Cauchy Bunyakovsky Schwarz Inequality I (visual proof)

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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. #math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #cauchyschwarz #algebraicidentity #mathshorts #mathvideo #mtbos

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Mathematical Visual Proofs

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You took that hep bass line for a walk and mathed up my brain.

missingtourist

In the library studying for my lin alg final but this music has me cracking up 🤣😭

PiceaGlauca

Great job! I enjoyed watching this nice visual proof.

mathflipped

It's a nice visualization. An algebraic proof of the n-dimensional version is also very simple : use that the
quadratic function in t defined as sum (xk+t*yk)^2 >= 0 .Then the discriminant condition is just the Cauchy-Schwarz inequality.

renesperb

Great explanation! Though at the end angular brackets have been used to denote coordinate pairs, which is a bit confusing since they are usually used to denote inner products (and inner product also features in the video!).

the_hidden_library

So gooood, once you get the hang of it, it flowws, thanks for sharing ^^

vpambspt

This guy always has the best videos. Keep it up.

horlickminton

Thanks.. quite helpful to remember, when in doubt..

harishsasikumar

why are the absolute value operators necessary?

duccline

the music is horrible but i love the simplicity of the explanation!

alexbourlis

This proof only works for the special case where the inner product is the dot product. This does not prove the Cauchy-Schwarz inequality.

ichigonixsun

А если поверхность не является однородным пространством?))😀

заряд-од

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