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mathematimpa
Brazil
Приєднався 23 сер 2020
Just a professor with little to no clue on how to edit videos.
Using probability to find the volume of hyperspheres (and other weird balls) #Someπ
Calculating the volumes of hyperspheres typically involves making a lot of integrals. In this video I show how we can get around most of them by reasoning in terms of probability. Not only that, but we can use the same reasoning for more exotic shapes called Lp-balls. Along the way you'll also learn a bit about how guesses can be used to find new results.
SoME discord:
discord.gg/WZvZMVsXXR
Good introduction for the Gamma function:
ua-cam.com/video/v_HeaeUUOnc/v-deo.html
Proof of the connection between the Gamma and Beta functions
en.wikipedia.org/wiki/Beta_function#Relationship_to_the_gamma_function
#Somepi #Someπ
SoME discord:
discord.gg/WZvZMVsXXR
Good introduction for the Gamma function:
ua-cam.com/video/v_HeaeUUOnc/v-deo.html
Proof of the connection between the Gamma and Beta functions
en.wikipedia.org/wiki/Beta_function#Relationship_to_the_gamma_function
#Somepi #Someπ
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Відео
What does a complex function look like? #SoME3
Переглядів 126 тис.Рік тому
Join me as I explore the different ways we can visualize a complex function, to find which one deserves to be called their true graph. 0:00 - Quick introduction 0:30 - Why can't we just plot a complex function? 1:45 - Mapping between 2 planes 2:35 - Grid mapping 3:07 - Reading a grid map 4:15 - The problem with grid mapping 5:35 - Colors to the rescue! 7:07 - Mapping hue and brightness 8:11 - C...
The hardest concept in Calculus? #SoME2
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The ε-δ definition of limits is infamous among calculus students for being confusing to understand and cumbersome to use. In this video I show what is the geometrical interpretation of that definition and give an example of how it is actually used in practice connecting the steps of the reasoning with the geometric picture.
The Strange Case of the Umbral Calculus
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In the XIX century a toolbox of algebraic manipulations that look like nonsense became popular as a starting point for proofs of properties of numerical sequences, particularly the Bernoulli numbers and Euler numbers. This later on became known as the Umbral Calculus. In this video I show some accessible examples and talk about the effort during the XX century to explain why the Umbral Calculus...
Goodstein Sequences and Huge Numbers - MegaFavNumbers
Переглядів 6 тис.4 роки тому
One of mathematics weirdest aspects shows up in the so called Goodstein sequences and the truly gigantic numbers they reach. #MegaFavNumbers Small correction: The number should read 3*2^402653210 - 1
here from Mathemaniac! this is really awesome
Hereditary mean coefficients LESS than base? Seems less than or equal to.
thanks for putting this together. Wonderful explanation.
A common 4th dimension is time, so the graph could also be a movie that dynamically shows how input leads to output. Wave patterns are often shown like that, because the input is repetitive.
Realize the cyclic nature. The “complex plane” is a projection, of a spiral, and the speed of the spiral is an additional dimension.
Crazy interesting videos. Its gonna be so nostalig if future me sees this after having pursued a career of mathematics
Excelente vídeo, professor! 😁
Akiva is truly one of the goats
WOW!! What an explanation...loved it!
17:39 typo with the dx
oops
Muito brabo, curti demais a ideia. Acabei de ver que o canal é brasileiro, chega ser irônico um brasileiro ensinando pro outro em inglês kkkkk. Parabéns pelo vídeo!
Valeu, eu tenho planos pra fazer uma versão em português do canal, mas ainda vai levar um tempo 😁
Also why i am not able to get the same figure in geogebra as you get for Lp balls...? Also if possible can you explain the processes from 13:28 to 14:28 because i feel i am completely lost here... as later you took a [-1,1]^3n as cubes and i am left with why and what and how ....
Roughly, the idea is that the sum of 2 squares was uniform inside a circle, because the scaling law made everything nice in 2d. The way things click in 3d is if you use the sum of 3 cubes (and in general in nd, you need the sum of n n-th powers to get a uniform)
Sorry but I didn't get it...😢
At 14.08 you said "sum of 3 cubes is uniform in interval 0 to 1" so you meant that probability sum of 3 cubes is directly proportional to there volume as you said random points/uniform is that if we pick a point in a dimension say 1D then the the probablity of it on the interval say a to b is proportional to length of ab carrying the analogy here you are trying to say that probability of point in 3D in p-ball is proportional to volume of p-ball. BUT what is the value of volume this weird shaped p balls we dont have any formula for them so how we came accross c ? I am some what confuse here so can younplease sort it out ?
The idea is that if you draw 3 numbers x,y,z in [-1,1] AND these numbers are such that |x|^3 +|y|^3 + |z|^ 3 < 1, THEN |x|^3 +|y|^3 + |z|^ 3 has the cumulative of a number drawn in [0,1]. Being inside the unit Lp-ball is important for the result to be uniform (technically, we'd need to use conditional probability to clean everything, but I thought it made things way too long)
But why is it necessary to be inside Lp ball as if it is any regular equation like x^2+|y|+|z|^3<1 the same will hold as it is same as picking a random point in interval 0 to 1 ?
