Math Teachers Don't want you to Find This out

[@michael_kek]

18:58 I'm pretty sure you meant to write "-" instead of a "+" there. 🤔

[@PapaFlammy69]

Yup, my bad! Thanks a bunch =)

[@johndoyle2347]

@@PapaFlammy69 Snarky comments of denial. Mental!

[@gmdFrame]

Cat 🐱

[@piotrek3650]

I was hoping that at least my math teacher would be honest with me, devoid of malicious intent. But once again I find out. Another person hiding the truth from me. Why do I always finding myself in this type of relationships?

[@geostorm8192]

Interestingly enough, exponential quotients and logarithmic quotients also present this behavior. (ln^2 (x) + 1)/ln(x) has a curved asymptote of ln(x). If we distribute, we'll see that this function is equivalent to ln(x) + 1/ln(x), which at infinity is asymptotically equivalent to ln(x)

[@ribalslim7685]

My teacher taught us how to find those oblique asymptots!!! Kudos to him 😂

[@PapaFlammy69]

nice!!!

[@mskiptr]

Oh, I remember finding these non-linear asymptotes in high school, when I was _not listening_ to the math class lol. I was playing with polynomial division, plotting what I got and comparing that with corresponding rational functions. After trying that with like a third degree numerator divided by a first degree denominator, I got some really nice shapes and there was just no coming back! We had vertical, horizontal and diagonal asymptotes as part of the curriculum. But getting a parabolic one was just so much cooler and more interesting, so that is what I went to explore instead. edit: Long division for polynomials is also pretty cool. And so is the Horner's scheme!

[@Damien-d9f]

I did the same!

[@SimonClarkstone]

You were the only one truely doing maths in your maths class.

[@mr.inhuman7932]

I always watch from beginning to End.

[@PapaFlammy69]

[@rainerzufall42]

17:25 Someone lost his direction (sign), but never checked it against the solution...

[@hollowshiningami3080]

This was a really interesting video, I learnt alot! We were only taught about vertical and horizontal asymptotes in school, and obliques in AP classes. one minor thing tho, at 13:27 I think you meant to write a division sign instead of a dot product. (or a ^-1) I found your methos of division quite interesting, as we were only taught to do it by inspection, I think Ill have to try it out sometime.

[@picassodilly]

So if I understand curvilinear asymptotes right, the function x=0 has a curvilinear asymptote defined by x=1/x. And more generally, if you take a function g(x) that defines the asymptote for a function f(x), then the f(x) defines an asymptote for g(x).

[@JohnBerry-q1h]

When he talks about dying in Mexico, I picture the 🎥 movie _The Boys From_ _Brazil,_ and all the expatriated Germans that skedaddled to Argentina. Gregory Peck was in it.

[@TommasoGianiorio]

In italy we tend to stress the importance of asymptotes when they are linear. In that case we show students that you can find their equation just by calculating lim f(x)/x (which gives you the angular coefficient of the line, lets call it "m") and then lim f(x)-mx which will give the intercept.

[@mskiptr]

Here in Poland it's pretty much like that as well.

[@TheMrAineas1]

Same in Greece

[@samuelcheung4799]

In Baden Württemberg (a German state) this is part of the curriculum as well.

[@dan-florinchereches4892]

It is also part of curriculum in Romania I had the idea about just dividing the polynomials too during summer break. But the Division by X limit will work for relations with square roots and everything @Flammy your division hurts me. I would just go with A(X)=B(X)*Q(X)+R(X) So R(X) is a normal polynomial not a fraction. We are interested in A(X)/B(X)=Q(X)+R(X)/B(X) Not sure why you using R(X) as a fraction straight up was so disturbing for me

[@JohnBerry-q1h]

You goofed the unary sign on the remainder. It should be… - (2/3x) . Just the same, no matter what unary sign you use, + or - , it doesn’t change the value of the overall limit. I did find it interesting that asymptotes do not have to be straight lines. I also find it interesting that the result of the polynomial division ends-up being the *line equation* of the slanted asymptote.

[@tiger12506]

(for the audience) Find a Precalc textbox, and you will see these concepts explored, even before you're fully taught the rigorous definition of a limit. Might have to get one from before the age of graphing calculators, though. It's a lot less important to know all the tricks and tools to graph functions by hand if a machine can do it for you instantly. Also, synthetic division is a thing, you don't have to guess and check your polynomial division.

