unlocked in me so many new possibilities. Possibilities that I've learned for code, but never thought to apply to math. A huge "thank you" for that!

@davidm.johnston8994 4 жыл бұрын

Solving a formula : representing data in a more useful way for the problem at hand. Second "mind blown" moment. I knew that I'd learn something by watching this video, even if I thought I was already quite familiar with the topic.

@beri4138 3 жыл бұрын

Code is modeled after math. Any computer program can be rewritten as a math function.

@mrpedrobraga 3 жыл бұрын

@@beri4138 I have to disagree, Reason: Algorithms. Other reasons: Non-numerical values

@neonblack211 4 жыл бұрын

I’m so glad your handwriting isn’t totally exquisite or I might have quit everything forever

@howardOKC 4 жыл бұрын

most satisfying comment. Feeling the same. How come such a perfect man exists.

@volatus2354 3 жыл бұрын

@@howardOKC lots of hard work, surely

@nanamacapagal8342 2 жыл бұрын

@@howardOKC what's perfect is that he's open about his imperfections

@darylgraham4313 4 жыл бұрын

Honestly with such an in depth explanation, it's so easy to recognize where the pieces for the original quadratic formula come from that I find it easier to remember the form with a, b and C now.

@Jackle02 4 жыл бұрын

You're an amazing teacher, man. It's great to see your face and see how much enthusiasm that just leaps out of the screen. I wish you were around when I went through high school.

@StreuB1 4 жыл бұрын

Seeing Grant get so excited when the live poll started working is just the best ever.

@kingwhiffy2932 4 жыл бұрын

People wonder why teachers don't get paid like superstars... well, if they were all like Grant, they would. This guy is a prodigy of math communication. The programming skills, the verbal fluency, the pacing, the warm-hearted nature... a true gem. Thank you for the vids, Grant.

@vincentwoltmann1139 4 жыл бұрын

I am sorry, and sure that you just wanted to point out your appreciation for Ben, but people don't wonder why Teacher don't get paid like Superstars, they wonder why they don't get paid like they impact the future of our children. And yeah Grant is great, but he probably couldn't do what he does having 5 classes with 30 people in them.

@kingwhiffy2932 4 жыл бұрын

Sorry, who is Ben? I am a high school teacher myself with 4 preps and 5 full periods (2 Algebra II sections and 3 different programming courses), so I concur with what you said. The job is hard! In my district, we get paid fairly well. I'm in my 6th year in public schools and I get about 78k, which I feel like is not too bad especially considering we get full benefits.

@FT029 4 жыл бұрын

I've been using the difference of squares trick to multiply numbers quickly (e.g. 17 * 22 is close to 18 * 22 = 20^2 - 2^2, so subtract another copy of 22 to get 374). The trick has been ingrained in my head ever since I understood the algebraic reasoning behind it. But somehow, I had never bothered to think of the geometric interpretation of (a-b)(a+b). I love learning things in different ways.

@AeroGallian 4 жыл бұрын

I dont know why but every time I see your videos, it reminds me of Professor Gilbert Strang. Maybe, I can already see you turning into one of the best math teachers as you grow old. The way you said Keep loving math, shows the love that you have for the subject and the passion with which you teach it.

@Sordorack 4 жыл бұрын

I do find it interesting, I live in Germany and we did learn that "simpler" quadratic formula, even through almost that exact derivation (tho that last fact probably changes as teachers do). In Germany it's called the "p-q-formula", as the polynomial is then usually described as *x² + px + q = 0* and the result is then *x = -(p/2) ± √((p/2)²-q)* I always thought it funny that many people I know from other countries found this version of the formula more pleasing and easy to work with, but seamingly only a few countries (obviously including Germany ^^) teach it that way. Not to bash on, or praise any country. Just some observation I had over the years

@theproofessayist8441 4 жыл бұрын

Yes, actually previously I've seen Grant's method described by Po Shen Lo but it's always the traditional formula that's derived from completing the square that's conventionally used in most countries. I'm very happy that more of the sum/product of the roots/midpoint version of the quadratic formula method and rhetoric is being spread out. NOT ONLY is the proof good but short BUT ALGORHYTHMICALLY it is a lot simpler to do the computation.

@volkhen0 4 жыл бұрын

We have it in Poland too. But pity that the meaning of it was not explained properly. It was just another formua to remember.

