Hello everyone. I just wanted to say thanks for all the support I've been getting from you guys. Means a lot. P.s. I will be starting my undergraduate degree in a few weeks so It might affect my upload schedule. Anyway I'll keep you guys updated on twitter. Peace~
I'm just a guy with an animation software and an access to the internet. Whenever I read about some topic that fascinates me I just want to share it with you guys so I make these animations:)
I find very interesting that many series and be "intuitively" seen, once you find the "perfect" scenario for each series, but the real problem is find the perfect scenario, for example who'd have though in solving this series geometrically, by using 3/4 of a square! By the way, I love the fact that in title of the video, I can see a "#1"!
Oh my god. Your content is just... so on it. Why do we put kids through years of grueling classroom math lectures when the answers are sitting right there on UA-cam, laid out so clearly, and set to Chill Lo-Fi Beats to Study/Relax to.
Consider the decimal 0.111111111... All of the individual digits are powers of 10, but the sum is 1/9th. This sum is similar, except in base 2 rather than base 10. 2/3 in binary is 0.10101010...
My way to visualize this sum is by remarking that all negative terms are all half of the positive terms. So, the serie in fact equals 1/2(1 + 1/4 + 1/16 + ...) = 1/2 * 4/3
Often when one of your videos starts I know the formula/result but I don't see how your approach is getting there. The feeling when it "clicks" in my head and I can foresee your punchline (0:34 here) is simply amazing in every single one of your videos. Thanks for your great content.
is it the right way to understand science : visualising in very particular dimensions theorems . you guys have reminded me of the Einstein's approach; trying to understand concepts by imagining thought experiments and finding physical interpretations of fundamental science. that is extraordinary . still is there a remarkable opinions about the nature of mathematics and it's concerns : Henri Poincarré said that one mathematical object can express a non-finite and different phenomena's and as as a consequence it can have an infinite interpretations . as I shall take an example of what I am talking about let us consider the Pythagorean theorem not from the geometrical view but from the one of probability and statistics: we have a pocket which contains "a" balls with different colours ("a" is whichever number we choose). Now, we can only pick 2 balls successively with reset . the number of possibilities ,of combination according to Pythagoras is equal to the number of possibilities if we use another pocket which contains "b" balls of different colours plus the number of possibilities in a pocket of "c" balls . and all of that done in the same conditions of experiment (successively and with reset) . and finally we have our new interpretation witch totally different from the one with cubes (geometric ) . a²=b²+c²
I derived this myself except for 1/2-1/4+1/8 using an equilateral triangle and going back and forth along its sidelength by factors of what ever the term was, it a point along the same horizontal line as the centre of the triangle, which is 1 third up the side length. Therefore it is equal to 1/3
Well as the sum from 1 to infinity of 1/x^n is 1/(x-1), then sum(1/x^n) for x=-2 would be -1/3. The alternating series is secretly not an alternating series. Amazingly enough the 1/(x-1) deal works for all ||x||
*a Tip: Use "an" when the following word starts with a vowel (a, e, i, o, u) and "a" when the folowing word starts with a constanant (a letter that's not a vowel)
That is a beautiful start; to use 3/4 of a square. However, I don't think you needed to show the full square first. In fact, that actually confused me; because I thought going from the full to 3/4 square was your first step, and I paused to ponder why you had done that.
Think Twice Thanks to you. you make that many people who dont understand or dont care about mathematics are surprised, to my that love maths, I am surprised and I cant stop showing these videos to people, although I know they will never like them as much as I do. Total thanks :)
you can start with any shape you want. In this case if we treat the area of 3/4 of a square as 1 and cut it up into 4 equal pieces it works out nicely. It's all about finding a suitable shape to start with.
The (very good) idea of starting with 3/4 of a square comes from the fact that we already know that the result will be 2/3 before trying to create this visual demonstration.
Think Twice it would have made way more sense to me to start with one whole square. The first three terms just get you to 3/4, since w minus 1/2 + 1/4 = 3/4. I honestly found this video confusing because of that.
Just in case you didn't know that comes from an infinite series which will give you the inverse tangent of a number. In general it is x - x^3/3 + x^5/5 - x^7/7 + ... so when you have x as 1, you are given the sum in your comment.
Since you said, you just finished school: what did it feel like to be recommended by 3blue1brown? (Ps awesome video as always! Really appreciate that he recommended you)
I was really happy of course! I've been a fan of 3b1b for a long time so I was excited when I found out that he will feature me on his channel. It's an honor to me :)
Hello everyone. I just wanted to say thanks for all the support I've been getting from you guys. Means a lot.
P.s. I will be starting my undergraduate degree in a few weeks so It might affect my upload schedule. Anyway I'll keep you guys updated on twitter.
