Sums of Fibonacci Squares

This is a short, animated visual proof demonstrating the sum of the squares of the first n consecutive Fibonacci numbers.
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To see a slower, wider high definition version of this visual identity (without words), check out this video: • Fibonacci Squares Sum ...
Also, check out my playlist on other finite sums:
• Finite Sums
This animation is based on a proof by Alfred Brouusseau from "A Primer for the Fibonacci Numbers by M. Bicknell and V.E. Hoggatt Jr (eds.). You can also find this proof in Roger Nelsen's first Proof Without Words compendium (page 83).
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#fibonacci #math​ #manim​ #math​video #calculus #mtbos​ #mathshorts​ #animation​ #theorem​ #pww​ #proofwithoutwords​ #visualproof​ #proof​ #iteachmath #series #finitesums #finiteseries #geometric #squares
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[@GeHeum]

Furthermore: this rectangle approaches the perfect rectangle!
(A rectangle with sides according to the golden ratio!)

[@user-mv8zx6sw7j]

That's only true because of the formula for fibonaci numbers...

[@rohitg1529]

Golden rectangle is the correct terminology

[@panzerofthelake4460]

but why didn't you do a spiral ☹️☹️☹️☹️☹️

[@HalfBreadOrder]

because it's ^2's

[@LokiSyntek]

To draw the "spiral" the squares would have to be added in either a clockwise or anti clockwise direction.

[@daniman7256]

This looks a lot like a nautilus shell 🔥

[@carmin.e]

BRO THSI IS SO UNDERRATED

[@sciencetechnician8787]

Amazing! superb thought.

[@gabrieletrovato3939]

I love it 👏🏻👏🏻

[@20icosahedron20]

Really nice proofs 👌🏻

[@20icosahedron20]

Amazing proof ‼️

[@Whitekin]

golden ratio in fibonacci confirmed? ‼️‼️🔔🔔🚨🚨🚨

[@nni9310]

thanks

[@gamingbutnotreally6077]

Beautiful!

[@MathVisualProofs]

Thank you!

[@SigmaChuck]

nice

[@aschetos]

Very good

[@MathVisualProofs]

Thanks!

[@Casp33]

But what if the third sequence moves to the left instead of the right

[@maynardtrendle820]

Noice!🌞

[@kennethmui88]

what about the sum of the cube of the Fibonacci numbers?

[@Rando2101]

Try to think about it 👍

[@ronnietwelvetoes1876]

it is ovious

[@justacommonguy7173]

This seems like Pythagorean theorem but with extra steps

[@calcKing]

no

[@humanodaterra]

_perhaps_ hehe

[@KC-dj2ur]

Um...no, it's 0 and 1

[@cheezitsarenoice]

Explain for a 6th grader…

[@johnnyletsgo8647]

Me no like math 😊

[@HalfBreadOrder]

basically you can count the sides and it will be the next number

[@NapasimisOrdibarata]

Domb