[@skuizhopatt5318]

My grand mother used to to know how to extract a square root by hand ! ^^ (I guess it was the Newton method behind the scene)

[@SimonClarkstone]

I learnt a method for fun that looks rather like long division: you find the biggest first digit you can, then subtract that off, then calculate the biggest next-digit "layer" you can add onto that, and subtract that off the remainder, and repeat. It's what computers do under the hood, but they have an easier time of it because in binary doubling is trivial and also multiplying by a 1-bit number never causes carries.

[@matthankins6206]

I don’t think that’s the standard approach to remainders. The remainder shouldn’t be multiplied by the quotient (I.e., you should have p(x) = q(x)g(x) + r(x), which would then imply that p(x)q(x) = g(x) + r(x)/q(x)). You directly found r(x)/q(x) and called it the remainder. Not a big deal but it sort of confuses the standard notion of a remainder. Also, in one of you early examples with an asymptote of 0, it could have been cool to point out that it asymptotically approaches 3/x (I might be misremembering what the constant was). The point being the inverse case isn’t two different than the case you focused on. These sorts of asymptotic equivalences are especially pretty important in engineering and physics.

[@matthankins6206]

Also, I guess you didn’t want to stress the polynomial division, but if the denominator is a monomial, it’s easy to just split the numerator by each term and get an immediate result. (Maybe you me approach was based on the intended audience of this video?)

[@ingiford175]

I remember doing this in the 80's when learning how to hand draw various equations

[@ghostmantagshome-er6pb]

my math teacher secrets were always safe.

[@severoon]

All of the polynomial division to find an alternate form of (x^2 - 2)/3x is unnecessary. Just split the numerator into two parts over the same denominator: (x^2 - 2)/3x = x^2/3x - 2/(3x) = x/3 - 2/(3x) Similarly: (3x^3 + 2x^2 + x + 1)/x = 3x^2 + 2x + 1 + 1/x

[@Inspirator_AG112]

*@[**06:17**]:* Omitting the non-leading terms is the convenient strategy for this, by the way.

[@msar7044]

Ich habe noch nie eine so komplexe Polynomdivision gesehen. Ja, Ansatz ist Korrekt, Koeffizientenvergleich kommt auch gut. Das ist Hichschulmathematik. Für Oberstufenschüler bleibe ich aber wohl bei der "schriftlichen" Polynomdivision. Ich meines Erachtens nach wesentlich einfacher und verständlicher.

[@PapaFlammy69]

Die schriftliche Division findet so gut wie jeder Schüler sehr verwirrend. Meinen Nachhilfeschülern zeige ich immer die Multiplikationsmethode und damit kommen sie um Welten besser klar. Es ergibt für die Meisten auch deutlich mehr Sinn. Polynomdivision wie sie regulär in der Schule "erklärt" wird fällt einfach nur vom Himmel, für den Algorithmus wird so gut wie nie eine Herleitung oder ein Grund aufgezeigt.

[@christopherrice891]

I watched this whole entire video hoping that the video would explain what is being pointed at in the thumbnail of this video because what is it that Math teachers don't want us to find out about? What is being pointed at in the thumbnail of this video? May i please have somebody explain this to me? I would really really appreciate that!!

[@PapaFlammy69]

This is a curvilinear asymptote...

[@christopherrice891]

@PapaFlammy69 What is the Algebra equation for the curvilinear asymptote in the thumbnail of this video? May i please know this important, necessary, information?

[@martys9972]

Americans no longer use a colon (:) to represent division. Instead, they use a virgule (solidus, forward slash, /) or an obelus (a hyphen with a dot above and below it).

[@carly09et]

Hmm I tend to partial decomposition, the results are similar, but it helps find O's

[@restcure]

Spotted what must be the most trivial mistake here: the graph at 9:37 is the graph of 3x / (x^2 - _3_ )

[@wanfuse]

Awsome stuff! Well told, please one thing, step off screen to left every once in a while( easier to see it!)

[@mattcarnevali]

Math departments HATE this one simple trick!