@talkingstreet3686 4 жыл бұрын

In for beginners it´s just derived differently than in the viedeo: ax^2 + bx + c = 0 | divide by a (b/a = p ; c/a = q) x^2 + px + q = 0 | -q x^2 + px = -q | adding (p/2)^2 to complete the binomial formula x^2 + px + (p/2)^2 = (p/2)^2 - q | rewrite with the binomial formula (x+(p/2))^2 = (p/2)^2 -q | take the root x + (p/2) = ± sqrt((p/2)^2 - q) | - (p/2) x = - (p/2) ± sqrt((p/2)^2 - q)

@trulyUnAssuming 4 жыл бұрын

You should probably state the state in Germany. I learned the abc formula (in Baden-Würtemberg) - without explanation.

@Nupid_Stoob 4 жыл бұрын

Ahhh...die gute alte Mitternachtsformel :) Context for everyone who isn't german: A wide spread nickname for the pq-formula is "Mitternachtsformel" = "midnight-formula" because when your maths teacher wakes you up at midnight they'd expect you to have it memorized.

@maverator 4 жыл бұрын

This video kind of underscores how I always felt about math - that it is an interconnected language that makes sense if you see the right patterns. My problem is I don't naturally perceive those patterns. I like that this video has given me a small glimpse.

@milanstevic8424 4 жыл бұрын

this is exactly why people don't find math useful or are confused by it. there is no relationship whatsoever between the language that is typically used to describe wildly different mental images. for some people with a) better educators, b) better access to knowledge, c) better arrangements of thought patterns, it's a completely different experience to analyze a symbol-ridden mental gymnastics from another world, only to conjure an admittedly beautiful solution, but the one that a 7-year-old could imagine just as vividly, given enough patience and encouragement to break through the language barrier. I'm 40 years old, and have been programming for 30 years, and solving progressively hard-ish-er math problems all the time, but was never formally educated at a level I'm readily operating with, and I'm always hardcore struggling with math papers; sometimes it truly feels the same as staring at the ancient egyptian hieroglyphs. like a child standing against the adults' way of passively forbidding me some hidden knowledge employing conspiratory ciphers for my "own good". but because I'm not a child, and things won't ever improve on that front, instead a voice inside me screams of gratuitous elitism, of an artificial language barrier and a consensual unwillingness to communicate in plain symbols. of course, I rationally understand that's only the half-truth. in the meantime, I am extremely grateful that Grant and people like Grant exist, because I have significantly pushed myself beyond the comfort zone in the last decade thanks to them. whatever my previous schooling did, had exactly the opposite effect on my self-esteem when it comes to mastering the math that I can apply to real problem solving.

@anastasiaanautodidact9856 3 жыл бұрын

I can't believe this is my new way of spending my free time.

@juanjesusarandaromero7699 4 жыл бұрын

It's incalculable your apport to the community with that, I really appreciate you!

@tianranhu4448 4 жыл бұрын

Can't imagine how good my math would become if I were to watch this several years before! Thank you soooo much for reigniting my enthusiasm for math when I am about to lose confidence during recent study! God bless you❤

@Imperial7575 4 жыл бұрын

I would like to start off by saying, Thank you grant! For taking the time to share such an interesting take on such a well known topic! As soon as you wrote down the 3 key takeaways, I saw that there was a connection to the the original quadratic formula and I actually tried proving it! I succeeded and was elated that I could do it. I wanted to write down the proof in the comments, when you explained it your self a few minutes later....

@jhaugsne 4 жыл бұрын

You have an elegant proof that a KZfaq comment is too small to contain.

@nuwandealwis3959 3 жыл бұрын

Thank you, my passion with math wane in highschool with poor marks and seemebly so much to memorize is such a short amounts of times, math educators like you are what make remember what I love about this subject:)

@vinayjumani839 3 жыл бұрын

What a great series!! I entered high school this year and this video has thought me to look math as a fun way of connecting many things to the real world instead of just memorizing multiple formulas. Thank you!!

@ryPish 4 жыл бұрын

This pen and paper format is very comfy, I dig it! 📝

@pranavsingla5902 4 жыл бұрын

At 36:03 he missed the - sign before b'/2.