Peace~
Undergraduate?!?!
undergrad degree wtf?? u must be a genius
I'm just a guy with an animation software and an access to the internet. Whenever I read about some topic that fascinates me I just want to share it with you guys so I make these animations:)
What sources on the internet do you use?
You're making some amazing stuff, man. An inspiration, really.
Probally one of the most intuitive representations of an infinite geometric series that I have ever seen. Thank you for everything you do.
All of these help so much more than actual words
this is just brilliance in action
These animations are incredible!
These visual proofs are amazing, never stop making them if you can help it!
I find very interesting that many series and be "intuitively" seen, once you find the "perfect" scenario for each series, but the real problem is find the perfect scenario, for example who'd have though in solving this series geometrically, by using 3/4 of a square!
By the way, I love the fact that in title of the video, I can see a "#1"!
yes I agree:)
I love your animations so much! They make maths less obscure
Series blew my mind when I first encountered them in calc
Same
Very beautiful animation! I have never seen this approach and it blew my mind!
Elegant as always!
thank you~
Got right to the point and super easy to understand. Great video!
Beautiful, as always
Beautiful as always
This is phenomenal
Thanks for these. All the best for future!
thank you:)
Always amazed when watching your video's
Oh my god. Your content is just... so on it. Why do we put kids through years of grueling classroom math lectures when the answers are sitting right there on UA-cam, laid out so clearly, and set to Chill Lo-Fi Beats to Study/Relax to.
The simpler ones are so amazing!
Damn, absolutely love your stuff
Your editing skill are insane
It's amazing how all of the numbers are powers of 2 but somehow in the end we get 2/3
No. It math.
c:
Consider the decimal 0.111111111... All of the individual digits are powers of 10, but the sum is 1/9th.
This sum is similar, except in base 2 rather than base 10. 2/3 in binary is 0.10101010...
My way to visualize this sum is by remarking that all negative terms are all half of the positive terms. So, the serie in fact equals 1/2(1 + 1/4 + 1/16 + ...) = 1/2 * 4/3
Yaël Dillies weird question to ask but are you from Martinique?
Beautiful, as always. Thank you very much
Simply beautiful
Amazing as always
Majestic
I love your videos so much, stay awesome! Like god damn I get such huge nerdgasms watching your videos haha
thank you
Super cool again m8 cheers up !
You're almost at 50k. Best wishes
Ingenious!
Often when one of your videos starts I know the formula/result but I don't see how your approach is getting there. The feeling when it "clicks" in my head and I can foresee your punchline (0:34 here) is simply amazing in every single one of your videos. Thanks for your great content.
Thank you for the support:)
God has joined the game
Dayyumn. That was good. Give us moarr!!!!
Im so happy i found this channel from 3b1b :)
glad you enjoy it:)
Woah, that was cool
great vid, would definitely recommend to a Calculus student that struggles with sums
Amazing!
great animation
thank you!
Awesome!
Wow no dislikes. Keep it up😀😀
beautiful... Elegant
You are making amazing stuff ... keep it up
Thanks for the support!
Beautiful
Yay I learned something!
your videos are awesome
Fantastic visualization! What program are you using for the animation?
I'm using Cinema4D
Great work !
thank you very much
Wow this is awesome .....I want some more pls
That was great!
This is fucking amazing! Can't get enought of this videos! Keep going. You have to.
beautiful videos, nice work
i really appreciate this video more knowledge 👍
Great video! A small suggestion: think about typesetting your math equations in LaTeX. They'll look prettier.
true, I'll have to learn the LaTeX syntax at some point
cool
these animations are fascinating, what software do you use?
thank you! I used cinema 4D for this one
This is so good
This is so nice
Splendid
I remember this 4 L shape thingy, but I didn’t know it can perfectly visualise this alternating series
lovely!
I really should be sleeping right now but I can't stop watching
is it the right way to understand science : visualising in very particular dimensions theorems .
you guys have reminded me of the Einstein's approach; trying to understand concepts by imagining thought experiments and finding physical interpretations of fundamental science. that is extraordinary .
still is there a remarkable opinions about the nature of mathematics and it's concerns : Henri Poincarré said that one mathematical object can express a non-finite and different phenomena's and as as a consequence it can have an infinite interpretations . as I shall take an example of what I am talking about let us consider the Pythagorean theorem not from the geometrical view but from the one of probability and statistics:
we have a pocket which contains "a" balls with different colours ("a" is whichever number we choose). Now, we can only pick 2 balls successively with reset . the number of possibilities ,of combination according to Pythagoras is equal to the number of possibilities if we use another pocket which contains "b" balls of different colours plus the number of possibilities in a pocket of "c" balls . and all of that done in the same conditions of experiment (successively and with reset) .
