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Smoother
United States
Registrace 9. 09. 2020
Visual proof | But why is PI under this infinite curve? #SoMePi
The video intuitively explains why PI is under the curve "1 / (1 + x**2)" by slicing the unit circle into segments and mapping their areas to bars under the curve. Summing these areas visually reveals PI. Additional insights are provided on the derivative of the tangent and the Cauchy distribution, connecting geometry, calculus, and probability. The video is designed to be fun and flexible in its proof, making complex ideas accessible and engaging.
Chapters :
0:00 Introduction
1:12 Probability Theory
4:08 Visual Proof
8:29 Extra
9:36 Ending
Chapters :
0:00 Introduction
1:12 Probability Theory
4:08 Visual Proof
8:29 Extra
9:36 Ending
zhlédnutí: 4 478
Video
Visual proof | Why ln(ab) = ln(a) + ln(b) ? #SoME3
zhlédnutí 85KPřed rokem
#some3 This is a math video that tries to show a visual way to think about logarithms. Those functions we all know and love ;) from highschool and math classes. The focus in this video was to loosly "proove", without any equations, the propriety that this function have, which is (ln(ab) = ln(a) ln(b) )). The proof is seperated into four results, each one of them is prooven using the previous on...
Maravilha
Nice 👍
Cool video!
Beautiful man!
👌👌👌👌👌
Very interesting, thanks!
great video! the physical/geometric analogy is really novel and always a joy to see! I'm a little upset that arctan'(x) = 1/(1+x^2) was never brought up explicitly. the common proof of this immediately follows the chain rule and it would have been fun to see how the two approaches connect.
Yeah, the meat of the video is essentially calculating the derivative of arctan geometrically, weird to not say it explicitly. The rest is just set up.
Thanks for the appreciation. I actually wanted to include the formal proof which include ‘arctan’ in the ‘Extra’ part. It can indeed be connected directly to this visual representation, I just couldn’t do it due to the time constraint.
Thank You
Integral of "Witch of Agnesi" function for a=1/2.
I looked at it now, I never saw this before i would have included it somehow in this .
Great expansion! Will you share the source code for the animation? How do you do your voice over?
Best SoMe I've seen this year so far (I haven't seen a lot but still I think it's very good)
yo
Thanks, appreciate that.
Very nice proof, I will remember this one. Thanks for your video
❤❤❤ beautiful visual proof ❤❤❤ music not necessary 🙏🙏🙏 thanks for the video ❤❤❤
math becomes easier when we visualise it. Unfortunately, that wasn't the way we've been introduced to it as students. This video is definitely a masterpiece 👏
0:00 foreign
A great work just continue
Outstanding - now that I've seen this (5 months after it was released), I can't wait for your next video - don't give up!
This is literally a masterpiece, keep going dear 👏👏👏
This video is great but there are quite a few places that makes me think we are running in circular reasoning, logic.
Very nice. But "Engeneering"? "Chimistry"? You put a lot of effort into this, how much extra would have spellcheck taken?
Wow
6:16 I love this little animation when moving formula corresponds to changing parameters
very brilliant video the geometric proof really was mind blowing and memorable, hats off to you man this video does have some spelling errors, bugs, but overall the content and presentation as well as the explanation were amazing, though i would suggest you go in a bit deeper into the explanation for the younger audiences who might not understand some things such as limits or how the area of 1/x gives ln(x) but overall amazing video and worth a watch
This was a neat presentation. Very elegant argument clearly presented!
Wow excelente ilustración
Qué bonitas animaciones te has sacado! Sigue así, este canal tuyo pinta bien
0:47 I Googled to see if Chimistry was a real thing I didn't know :P
I have been seeking an intuitive basis for logarithms in the sense of what they were created for. Formulas can only do so much, and this is the first visual proof I’ve seen, so it helps a lot. I subscribed and will be on the lookout for more.
Nice! But I think it could be half as long without losing anything. Sometimes it is good to be as brutal as possible when editing the script and the final video.
Pretty elaborate proving stuff from the scratch, the visualizations were so impressive...
But how do you prove that the integral of (1/x) = lnx visually.
Also wouldn't it be faster to prove that for a rectangle formed by (1/x)dx where x=a, is b/a times larger a rectangle of the same dx formed at x=b. Then you reduce the height of the rectangles by multiplying 1/b and scaling the width by b times to keep the area the same, and then move all the rectangles rightwards so that leftmost rectangle touches x=b, since the original sum of width of all the rectangles was (a-1), after scaling the width of the rectangles by b, the total width will be b(a-1)=ba-b, the x coordinate of the rightmost rectangle will be ba-b+b=ba, since we know the area bounded by 1 to a, is same as b to ab, ln(ab)-ln(b)=ln(a), hence you get ln(a)+ln(b)=ln(ab)
Basically I'm taking every rectangle within 1/x from x=1 to x=a, stretching them and squishing them, and relocating them to the region between x=b and x=ba, basically same idea as the video, but without the parallel line thing. Although the parallel line thing is kinda cool
Also about the proof of the same area for rectangles in parallel line, one could use similar triangles to prove it, basically the ratio of the sides of the triangle is same, and since the similar triangles is "flipped", the length and width are scaled up and down by the same factor, causing the area to be same
Great content but the music is so annoying
The best explanation of logarithms I have ever seen in my life. ❤
exp(ln(a b)) = a b exp(ln(a) + ln(b)) = exp(ln(a)) exp(ln(b)) = a b
The student meets the logarithm in high school math, in second-year algebra, but this proof requires a familiarity with integral calculus.
Сразу видно, образование у вас не советское, советские первоклассники придумают намного более простое доказательство.
Very useful presentation Learn visually Sir. Thank you
I was unable to grasp why the parallel line from point b on the ordinate to the abscissa measured the distance/area ab. I would suggest that an insert into the video making this step clear is desirable. Your pupil, David Lixenberg
beautiful
Full of orthographic mistakes and the proof is extremely roundabout. A shorter geometric proof: define ln(a) as the signed area under 1/x for x between 1 and a. Now, fix b>0 and consider the transformation of the plane (x,y) -> (bx, y/b), which preserves the ares. The graph of 1/x goes into itself, and the area that was under it between 1 and a goes to the area between b and ab, from which you immediately obtain the result.
Sorry, but I didn't get, how and why there was a leap from 1/x to ln(x) as so it proves the considered property of ln. May be there is an implicit presumption of an integral from a to b of 1/xdx is equal to ln(x), it had to be clearly stated before the proof?
Arithmetic Geometry Harmonise Quadrilateral Visuals mean level???
Love this, looks amazing. What software are you using?
More videos plz
I wonder about the lengths covered by each rectangle. What is the relationship between how much of 1/x is covered and what the area is? Also, are each of these rectangles unique on their respective sides?
video lacks definite integral definition - the area under the curve equals the definite integral pre-calc viewers may find it hard to understand this - but - I'm not discrediting this video and I think it's brilliant
video lacks definite integral definition - the area under the curve equals the definite integral pre-calc viewers may find it hard to understand this - but - I'm not discrediting this video and I think it's brilliant
Hopefully 1 day I will understand the math
Incredible! ❤️
10:03?
Thank you for this. One small point - music was unnecessary and made it a little difficult to hear you.
Wonderful geometric proof. I loved it. Simple.