@cubicardi8011 4 жыл бұрын

@@pranavsingla5902 no He didn't

@sudharshankrao9839 4 жыл бұрын

Which software he's using by the way?

@AkshayGundeti 4 жыл бұрын

Thank you Grant for the Welch Lab plug. Just finished watching his series on Imaginary numbers. Glad to have stumbled across the series.

@PrincipledEnt 4 жыл бұрын

Great video!! Totally loved it and went so deep into your lecture that now I got to know it's 2 AM and I forgot I have to sleep (this is the level of our interest you build among your viewers). Would love to watch more videos on other hard topics (for someone like me) like PnC, differential equations, Binomial theorem, etc etc. Love ❤️

@marekurban6110 4 жыл бұрын

You are doing crucial work for our community. As a student, I find these videos very important for further studing, bacause of the way you explain all the topics. Please, keep doing that. Dont be afraid to include even more challenging topics. Thank you in advance.

@pepi453 4 жыл бұрын

35:12 'What does/is that MEAN', that's a very subtle, though awfully funny pun

@garethhoward9150 4 жыл бұрын

I’m watching this as a graduated engineer and this video honestly opened my eyes to see the quadratic formula in a new light. Thank you!

@himatic 4 жыл бұрын

43:00 actually introducing the mean and deviation into the problem, making the "hard" way of solving more easy, is exactly analogous to involving a catalyst in a chemical reaction.

@tsvallender 4 жыл бұрын

Thank you! This was fantastic and helped me think of this topic in a new and much more sensible light. I'm also working towards being a secondary school teacher and seeing these less common ways to teach is hugely helpful and inspiring.

@FourthDerivative 4 жыл бұрын

I was so confused why everyone was so fixated on the number 69, thank you for the explanation!

@randomkanaal8401 4 жыл бұрын

I cant tell if you're being sarcastic

@carlosgaspar8447 4 жыл бұрын

bryan adams even wrote a song about it.

@godduck701 4 жыл бұрын

I can’t tell if Grant was being sarcastic lol

@ratamacue0320 4 жыл бұрын

@@godduck701 purposely obtuse, methinks.

@cmarley314 4 жыл бұрын

smart underage Asian kids, so COPPA compliance

@MGJ988 4 жыл бұрын

Holly molly he's also very handsome!

@ihfssfdg2782 4 жыл бұрын

he do be kinda hot ngl

@ali-1353 4 жыл бұрын

Zac Gagnon he do be tho

@invalide 4 жыл бұрын

oh he do be

@jhuny 4 жыл бұрын

@@invalide he do be do be do

@ASLUHLUHCE 4 жыл бұрын

Be do he

@martita505 Жыл бұрын

I am now in MSc in Engineering and even though I had most of your subjects already I still find your channel amusing. I wish I had your depth of understanding and imagination. And, like you, I wish we had people teaching us with passion, not just commitment. Greetings from UK

@marekstefanecofficial 4 жыл бұрын

Hi, I just want to tell you a big Thanks for these videos. They are of a great value for me as I can revise this interesting stuff and learn something new along the way. I really love your channel and what you came up with is simply wonderful.

@artskyd_ 4 жыл бұрын

I'm glad I can put a face to the beautiful voice.

@roygalaasen 4 жыл бұрын

I was going to write about a character that has truly been elusive for years, but just did a search on google to verify my claim. Boom! CGP Grey??? With a face??? Nooooooooooooo! (Joking, but his face has been a myth for so many years.)

@limboproductions224 4 жыл бұрын

I think this method of simplifying formulae to contain terms that can be thought of in concrete terms (and are not like the a,b,c,d in the quadratic formula which don't form any mental image) would be extremely helpful for *Coordinate Geometry!* Equations of a circle, parabola, and other curves all have terms like a,h,b,g,f but they don't project any mental image. It's hard to think how the curve's shape will change if we tweak one of those variables. It would be really great if you consider this as an idea for a future episode

@richardschaffer5588 4 жыл бұрын

The just start guessing numbers was the way I was taught to solve quadratic equation in school!

@AdhiNarayananYR 3 жыл бұрын

I remember watching this a year back, and hear I’m watching it again. I wish 3b1b does more of these this year too

@ruhaanchopra8878 4 жыл бұрын

im suddenly more thankful to the indian education system, because these nice formulas which u explained are actually being taught to us.