and finally we have our new interpretation witch totally different from the one with cubes (geometric ) .
a²=b²+c²
they should be teaching math this way in schools
I derived this myself except for 1/2-1/4+1/8 using an equilateral triangle and going back and forth along its sidelength by factors of what ever the term was, it a point along the same horizontal line as the centre of the triangle, which is 1 third up the side length. Therefore it is equal to 1/3
Well as the sum from 1 to infinity of 1/x^n is 1/(x-1), then sum(1/x^n) for x=-2 would be -1/3. The alternating series is secretly not an alternating series. Amazingly enough the 1/(x-1) deal works for all ||x||
Nice.
Wow..😍😍
is that an "spirit away" remix?
yes~
and very cool video!
*a
Tip: Use "an" when the following word starts with a vowel (a, e, i, o, u) and "a" when the folowing word starts with a constanant (a letter that's not a vowel)
sorry, I'm not english basically...
Amazing
That was great
wooow its so cool
True genius
That is a beautiful start; to use 3/4 of a square. However, I don't think you needed to show the full square first. In fact, that actually confused me; because I thought going from the full to 3/4 square was your first step, and I paused to ponder why you had done that.
Nice vedio man I never expected the answer to be 2/3 I guessed 3/4 or I thought the denominator had to be even
wow I LOVE IT
thank you :)
Think Twice Thanks to you. you make that many people who dont understand or dont care about mathematics are surprised, to my that love maths, I am surprised and I cant stop showing these videos to people, although I know they will never like them as much as I do. Total thanks :)
Math porn was created here. The. best. videos. ever.
mind = blown, have a like duce 👍
Me : *amezed noise*
Brotha : What?
Me : Just Sigma(see my) favorite UA-camr's video
lovely
Please make one video showing the visual for 1+2+3+... = -1/12
That's so hard to figure out
Thank you
:DD
Why you have taken a cube of part 3/4 and not total square
Gorgeous...
thanks!
Daym, neat
What do you use to animate these? Do you code them?
Mind = blown
Can u do visual proof of 1-1+1-1+1-1+1-1+1-1+1-1+....
=1/2
Smart smart, nėra pakankamai ilgo gabalo, tai tiesiog padalinai vieną video į kelis :D
haha jo, cia Lauris?
yup :D
as to ilgo video net neikeliau, sita trumpa greit padariau vietoj to:D
aaj, bet kelsi ir tą, ane? Aj, ir nice outro.
cj nekelsiu kolkas. nelabai gerai atordo :D. Dekui
Woah...
Do a visual proof that the volume of a pyramid is a third of the prism with the same base.
Hi guys. Can anyone link an algebraic proof of this series? Very hard to find not knowing how to type math notation into search engines. Thank you.
Is the right direction but could more awesome
The way I did it was to split it into 2 different convergent series. The answer is the same, it just feels cooler.
Say, if n=1, it becomes 1-½ = ½. So how is your answer correct ?
Arijit Chakraborty you change the value of n, so it becomes (-1/2)^n => (-1/2)^1 = -1/2. You inverted -1/2 wirh n, be careful with these.
No no, that's not what i meant, and also, my question itself is kinda wrong, which i just figured out. Anyways, thanks for the tip.
I dont understand why are we starting with 3/4 of a square
you can start with any shape you want. In this case if we treat the area of 3/4 of a square as 1 and cut it up into 4 equal pieces it works out nicely. It's all about finding a suitable shape to start with.
The (very good) idea of starting with 3/4 of a square comes from the fact that we already know that the result will be 2/3 before trying to create this visual demonstration.
Think Twice it would have made way more sense to me to start with one whole square. The first three terms just get you to 3/4, since w minus 1/2 + 1/4 = 3/4. I honestly found this video confusing because of that.
W should be 1 in the above comment
👍
If you do 1-1/3+1/5-1/7+1/9... and so on then multiply by 4 you get PI
Just in case you didn't know that comes from an infinite series which will give you the inverse tangent of a number. In general it is x - x^3/3 + x^5/5 - x^7/7 + ... so when you have x as 1, you are given the sum in your comment.
Taylor series, my arch-nemesis
yess because 1-1/3 +1/5-1/7.....=π/4
haaahahaha
3blue1brown have a video of explain how you get pi/4, go to see it
Spirited away????
yup:)
3blue1brown?
Since you said, you just finished school: what did it feel like to be recommended by 3blue1brown? (Ps awesome video as always! Really appreciate that he recommended you)
I was really happy of course! I've been a fan of 3b1b for a long time so I was excited when I found out that he will feature me on his channel. It's an honor to me :)