Four squares with constant area | Visual Proof | Squaring the segments |

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==Hello everyone==

Another visualization and a proof of some simple euclidean geometry. I think it's pretty neat :)

Two chords of a circle intersecting at 90 degrees make up 4 segments. The squares of these 4 segments always add up to the diameter squared. Hope the video is clear and understandable.

Quick update:

We made it over 2k subs! Thanks everyone for all the comments and support. I wouldn't be here without your help and other bigger YouTubers that help me out along the way.

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You can also support me on:

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Programs used:

- Processing

- Adobe Premiere Pro

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MUSIC:

Cellophane Roses - Reaching

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I would like to thank everyone for the support that I've been getting. As some of you may know my health condition isn't that great at the moment so all the nice comments really help to cheer me up through out the day. Hope you enjoy watching the video and have a nice day :)

ThinkTwiceLtu
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Nothing can be more beautiful than this. Man, your videos are what I call as "Happiness".

yamansanghavi
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I love this kind of little geometry proof. Simple and straightforward and show how beautiful maths is

redsalmon
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I discovered this channel yesterday ... the most beautiful thing that happened to me all year.

MyWissam
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This is one of those moments when you go like "Awww!" because of the sheer beauty of it. Thanks for making my day!

ulkar_aghayeva
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I must be missing something because it is not obvious to me that the line you create at 1:16 is actually the diameter

IncaTrails
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Love the Euclidian geometry proofs, very intuitive and can always be useful somehow hahahha.
Keep going!

vpambspt
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May I know how could you assure that the two line segments must touch to create a right angle? Couldn't it be acute/obtuse?

ericyip
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Sometimes the beauty of mathematics is hidden and arithmetic proofs don't have the same beauty to it... The content of this channel brings out mathematics in its raw form and discloses the deep meaning hidden in plain sight.. Thank you @Think Twice for all the efforts..

garvjain
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I'm so glad I found your channel.

This is what mathematics is.

phatkin
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Honestly these videos are just so beautiful

laurenpearson
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Hence, it gets proven, maths is fun! And, the people who make it fun are great!

tanushka
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My only problem: Why is it that the squares A^2 + D^2 and B^2 + C^2 (both visually equal) are perpendicular when rotated along the circle. How is this and also, how does this translate mathematically and visually when the squares are not equal?

Love the video!

syfontenot
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This is such an amazing site to learn, once again, the concepts we knew only as written proofs. Please keep up the good work and you may want to take a look at the geometrical shapes of the ancient Astronomical Clock "Jantar Mantar"

fbtrytk
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i wish teachers would use this alongside the proofs where they just derive from equations;;;; my maths life would have been soooo much more clearer

toneee
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I don't think I'm looking at this right, but isn't that Pythagorean's theorem being used at 1:24? If so, shouldn't the equation be
"(A^2)+B^2=C^2"? Pluging (A^2)+D^2 from the bottom square for A and (B^2)+C^2 from the square from the right with C, do you not get I don't get this...

Jo_Wick
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this would look really cool as a loading screen logo!

didjterminator
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Wonderful videos which you are creating, Think Twice! Thanks a lot for this.


In this one unfortunally I still don't see why the two segments form a right angle when the endpoints are brought together.

keinKlarname
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These videos made me like math again, tyvm

hafiraa
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This one does just assume (even though true) that the two unequal squares finally forms a rectangle at the joining point. But nice video nevertheless :-)

wens