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diplomatic fish
United States
Registrace 16. 08. 2022
A channel dedicated to using visual animations to provide strong intuition for various mathematical topics.
Solving the Most Ridiculous Systems of Equations (ft. a cool theorem) #some3
Join us on an algebraic journey as we solve several crazy systems of equations, building up to formulating and proving the Fundamental Theorem of Symmetric Polynomials.
This video was a serious undertaking for us and is quite different from our previous video, so let us know what you think of it! We've got lots more ideas that we hope to post more frequently, but we're still figuring out our style and groove.
The video we made for SoME2: czcams.com/video/BfbZPEevM64/video.html
Living Mice Synthwave Remix: czcams.com/video/FgOhfMQeWac/video.html
Special thanks to Talia S for the fish!
Timestamps
00:00 Intro
00:35 Solving the First System
06:13 Solving a Second System
16:21 The Fundamental Theorem of Symmetric Polynomials
27:14 Outro
This video was a serious undertaking for us and is quite different from our previous video, so let us know what you think of it! We've got lots more ideas that we hope to post more frequently, but we're still figuring out our style and groove.
The video we made for SoME2: czcams.com/video/BfbZPEevM64/video.html
Living Mice Synthwave Remix: czcams.com/video/FgOhfMQeWac/video.html
Special thanks to Talia S for the fish!
Timestamps
00:00 Intro
00:35 Solving the First System
06:13 Solving a Second System
16:21 The Fundamental Theorem of Symmetric Polynomials
27:14 Outro
zhlédnutí: 81 915
Video
What's So Natural About e? #some2
zhlédnutí 282KPřed rokem
Join us on a journey where we explore a visual approach towards e, uncovering the intuition behind some of its common definitions and features. This Wikipedia page has rigorous proofs of the facts presented in the video: en.wikipedia.org/wiki/Characterizations_of_the_exponential_function Timestamps 00:00 Intro 00:41 Tally's Growth Rule 04:30 Infinite Series Formula 13:04 Limit Formula 17:39 Wha...
Hello where are you
10:36 pussy. let s_0 be the sum of none of the variables, aka 1
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?!?!?!
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?
Lets see what you cook for the next some
これを用いてフラクタルを作れませんかね？
I kept waiting for quaternions to make their entrance.
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.
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.
Is there a way to systematically find the term with the biggest multidegree in every step without doing unholy amounts of algebra?
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 ).
"How tall are you" "e"
it is hard to comprehend
next ochem tutor ?
suggested resources to delve deeper into the topic?
The music is sublime🤌🏼
Lousy video
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.
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.
I want to know how to solve for the complex numbers x,y, and z in the beginning of the video.
Cool content new sub from me😮❤❤
Color is problem
1:14 But if we apply this to her AFTER this day, will e become more e ?
It is amazing ❤ Thank you very much❤
That was beautiful boys! Bravo!
2:10 Why didn't you plug them into the first equation (x + y + z = 1)?
Nevermind, it simplifies to show you the crazy fact that 0 = 0 (mind blown)
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.
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
Thanks
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.
We used manimCE for all the animations ( www.manim.community/ )
Why make this simple problem so difficult?
I love math vieos but even more I love math videos with Minecraft soundtrack
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
I love that the song in the beginning is a minecraft song
what if tally's mass triples. will that become another constant??
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!
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.😋
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.
nerd
but thank you
平面方程式 plane equation
空間向量 向量空間 vector space
i also like how there is playing minecraft music
like how the lines face looks kinda scary
Its even in hyperbolic functions...
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)
who felt nostolgia abt minecraft becz at starting of video it was minecraft music ?
mee
Subbed
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
Tally is like 0.000001 ultra violet
5:38 the instant I saw the yellow line I screamed “THE TAYLOR SERIES” in my head
Similar problem integrating cos^2x sinx but with a sinx sub and getting a sqrt sign
A line is 2 dimensions
The Minecraft Music at the start was hard to believe XD
gave me stomach cancer
why does this sound like soup earth society