@CanelaAguila 4 жыл бұрын

"How many people are gonna give an answer greater than 0?" Such a programmer way to ask stuff ^^

@klaik30 4 жыл бұрын

That's pretty crazy. In Sweden, this is actually the formula we get learned from the beginning when solving quadratic equations but here in Sweden we call it the PQ-formula where "p" is b'/2 and is basically your "m" and your "p" is our "q". Never thought about it in such a way that was presented in this video tho so this was definitely still a learning experience for me :) Thank you for doing this Grant!

@uabjf 4 жыл бұрын

I love it when someone helps me think about something in a way I hadn't before

@slimothy02 4 жыл бұрын

My mind was blown in the first five minutes, this was great

@luxeproultimate360 4 жыл бұрын

I'm an aerospace engineering student, why am I here? This is so great

@pink_crabb 17 күн бұрын

I have always wanted to know how the quadratic formula was derived and for some reason, I never learnt it. I'm so glad that I realized it today. That is such a beautiful explanation. Thank you so much, Grant!

@TheMadMagician87 4 жыл бұрын

As soon as you pulled up the graphing of showing the scaling of a quadratic function relative to the roots, this whole method clicked for me. Brilliant. Sure beats what i was taught at school all those years ago.

@MilosMilosavljevic1 4 жыл бұрын

That library in the background looks awesome! Really would like to see a tour of it!

@vikranttyagiRN 4 жыл бұрын

Absolutelyy

@joernc 4 жыл бұрын

I see some Richard Stevens: two volumes of "TCP/IP Illustrated" and "UNIX Network Programming".

@agradman 4 жыл бұрын

@@joernc To the right of his head (our right) I see the three-volume collected Calvin and Hobbes

@softlocked9586 4 жыл бұрын

Milos Milosavljevic his library is available on git hub. But I would like him to make a simple tour video.

@gopinathgaonkar119 4 жыл бұрын

I really want to tell you this : last month I had my maths exam and the day before the exam I looked at some quadratic equations which they wanted you to factorise . I was very calm about this stuff until after an hour I was completely freaked out cause I realized that man I took so long to solve such problems . Then trust me I figured this out (what you did in the video) and was completely shocked cause I started to find the solutions in my mind and they were 100 percent correct. And I solved every question in my test and well before time. PS I really enjoyed this video. Learning something during lockdown. Keep doing such good work !!!

@nawaf_ksa0 2 жыл бұрын

I remember in my Physics exam there was a question about projectile motion and it can be solved by the quadratic formula even though I know how to derive it but the time was tight. But now I leaned a more efficient way for such situations thanks Grant!

@ffggddss 4 жыл бұрын

23min: The "song" is now a jingle. Say, Grant. You can also think of m and d as center and radius (of a 1-dimensional ball). On that "Ramanujan constant" - I saw a "kicker" to this incident on some other math YT channel I can't recall now (Mathologer? Numberphile?). The story was that Ramanujan was familiar with this property of that number, because of his trials at solving Fermat's Last Problem. It's a near solution (missing equality by a single unit!) of x³ + y³ = z³ with x = 9, y = 10, z = 12 Overall, I think this video/lesson/fun excursion had a great flow, as always. Fred

@karenamma7716 4 жыл бұрын

Its basically the same thing as the main general formula. Since x= (-b±(√b2-4ac))/2a Since a=1 It becomes x=(-b±(√b2-4c))/2 On division it becomes- x=( -b/2)±√((b2/4)-c) Taking -b/2 as (m) We get m±√(m2-c)

@30indrayudhdas28 4 жыл бұрын

Obviously it is. But he showed it differently because he wants to visualise the formula and how it finds roots.

@karenamma7716 4 жыл бұрын

Yeah and I,as a 11th grader wanted to look cool showing that I understood how he did that😂

@30indrayudhdas28 4 жыл бұрын

@@karenamma7716 I am also a 11 grader.,😁😁😄 Or who would have because of of lockdown our exam are still not over though classes of 11 started online

@blacklabelmansociety 4 жыл бұрын

Hey Grant! Great lecture as always. I’d like to suggest you to do a video on books you enjoyed reading. I know it is a bit off topic, but that amount of books behind you just activated my curiosity

@prashantmishra6684 4 жыл бұрын

Yup mee too.... that will be an amazing video....🤩

@rightycat 2 жыл бұрын

My cram school has introduced us to a similar method of doing quadratic formulas using the sum and product of its roots, however we were never taught any proper way to find those products without being given the roots. That rescaled formula looked familiar and your video was very enlightening as to how I could use it when solving problems, much appreciated Grant.

