Visual Cauchy-Schwarz Inequality

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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.
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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/... - page 69).
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Опубликовано:

21 сен 2024

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Комментарии : 62

@ruthvikas Год назад

I love the graphical representation of maths. It just feels different and more clear.

@buffalonels988 Год назад

this was real intense for me

@MathVisualProofs Год назад

too much for the shorts format? Too fast?

@rayansuneer Год назад

Theres too much information going on that it's a bit hard to understand Maybe make this a video?

@MathVisualProofs Год назад

@@rayansuneer Here it is without words: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mKg_gVagHy8.html . Perhaps the "matrix" cyberpunk music might not be your style :)

@rayansuneer Год назад

@@MathVisualProofs it was perfect. Down to the smallest detail

@realcontentgamer Год назад

This man is literally better than my school teachers

@MathVisualProofs Год назад

👍

@ts.nathan7786 Год назад

First thing school teachers can not make graphical animations on blackboard. Secondly , they may not know the graphical representations.

@Zangoose_ Год назад

This is what I needed back in college. Thanks, man

@Tiago- Год назад

I didn't get any of this, but the shapes were pretty

@oliverpackham6278 Год назад

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.

@abdullahyasinyagmur4687 Год назад

This is just amazing. It's always nice to see the intuition geometrically

@rafaelrezende7953 Год назад

NEVER STOP THIS VIDEOS

@asparkdeity8717 Год назад

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

@MathVisualProofs Год назад

@imchillbro479 Год назад

That's wonderful

@MathVisualProofs Год назад

Thanks!

@flamurtarinegjakyt3745 11 месяцев назад

I needed this for calculus II, thank you

@wryanihad 11 месяцев назад

Wonderful proof

@StratosFair Год назад

Ok, I have to subscribe to your channel after this

@MathVisualProofs Год назад

Welcome!

@matthewbell4273 Год назад

My main takeaway was how shapes can be really pretty

@mathematicsman7454 Год назад

You are doing great like mind your descision

@alvargd6771 Год назад

when I saw Cauchy in the title got scared 😅 but it wasnt nearly as bad as I expected

@AnglandAlamehnaSwedish Год назад

Lol ik cauchy i was like wtf no way lol

@SeanSkyhawk Год назад

When will you be posting the Pythagoreran Theorem proof as recently published by Jackson and Johnson?

@MathVisualProofs Год назад

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.

@SeanSkyhawk Год назад

@@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.

@MathVisualProofs Год назад

@@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 :)

@TheCyanKiller Год назад

The number of times the word absolute was said was more than the number of times a word that was not absolute was said

@Rócherz Год назад

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.)

@MathVisualProofs Год назад

But it is a good suggestion regardless :)

@Joffrerap Год назад

prerequisite: - pythagorean theorem - area of a parallelogram - triangle inequality and absolute value property ok not as much as i thought.

@viking148 Год назад

Lovely just lovely I wish I had you in my school

@jupjup9737 Месяц назад

You can also prove this using the dot product formula: abs(a•b=|a||b|cosθ) Since |cosθ| is less than or equal to 1 this also proves the inequality. However the proof for the dot product formula is more complicated than the one on the video.

@teaaa2525 Год назад

Very nice

@srikrishnaghosh7660 Год назад

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)|

@arvindsrinivasan424 Год назад

I feel like this is better visualized with the vectors and using projections defined using dot products

@AnglandAlamehnaSwedish Год назад

Woah really u musta had a protractor born in ur hands n attached to ur hip ur whole life jk

@robertogajim470 Год назад

Tanks bro😮😮😮😮

@lolzhunter Год назад

Oh yeah of course

@yeeter2785 11 месяцев назад

damn bro explained common sense wowowowowowowowow

@mikaeo23 11 месяцев назад

I'll watch this again when I'm sober, stoned me can't understand 😅

@javohirtursunaliyev5036 Год назад

I love inequalities but didn't know any book please tell me friends inequality books😢

@MathVisualProofs Год назад

A good one for visualization is "When Less is More: Visualizing Basic Inequalities" by Roger Nelsen.

@robertogajim470 Год назад

¯⁠\⁠_⁠(⁠ ͡⁠°⁠ ͜⁠ʖ⁠ ͡⁠°⁠)⁠_⁠/⁠¯

@robertogajim470 Год назад

.⁠·⁠´⁠¯⁠`⁠(⁠>⁠▂⁠

@marshelldoonan7798 11 месяцев назад

My mind blue screened

@OmnivorousOtter101 Год назад

Is that Mozart d minor fantasia in the background?

@MathVisualProofs Год назад

Yes

@aidenhastings6341 11 месяцев назад

Is there an error when changing the inequality as sin(z) is removed? If 0

@MathVisualProofs 11 месяцев назад

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).

@aedes9902 Год назад

а Буняковский..

@MathVisualProofs Год назад

Yes. I should have included that. It is in the original video description (ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-mKg_gVagHy8.html)

@robquinnpc Год назад

But why? Why do any of those things? Make it applicable.

@DOLfirst Год назад

Alrighty then

@siguy715 Год назад

I know some of these words

@AnglandAlamehnaSwedish Год назад

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