Wait a minute you made an equivalent of 4D hypercube as 2 , 2D squares but you did not created an equivalence yet i.e not shown that this is possible and right as you have shown in F A( C) and F x^2+y^2 (C) i.e A and x^2 + y^2 are equivalence....so how is points in a hypercube is same as points drawn independently in 2 squares ? Am i missing at something...if so...sorry.
The idea is that you are drawing 4 numbers at random. You can interpret these 4 numbers as being a point in 4d or two pairs of points in 2d. Being 100% technical you need to assume the numbers are being drawn independently too, but I thought this would just add an extra concept that is already kinda intuitive.
Ty ❤
How is volume of hypercube 16 ? you said by multiplying all sides but all sides are 1...so it should be 1. Sorry if the doubt is obvious but currentl i am not getting it ...
@@RUDRARAKESHKUMARGOHIL The sides go from -1 to 1, so each side has lenght 2
Thankyou...also as you sated Two variables(random) with same cumulative distribution are equivalent...I wanted to know that why is it so...and what is the equivalence here ? thankyou also can we do it for area of sphere I.e disintegrating it in 1d line and a 2d square ? Also great work best wishes for your SOME WIN 🏆 👍 .
If X and Y have the same cumulative, this implies a few things. First, the probabilities that X=a and Y=a is the same for every a. Also the probability that X is in [a,b] and that Y is in [a,b] are also the same. This means that you pretty much can't tell them apart from their values. Every property will be the same and that's why you can use them interchangeably.
Also could you provide a intuition for volume of Hyperpyramids...i.e about the division by n in formula i got the intuition about the base through the video. ...Sorry for so much doubts.😅.
@@RUDRARAKESHKUMARGOHIL The division by n thing requires calculus to fully explain. The idea is that you can consider a section of the pyramid parallel to the base, you get a scaled down version of the base. You can use the scaling law to write this volume as a function of the base volume. If you integrate this section volume you get the volume of the whole thing (The 1/n ends up coming from the scaling law, but you need to put it down in paper to see this)
eu juro que tentei tankar o sotaque
I need your help
Great video on an interesting topic. The explanation in terms of linear operators was an unexpected (and satisfying) twist.
looks complex
Tw0 dimesion qua cubed
Yes
Morbius equation is a zeta function
Well, no. That's the number of STEPS after the Goodstein sequence of 4 terminates. It's not the the largest number in the sequence. We don't know that. Simply because nobody ever will be able to calculate all the numbers in a sequence with 3* 2^402653209 STEPS. Too much calculation. It would take an eternity especially considering how difficult is to wtite an effective algorithm for the sequence but the sheer number of steps also makes it impossible.
Well, no. We DO know that is the largest number in the Goodstein sequence of 4. The number of steps is bigger than that. It is proven that it gets to that number and then begins a VERY SLOW descent down to 0. This is because, at that point, the actual number ends up becoming smaller than the hereditary base and doesn't increase anymore, so the -1 slowly but surely eats it up.
@ibrahimali3192 Your logic doesn't make any sense. After each step you have bigger and bigger jumps between the numbers how would you be able to tell which number is the last before descending in a very long sequence?! You said that number of steps is even bigger than 3*2^402653209. (Which it isn't. That's the exact number).
@@NorbertKasko i did a little more research; the number of steps is 3*2^402653211 - 2. The biggest number is 3*2^402653210 - 1. (so we were both wrong)
Did not expect linear algebra to come out in this video. I did not know what I was in for when entered, but it was interesting and everything settled by the end of the video. This somewhat reminds me of the Z transform, though probably not related
This IS parametric architecture. Complex calculus and complex analysis should be requisite for architects.
the strange case of Dr. Calculus and Mr. Umbral
thank you for the explanation, even though this is really a good video I still have a hard time to understand this, maybe because I'm still in high school
Literally the best video I've seen about this.
just one criticism: 16:31 you say that the graph of 𝑓(𝑥) is {(𝑥, 𝑓(𝑥)) ∀ 𝑥 ∈ ℝ} when in reality that only counts as the graph of a function 𝑓(𝑥) with domain ℝ, but not for any function whose domain doesn't span all real numbers. for the rest, the video is an amazing learning tool, hope you the best!
you don't know what you're talking about
I thank God and then I thank UA-cam for recommending this amazing icon to me ((Free Palestine))
10:35 looks like 3 quarks forming into a baryon
i hope not winning anything from some3 doesn't discourage you i loved the content and you should definitely make more videos
I do have ideas for more. Just need to find time
God bless you Awesome lecture
only once did my teacher visually show the complex region on the white board, but this video helped it explain what it looks like. cool!
I'm a mexican collegue student and i enjoyed the video, i always wanted to understand how to visulize a complex function and this is the first video that explain it well.
Wow this looks really complex 🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣
POV: You are Colour-Blind
At least the graph of Re(f(z)) is still usable
never could've imagined that by simply taking the sqrt(-1) we would ever get to 4 dimensions.
Such a concise and well explained video!
You got my sub just for simple "hope you liked bye"
amazing!!
I love how this video is 20 minutes long and it felt like 5 minutes. Everything was well explained and it just kept getting more and more interesting. Congrats!
my colorblindness going wild on this one lmao
😂😂😭
so z^2 is a potato chip nice to know
This will kill me
Rip Name-xd1hv
very very interesting! we find fractal equations...
Outstanding discussion!
Gotta watch 24h version of spinning chip now
With the "spinning seal" song in the background
It was so original! though I have to watch this few more times to understand better