@kennethlandin3341 Жыл бұрын

The most fantastic and beautiful thing I have ever seen on solving for the roots of a quadratic formula. How sweet (and easy) it is!

@castur_ 4 жыл бұрын

Blimey, I just realized that this is the pq formula! It's the standard formula taught in Sweden for solving quadratic equations. Brilliant explanation, as always! I hope I'll catch your next stream.

@mxxone16 4 жыл бұрын

It's the same in germany. I really wondered what else you normally learn for solving quadratics in the US.

@Trinity0809 4 жыл бұрын

i always wondered why teach the overcomplicated version? divinding by 'a' doesnt change the result. there is no reason to not use the "pq formula"

@davemorgan8349 4 жыл бұрын

Seems like I'm in a minority here but I find the standard formula quick and easy to use. If a != 1 and you have to normalize the quadratic, I think my (former) students would be more likely to make an error.

@rns01111 4 жыл бұрын

Isn't completing the square a 'thing'

@PW-qi1gi 4 жыл бұрын

34:05 What you wrote down here is basically what I know as the "pq formula". We only learned that one in school (in Austria) and I'm surprised people all around the world learn the general one

@klausi8552 4 жыл бұрын

Most of Europe gets taught the simplified version

@photonicpizza1466 4 жыл бұрын

The real name is Viète's formulas (for the case of quadratics, it can also be expanded to higher order equations). In the Czech Republic it's taught as well, along with the sing-songy general formula.

@Edgarisftw 4 жыл бұрын

Yea in Sweden we learn the pq formula and not the general one.

@nikita-ks3nl 4 жыл бұрын

Yep, we know it as Viète's formula in Russia

@swaree 4 жыл бұрын

They teach the general equation here in Spain

@mcrrocks897 4 жыл бұрын

You possess a great deal of explanatory power. Thank you for doing this!

@WNYmathGuy 4 жыл бұрын

Love it! Back in 1997 in a CS class at UB we were asked to write a simple factoring program to test for prime. I was the only one who applied the Newtons Method to limit the numbers it would test to see if there was a factor less than or equal to the square root of the input number. Other programs with big number inputs ran forever and mine would finish quickly.

@carmineceraolo5610 3 жыл бұрын

Before the vaccine works out, we need a lockdown math season 2!! XD

@bramble-east 4 жыл бұрын

I was thinking to myself "Well, this is no fun" before I realized that even a sum of squares is indeed a difference of squares.

@jesusthroughmary 3 жыл бұрын

I have a year of graduate level math under my belt and I never realized this until right now

@captain_clark868 3 жыл бұрын

This content is gold, showing you how to think about patterns and math the right way!

@rajatchopra1411 2 жыл бұрын

The world desparately needs more teachers like him

@WyattNelsonN0S13NM 4 жыл бұрын

Hey Grant! Wonderful video, as always. I'll be showing this version of the formula to my students as well! Just one thing: My "pausing and pondering" caused me to fall far enough behind the live stream to miss out on the polls at the end! I could have just skipped ahead, but I enjoy the comparison of problem solving methods too much. Oh well, next time!

@N0Xa880iUL 4 жыл бұрын

You make a really good point.

@noahve 4 жыл бұрын

That happened to me as well!

@pancakes5225 4 жыл бұрын

If you fall behind on the stream (either from pausing or from buffering) you can increase the playback rate, which will let you catch up without missing anything

@3blue1brown 4 жыл бұрын

Excellent point. Hopefully in future streams, when we have the live question dynamic, I'll give more downtime for everyone to "pause and ponder" that way.

@UnderscoreZeroLP 4 жыл бұрын

this must have taken far less time than his standard videos but I feel like I'm learning far more directly. Because of the familiarity of the setting I am taking in knowledge more easily. It's nice to make eye contact with the person teaching you something

@math4life95 4 жыл бұрын

Wow. I have never enjoyed a lesson about quadratics like this one. So conversational. So sensible. So understandable. Truly a pleasure to learn mathematical thinking from him.