[@PapaFlammy69]

:D

[@kurzackd]

0:06 -- "Good morning, shadow mathematicians! Way ye come back to... Now video!" ...what?! O_o .

[@funkfusiontale]

"Good morning, shallow mathematicians!" getting right to the point

[@mallxs]

It took you 20min to make me feel stupid again, but i got the hint and on my way to Mexico.

[@PapaFlammy69]

nice.

[@shutupimlearning]

This video is asymptotically cool

[@Only_Nub]

Finally a vid I understood literally anything in since this happens to the the exact topic we are currently covering in maths Thanks papa

[@PapaFlammy69]

very nice! :)

[@OctavioAlvarez]

23:07 - LOL! Greetings from Mexico hahahaha 👋 BTW, about the result in 18:38, for single term divisors like this, we can also use the shortcut of just splitting the divisor into both terms of the dividend, just like a fraction denominator but of course we would have missed the full explanation. Thanks for the great content and keep it up! [Edit: you meant -2/3x in 18:59 but it ends up not affecting]

[@PapaFlammy69]

yup, my bad!

[@hustler3of4culture3]

I teach parabolic and cubic asymptotes myself. But I'm an odd teacher.

[@hustler3of4culture3]

In fact there are only two types of asymptotes: vertical asymptotes and non-vertical asymptotes.

[@VincentKok458]

Awesome papa flammy

[@sebastiant1094]

Damn thx for this video, I'm doing my phd as an engineer and damn I'm always surprised of how little we are showed for the sake of simplicity and application.

[@KazACWizard]

Hey my boy, i was wondering what blackboards you use and where I can buy them? I have a blackboard already but mine smudges like crazy and yours is just pristine.

[@jorgealzate4124]

Perhaps it isn't the blackboard but the chalk. I'm guessing he uses the good one, Hagoromo

[@KazACWizard]

@@jorgealzate4124 hmmm good point, sadly hagoromo is out of production ;(

[@KazACWizard]

@@jorgealzate4124 and its not exactly cheap

[@sungejin9354]

Handsome teacher

[@ricardoparada5375]

Asymptotes were always pretty fun to compute in school :D

[@deleted-something]

What was that first image bro

[@whtiequillBj]

I don't agree with your shirt that "if it's in physics, then it's invertable". We should talk about chirality some time and see how invertable physics is.

[@jensphiliphohmann1876]

00:20 f _ERATOSTHENES found out that if a [natural] number is not a multiple of a smaller [natural] number [except of 0 or 1], it must be a prime._ Isn't this the very definition of a prime in the first place?

[@henryrroland]

Please, a lecture about Puiseux expansion and others expansions at x → ∞

[@ScienceGhar_LEARNING_HOME]

*I m math teacher* But I will pretend I didn't watch this _lov u flammy_

[@Wielorybkek]

that was really cool, I only think the introduction was a bit too long before it got to the actually interesting stuff

[@PapaFlammy69]

Thx for the feedback! That's why I added the timestamps =)

[@KazACWizard]

i mean this content isn't just for the people who already know this stuff. i think you'd also appreciate being given an introduction to concept you've never used or had forgotten it.

[@schizoframia4874]

5:01 you gotta get your asshole checked 🥶

[@PapaFlammy69]

:D

[@divyakumar8147]

awsome!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

[@antifa_communist]

Teachers: there is no war in Ba Sing Se

[@Chaniaaa-s8n]

what about your first video

[@PapaFlammy69]

? wdym

[@Darxad-po4fw]

what about your first video

[@symphonyofsolidarity]

what about your first video

[@Chaniaaa-s8n]

what about your first video

[@MASTEREZA-]

​@@PapaFlammy69search "oh no Daddy anata wa wuck desu" and that's your video that uploaded on 1970

[@paulestrada961]

[(X^2-2)/(3x)] does not equal {x/3 + [(2)/(3x)]} I love this channel, but you messed up flammy. I had such a difficultly following what you did in this video after seeing the small mistake and assumptions that were made.

[@johndoyle2347]

I click to learn parabolic math, ambiguities and dualities, electromagnetic applications, stable and unstable particles joining, and connections to SSS solving triangles/Big Bounce physics. You are a spooky dude, who immediately tried to muddle the mathematics and physics with he vs. she thinking. Get your head right!

