Visual Cauchy-Schwarz Inequality
Вставка
- Опубліковано 12 кві 2023
- This is a short, animated visual proof of the two-dimensional Cauchy-Schwarz inequality (sometimes called Cauchy-Bunyakovsky-Schwarz inequality) using the Side-angle-side formula for the area of a parallelogram.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoffee.com/VisualPr.... Thanks!
To see a longer (slower) version of this video, without words, check this out: • Cauchy Bunyakovsky Sch...
This animation is based on a visual proof by Sidney H. Kung from the February 2008 issue of Mathematics Magazine (www.jstor.org/stable/27643084 - page 69).
To learn more about animating with manim, check out:
manim.community
#math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #cauchyschwarz #algebraicidentity #mathshorts #mathvideo #mtbos
![Functional Analysis 10 | Cauchy-Schwarz Inequality [dark version]](http://i.ytimg.com/vi/KR2LmVKij9U/mqdefault.jpg)
I love the graphical representation of maths. It just feels different and more clear.
this was real intense for me
too much for the shorts format? Too fast?
Theres too much information going on that it's a bit hard to understand
Maybe make this a video?
@@rayansuneer Here it is without words: ua-cam.com/video/mKg_gVagHy8/v-deo.html . Perhaps the "matrix" cyberpunk music might not be your style :)
@@MathVisualProofs it was perfect. Down to the smallest detail
I didn't get any of this, but the shapes were pretty
This man is literally better than my school teachers
👍
First thing school teachers can not make graphical animations on blackboard.
Secondly , they may not know the graphical representations.
I always loved dot and cross product equalities. Michael Penn has a linear algebra playlist will all sorts of cool ones. The vector dotted with itself = it's magnitude^2 is a fun and easy one you could do a short on.
This is what I needed back in college. Thanks, man
NEVER STOP THIS VIDEOS
This is just amazing. It's always nice to see the intuition geometrically
The number of times the word absolute was said was more than the number of times a word that was not absolute was said
That's wonderful
Thanks!
My main takeaway was how shapes can be really pretty
When will you be posting the Pythagoreran Theorem proof as recently published by Jackson and Johnson?
Is a good idea! I will see if I can get around to it. I saw a few other videos done about it, and I haven't looked into it carefully yet.
@@MathVisualProofs It's quite elaborate and deals with infinite sums but in the end it's surprisingly clear and independent. As far as is known, this was the first proof that completely bypasses the so-called Pythagorean identity, which come to think of it can itself be proven via infinite series.
@@SeanSkyhawk yes I know the details. I also know there is at least one other trig proof of the Pythagorean theorem though (see cut the knot website for instance). But the new one is much nicer (uses law of sines only). It’s a great accomplishment by them for sure. I’ll see if I can figure out a way to do it justice :)
Lovely just lovely I wish I had you in my school
Wonderful proof
You are doing great like mind your descision
prerequisite:
- pythagorean theorem
- area of a parallelogram
- triangle inequality and absolute value property
ok not as much as i thought.
I needed this for calculus II, thank you
when I saw Cauchy in the title got scared 😅 but it wasnt nearly as bad as I expected
Lol ik cauchy i was like wtf no way lol
Ok, I have to subscribe to your channel after this
Welcome!
This is so beautiful! Every linear algebra proof of Cauchy-Schwarz that I have come across is so messy and always involves the determinant of some quadratic, but u couldn’t have explained this in any simpler way, using nothing more than simple trigonometry. Thank you so much
:)
Now animate the 3D inequality *with cubes.*
(It’s the meme of “now draw her stealling the Chaos Emeralds”, I’m neither actually asking nor demanding it.)
But it is a good suggestion regardless :)
Very nice
I feel like this is better visualized with the vectors and using projections defined using dot products
Woah really u musta had a protractor born in ur hands n attached to ur hip ur whole life jk
I'll watch this again when I'm sober, stoned me can't understand 😅
My mind blue screened
I love inequalities but didn't know any book please tell me friends inequality books😢
A good one for visualization is "When Less is More: Visualizing Basic Inequalities" by Roger Nelsen.
¯\_( ͡° ͜ʖ ͡°)_/¯
.·´¯`(>▂
I have become fan of yours. Assuming this particular equation will be dealt with only after having the idea of dot product , it is quite straight forward that,
||(a,b)•(x,y)||=||(a,b)||•||(x,y)|||cos(z)|
Tanks bro😮😮😮😮
damn bro explained common sense wowowowowowowowow
Oh yeah of course
Is that Mozart d minor fantasia in the background?
Yes
Is there an error when changing the inequality as sin(z) is removed? If 0
When you remove the sin(z) on the right it is removing a multiplication by a number less than 1. So the equality is gone and the right hand side got larger (or stayed the same).
Alrighty then
а Буняковский..
Yes. I should have included that. It is in the original video description (ua-cam.com/video/mKg_gVagHy8/v-deo.html)
Dot product i didnt know i would see that. Cool as f if its the dot product from physics i didn't do it in my notebook n stop n pause n rewind a million times i got not enough notebooks gotta by some more n pens n find my dam markers for my marker white board
I know some of these words
Jesus Christ......
But why? Why do any of those things? Make it applicable.
I'm too high for maths
totally unintelligible explanation... awful, even knowing it this is absolutely unnecessarily complicated