10:36 pussy. let s_0 be the sum of none of the variables, aka 1
@conductorfishy3028Ай бұрын
but the yellow line isn't a straight line meaning that it doesn't create a triangle which also means you can't use the area of a triangle to find the green line, why would you mess up now?!?!?!
@abshariadamАй бұрын
7:50 I seem to have a problem understanding why does the height and the base of the graph use the same variable (In this case t). Can anyone elaborate?
@hmkl68132 ай бұрын
Lets see what you cook for the next some
@shikaishik2 ай бұрын
これを用いてフラクタルを作れませんかね?
@benbookworm2 ай бұрын
I kept waiting for quaternions to make their entrance.
@lenardlontoc35852 ай бұрын
I love your imaginative ways to describe or ascribe the theory into visuals. What I didnt take away from this is how to get an understanding of how to d etermine growth of Tally at day 1 in a formula because e^x by itself was explained as a rate of change that is the same. Shouldn't there be a constant in the exponent if growth was to be depicted differently as each new increment abounds throughout the day? Im caught between thinking I am asking something pertinent and wondering if I am just not visualizing this correctly. Maybe I just need further examples of its applications to more things. Thank you for your dedication to such intricate subject matter and its theory and editing. You worked hard on this and I am grateful to you for this.
@diplomaticfish2 ай бұрын
We started by establishing Tally's growth rule: every bit of mass doubles itself in a 1 day period. This is how a day became the relevant unit of time, and why we don't need a constant in the exponent of e^x. We then defined e to be Tally's height after 1 day. We then showed that, based on how her growth works, her height at time x (where x is the fraction of the day that has passed) must be e^x. Of course, we could have rescaled things so that each bit of mass doubles in an hour, and then her height after 1 hour would be e. Let me know if that answers your question.
@marttielvisto35192 ай бұрын
Is there a way to systematically find the term with the biggest multidegree in every step without doing unholy amounts of algebra?
@diplomaticfish2 ай бұрын
Yep, if you have a product of a bunch of polynomials, the term with highest multidegree is the product of the terms with highest multidegree in each factor. You can also use symmetric sum notation to greatly reduce the amount of writing you have to do when multiplying things out ( artofproblemsolving.com/wiki/index.php/Symmetric_sum ).
@jupitahr2 ай бұрын
"How tall are you" "e"
@Fire_Axus2 ай бұрын
it is hard to comprehend
@Evanescent30033 ай бұрын
next ochem tutor ?
@AryanKumar-vo1ic3 ай бұрын
suggested resources to delve deeper into the topic?
@TheBluePhoenix0083 ай бұрын
The music is sublime🤌🏼
@michaelyap9393 ай бұрын
Lousy video
@erawanpencil3 ай бұрын
Excellent video! You know, people confidently act like e/natural logarithms are trivial and just a computational convenience one can glaze over, but honestly I don't think modern math or physics really has a grasp as to how deep its implications go and how profound it really is. It's not at all obvious that 'continuous growth' wouldn't be infinite, or that all of the fundamental mathematical operations can be reduced to mere sliding circles (i.e. slide rulers). Change isn't sequence; it's not a mere linear or recursive successor function.... change or time somehow self-grows in a way we don't understand.
@diplomaticfish2 ай бұрын
Great point! People usually try to explain continuous growth as a limit of discrete processes, but in this video we tried to describe the growth as inherently continuous, which is definitely tricky to wrap one's head around.
@christopherrice8913 ай бұрын
I want to know how to solve for the complex numbers x,y, and z in the beginning of the video.
@LightUpSCIENCE3 ай бұрын
Cool content new sub from me😮❤❤
@panchananpramanik82763 ай бұрын
Color is problem
@redstocat54554 ай бұрын
1:14 But if we apply this to her AFTER this day, will e become more e ?
@omargaber31224 ай бұрын
It is amazing ❤ Thank you very much❤
@trelosyiaellinika4 ай бұрын
That was beautiful boys! Bravo!
@aze43084 ай бұрын
2:10 Why didn't you plug them into the first equation (x + y + z = 1)?
@aze43084 ай бұрын
Nevermind, it simplifies to show you the crazy fact that 0 = 0 (mind blown)
@chrischiesa6095 ай бұрын
Wow. I do calculus for fun and have been doing so for 40 years. E and exponents and logarithms and whatnot have been old friends of mine for decades. And yet I still found this video very difficult to follow and would never ever use it to introduce anybody to the concept of e or how it is obtained. Cringe.