[@PapaFlammy69]

What?

[@johndoyle2347]

@@PapaFlammy69 The intro to your video.

[@5374seth]

Did you end up finding your medication?

[@peterclarkson8215]

For an f of (±x) @ we find x=y acts like a stairway to heaven |X| Now 1/x behaves like a spoiled brat and spits out it's dummy |Y| x^x , -x^x, x^-x , -x^-x , to thread the needle , yes ±x^±x = a family |Z| x/n ^ x/n for n=1 is as above but not for 2 nor for 3 or any other |N| Ye got me growing in spiral circles that appear to be sinusoidal |R| Knock knock, you will hear a word from our sponsors for a second |S| for @ √2 seconds the cannon ball falls from a height of 9.80665 metres |M| PeaT

[@akirakato1293]

asymp-toe 🤤💀

[@Kero-zc5tc]

Get out 🔥 🗣️❗️

[@sHexuality]

arent you a math teacher

[@levifrunk1488]

Telling us what he doesn't want us to know. Reverse psychology 💯

[@Wielorybkek]

it's actually pretty fun, you can take a sum f(x)+a(x) with literally any function f(x), like cosh(x), and add to it a(x)=1/x, 1/x^2 or something like this and get an interesting asymptote. if you want the asymptote to go really close to the function do 1/(ax^n) with some large value of a.

[@landsgevaer]

Or, cosh(x) itself has an even more interesting curvilinear asymptote, approaching the function cosh(x)+1/x ...? If curvilinear asymptotes are a thing, then you cannot distinguish between which curve approaches what other.

[@Raciel1894]

I'll probably die somewhere in Mexico (I'm mexican)

[@PapaFlammy69]

r i p

[@suyunbek1399]

You look and act exactly like Justin Hammer. Why?

[@ludolfceulen]

hehe, so much enthusiasm and excitement - and meantime it is an absolute basis in the first semester of mathematical analysis in our country and nobody is exited about that: sk.wikipedia.org/wiki/Asymptota ... i really do nor understand the enthusiasm and excitement bothering with knows facts source of mine enthusiasm and excitement in math: the human kind DOES NOT KNOW EVEN ONE typical real number !!!!!!!!! do you think irrational & transcendental PI, e, ln2 are typical real numbers? WRONG !

I can see that fascination. I only really care about unknown things. But wouldn't it need to be some definition or a at least characterization of "typical" real number to make that question meaningful? What is the characterization of a "typical" real number?

[@ludolfceulen]

Real numbers are divided into two disjunctive sets: rationals (Q) & irrationals (I). Both infinite. But it is well known not all infinities are the same, if fact there exist infinite "kinds" of infinity. Not equal. There can be "smaller" ones and "bigger" ones. The smallest two of the infinities which mathematicians use are: alehp0 and continuum, where the second is the larger one. We know the cardinality of the Q set in aleph0 and the cardinality of the I set is continuum. It means "NEARLY ALL THE REAL NUMBERS are IRRATIONAL". In other words: randomly picking a real number, the probability of being irrational approaches 1 and the probability of being rational approaches 0. We also say the "asymptotic dence" of rational numbers in real numbers is ZERO! So: rational number is NOT a typical real number. If the Pythagoreans, who thought that all real numbers are only rational and nothing else exists, they would have committed mass suicide, not just one of them. And it turns out that rational numbers are only such an infinitesimally rare solution in a continuous ocean of ​​real numbers, that is, "almost all" real numbers are NOT rational. A "typical" real number is: ---> non-algabraic and also ---> irrational and also ---> transcendental and also ---> z-adic normal and also ---> non-computable (!!!) Even if we know PI,e,ln2... are irrational and transcendental, NO ONE knows if they are also z-adic normal. Because no one has proven it. BUT even doing so and we will have such proof, they ARE NOT typical real numbers, because typical real number is non-computable. The cardinality of the non-computable subset of the real numbers set, is continuum. In other words: ALL THE NUMBERS human kind ever thought of and manipulated with, are from the smallest subset of the real numbers. The real numbers are an elusive and abstract concept. WE DO NOT KNOW even ONE typical real number. We have "constructed" some concept of non-computable real number, but no one will be never capable of proving, if it is also z-adic normal or transcendental or irrational ...