Cauchy-Bunyakovsky-Schwarz Inequality II (visual proof)

This is a short, animated visual proof of the two-dimensional Cauchy-Schwarz inequality (sometimes called Cauchy-Bunyakovsky-Schwarz inequality) using "Garfield's trapezoid" and scaling of right triangles.
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To see an alternate proof of this fact, check out
• Cauchy Bunyakovsky Sch... (wordless)
• Visual Cauchy-Schwarz ... (shorts version)
This animation is based on a visual proof by Claudi Alsina and Roger Nelsen from the April 2015 issue of Mathematics Magazine (www.jstor.org/... - page 144-145).
#math​ #inequality ​ #manim​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #algebra #areas #mathematics #cauchyschwarz #algebraicidentity #mathshorts​ #mathvideo​ #mtbos
To learn more about animating with manim, check out:
manim.community
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Music in this video:
When We Found The Horizon by Late Night Feeler

[@MathOrient]

Amazing job. Fantastic. Keep up the great work.

[@MathVisualProofs]

Thanks!

[@asparkdeity8717]

First! Looks like nobody else is here yet. Thanks for another great video, I have never come across the 2-variable version of this 👍
I also have a video idea - showing that
sin(54) = φ/2, where φ is the golden ratio

[@MathVisualProofs]

Thanks! Yes sin(18) is on my list and so maybe linking that with sin(54) is a good idea.

[@AliHassan-e2w2g]

Please make a vedio upon the division of two irrational number because it is not making any visual image of division under my consideration

[@abdulwadudsekh9354]

Make video on Vector space

[@MathVisualProofs]

?

[@kingeddiam2543]

Are there practical applications of this or is it just pure maths?

[@asparkdeity8717]

Cauchy Schwarz (in 3 dimensions mainly) comes up all the time in all fields such as quantum mechanics, it is extremely useful in applied maths

[@kingeddiam2543]

@@asparkdeity8717 cool thank you very much!

[@rafiihsanalfathin9479]

Cauchy scwarz ineq is so useful, it is a basic ineq so there is many applications, not only it is basic but it also practical because it works for all real numbers

[@quay6292]

This only works in flat space, right?

[@asparkdeity8717]

Sorry what do u mean by flat space?

[@quay6292]

@@asparkdeity8717 Euclidean. Triangle equality always works in space with constant curvature, but not necessarily in space with varied curvature.

[@МаксимАндреев-щ7б]

It works in Hilbert spaces.

[@asparkdeity8717]

I would assume so, unfortunately geometry was one of the courses I didn’t take so I can’t answer the question - this inequality is only associated with the Euclidean Norm, so I imagine it wouldn’t work with hyperbolic surfaces

[@rafiihsanalfathin9479]

@@quay6292i think it works for other space but don’t quote me on that

[@KinuTheDragon]

The |a||b| for each triangle's sides could have been written as |ab|. Other than that, great video!

[@MathVisualProofs]

Yes for sure! I also probably should have started with just the a,b triangle and scaled that twice...

[@pritamyadav17]

@@MathVisualProofs very fabulous video
My whole family watches your videos together.please keep it up.

[@MathVisualProofs]

@@pritamyadav17 thanks for watching!

[@SirP-rd5yh]

Wastage of time ,

[@MathVisualProofs]

?

[@cat000]

??