@vansf34335 ай бұрын
None of human invented notions of mathematics is actually natural. The adjective " natural" is merely a symbolic label Even when you have got PhD or post PhD level of mathemstics, you will not actually understand such human -invented notions because all what you have done is copying well such notions without actually understanding them That quantity does not actually exist anywhere in the real physical world because all real quantities which can represent forms of matter or physical entities are well-defined, without any ambiguity. It is merely an arbitrarily or subjectively defined quantity
@PaProblem5 ай бұрын
Thanks
@ark75415 ай бұрын
Which tool did you use to simulate the Tally's growth? I also wanna simulate that myself to explain it to my sister as she is taking her first differentiation class.
@diplomaticfish5 ай бұрын
We used manimCE for all the animations ( www.manim.community/ )
@tulliusagrippa57525 ай бұрын
Why make this simple problem so difficult?
@capmat82325 ай бұрын
I love math vieos but even more I love math videos with Minecraft soundtrack
@joso56815 ай бұрын
The mistake is in how you interpret the equality, from π/2=0, you conclude π=0, when in reality, if you examine how the functions behave in the [0,π] interval, it becomes clear the limit of 2 as x approaches π is possitive infinity
@user-lf8hz9st6d5 ай бұрын
I love that the song in the beginning is a minecraft song
@chessmaster20415 ай бұрын
what if tally's mass triples. will that become another constant??
@diplomaticfish5 ай бұрын
Good question! If each bit triples in a day period, then since growth is linear, each bit of mass will double in half a day. So it makes sense to change units and let h be the number of "half-days" that have passed. Then by the same logic as from the video, Tally's mass at time h will be e^h. Now we can change back to standard units; let t be the number of full days that have passed. Then at time t, 2t half-days have passed, so Tally's mass is e^(2t), which is also (e^2)^t. Thus, the relevant constant is e^2, rather than e. Hope this helps!
@davidroddini15125 ай бұрын
But Tally grew at a continuous rate. That's not how things grow in nature. Rather the rate of growth will change over the course of a day/week/year/etc. This means that Tally's growth is unnatural. Since we used her growth to deduce e, it must also be unnatural.😋
@pacolibre54115 ай бұрын
You’re correct that there are biological complications that arise if you look as mammals (such as a day/night cycle), but if you look at simpler life, like a bacterial colony, or other cell structures, exponential growth is pretty accurate. And the replications happen at such a rapid rate that it is basically continuous compounding. The number “e” is a natural number for describing all sorts of “feedback loops” and biological growth is just an example that people tend to be familiar with, unlike RC circuits or radioactive decay.
@PoopFarter15 ай бұрын
nerd
@PoopFarter15 ай бұрын
but thank you
@ryanchiang95875 ай бұрын
平面方程式 plane equation
@ryanchiang95875 ай бұрын
空間向量 向量空間 vector space
@tinkej57035 ай бұрын
i also like how there is playing minecraft music
@tinkej57035 ай бұрын
like how the lines face looks kinda scary
@mihaleben60515 ай бұрын
Its even in hyperbolic functions...
@rubensf77805 ай бұрын
Also, the natural log is simply for when you know that something grows like this and you know the end result, so you want to know for how long it was growing (or at least that’s it’s most intuitive use)
@craftyminer15045 ай бұрын
who felt nostolgia abt minecraft becz at starting of video it was minecraft music ?
@CubingEmperor3135 ай бұрын
mee
@MrMacetuck5 ай бұрын
Subbed
@ryantrusty89335 ай бұрын
a lot of this flew over my head in how we ended up at E but the derivite of e to the x part was a nice resolution to a fact that we were just told "that's the way it is" in class for
@nutsi35 ай бұрын
Tally is like 0.000001 ultra violet
@hydropage28555 ай бұрын
5:38 the instant I saw the yellow line I screamed “THE TAYLOR SERIES” in my head
@meraldlag43365 ай бұрын
Similar problem integrating cos^2x sinx but with a sinx sub and getting a sqrt sign
@ItsAJ245 ай бұрын
A line is 2 dimensions
@kdance91315 ай бұрын
The Minecraft Music at the start was hard to believe XD