Area of dodecagon | Beautiful geometry | Visual mathematics

Just a short and simple animation of how to find the area of dodecagon by knowing its radius. Obviously there are many different ways to do it, but I thought that this one was the most visually appealing.
We've reached 600subs faster than I thought so just wanted to thank everyone for the support:) (really)
Your comments, thoughts and ideas are always appreciated.
See you soon,
TT
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Support my animations on:
/ think_twice
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Any further questions or ideas:
Email - [e-mail]
Twitter - / thinktwice2580
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Programs used:
Cinema 4D
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[@Mathologer]

Definitely one of the nicest visual proofs of this fact :)

[@3blue1brown]

Agreed!

[@tranl1050]

I like how this is kind of a proof that the formula of the area of a polygon approaches that of a circle. e.g. Area of: square = r^2 Hexagon = [3^(3/2)/2]r^2 ≈ 2.598r^2 Dodecagon = 3r^2 Circle = πr^2 ≈ 3.142r^2 Beautiful

[@minnarew]

woah TWO of my fav math peeps? WOOHOO

[@minnarew]

im so lucky

[@rcb3921]

The algorithm brought me to this channel a few weeks ago. Now with approval of Mathologer and 3b1b ... i can definitely subscribe.

[@digama0]

It's also worth mentioning that this is a really low tech way of proving that pi > 3

[@matthewniles2817]

no way that's insane

[@ahmadzia1927]

I hope you get well soon! And don't pressure urself for not uploading longer vids, we understand the situation and why u would want to take some time off. And the video was fantastic as always!

[@ThinkTwiceLtu]

Ahmad Zia thanks for understanding:) I'll try to recover fast

[@AgentMidnight]

Very elegant indeed

[@ThinkTwiceLtu]

Cubik thank you

[@willfeav]

You should watermark these, gifs are often made of beautiful geometric videos like this and shared without attribution... nice work

[@ThinkTwiceLtu]

willfeav true, I could put a small one somewhere in the corner but then it could be easily covered up. And If I put a big one at the centre, it would make the animation look a bit worse. what do you think?

[@EdwardNavu]

For this one video, the dodecagon can be watermarked in a way that the TT logo show up on 1 or 3 squares when they're assembled The problem is what the dodecagon would look like before assembly tho.

[@aidenwallin3523]

@@ThinkTwiceLtu You could make the watermark or logo into the background, similar to end of the video. I would just fade it out slightly, so that it isn't distracting.

[@chomkypanda]

OMG!!! WHY HASN'T THIS CHANNEL BECOME HUUUGE YET???? Something is definitely wrong. Your videos are amazing! Keep up the good work

[@ulkar_aghayeva]

This is a thing of beauty, - a beauty that is first hidden and then revealed in a most surprising way! :) And one could write this under every video you make.

[@yuyiya]

_Love_ these short, sweet and very visual videos. More powerful than thousands of words!

[@assmuncher2396]

Dude i fucking love your simplistic animation style. its quite frankly very beautiful and nothing on youtbe compares! Please don't change this format and I would love to see more beautiful visual proofs of "simple" geometric concepts. You are truly creating art here, and I love that you are now making the animations without as much annoying text. Keep up the great work!

[@ThinkTwiceLtu]

Thank you:) Ya I'm trying to use less and less text, no one likes text heavy videos. However sometimes it's quite hard to explain smth without words so I'll have to use some text from time to time. Appreciate your support, and thanks for commenting:)

[@assmuncher2396]

i think as long as the text is pretty you'll be good

[@arnavdas3139]

Smoother than silk

[@ohorok2]

Wooow Math IS poetry, philosofy and one universal language.. the language of the Universe...

[@toastybread7375]

if the number of sides tends to infinity, does the 3 tend to pi to give A=pi*r^2?

[@inna9882]

Yes

[@aidenwallin3523]

Yes, because a circle could be described as a regular polygon with infinitely many sides. As you stated, the area of a circle is πr^2, which is also the area of a regular polygon with infinite sides.

[@Madsy9]

Gorgeous animation and area proof. All the best wishes and get well soon!

[@ThinkTwiceLtu]

thanks a lot:)

[@sumathi387]

Best derivation by rearrangement ever I've seen that's superb keep it up

[@flappyfungus5415]

This will help me so much in geometry, thank you

[@jkim319]

Hope you get better soon! We are always here supporting you and your videos! They are great! Xx

[@ThinkTwiceLtu]

jeongrim kim Hey! thanks:) didnt know you were actually watching them.

[@jkim319]

Think Twice haha of course I am! Don't forget that I always watch them 😉😉

[@ThinkTwiceLtu]

jeongrim kim I won't😊 say hi to Sol from me

[@Jen_TheSnail]

Awesome!

[@dejnol]

Very, very satisfying video. Get better soon!

[@vpambs1pt]

Don't worry about posting longer videos, these are excelent, and hope you get well as soon as possible!

[@ThinkTwiceLtu]

Nuno Mateus thanks man:)

[@lukedope36]

wow!this really shows that as the sides approach to infinity,to find the area is like multiplying a square to m (as the sides approach to infinity,m=pi)

[@lukedope36]

now, all we need is a formula to distribute any sides as to form pi

[@jhonlawrencebulosan741]

Doesn't fail to amaze once again

[@TheLastEchelon]

Just discovered this channel and i must say sir, you have quality content.

[@ThinkTwiceLtu]

Thank you

[@noneuclidean_]

this is some super satisfying 3blue1brown shit

[@OliverTheAmpersandCat]

i literally said WHAT after i realized the math ion my head lol

[@tannerleonard4412]

Amazing! I hope that you have a quick and safe recovery!

[@liamandliahtoysplay]

amazing video

[@chiletv2936]

this is simply incredible..

[@thegrandestbazaar4800]

Very good

[@addityasinghal897]

Silent and beautiful

[@andyandrw]

Simple, concrete but powerful video :)

[@jameswise9171]

I'm just gonna go question everything I thought I knew.

[@فارسالزعبي-ف3د]

Amazing

[@cuzeverynameistaken1283]

How does one even come up with this? This is amazing.

[@neidenMetalun]

Philosophy was invented by Think Twice when he tried to think twice at the same time

[@narmadraval25]

Great work !! It would be pleasure seeing the Libneits/Madhava's pi series geometrically. Thanks

[@theinventionofzero1896]

Amazing! Feel better soon

[@ThinkTwiceLtu]

The Invention of Zero thank you!

[@omniscientomnipresent5500]

I already thought of that but cool

[@driftliketokyo34ftw35]

Looks like a super computer initializing.

[@Pedritox0953]

0:38 Mathgasm

[@BatuhanEvren]

magic

[@infamouscoffee4934]

That's pretty clever

[@christiansinger2497]

Sehr gut!

[@math4fun378]

Amazing!!

[@ThinkTwiceLtu]

MathIsFun :)

[@anishgupta4260]

Beautifulll❤❤

[@Mr.Malfunction-t3j]

gimme a sec, i'm gonna cry real quick

[@hugotosone223]

La relacion entre las áreas del dodecaedro inscripto y el circulo es: (3 r x r) / ( pi x r x r ) .... resultand aproximadamente 0.955. Lo que equivale al 4.5 % menor

[@hugotosone223]

Alternativa elemental: Son 12 triángulos isósceles con 2 lados =r y el lado corto = 2 (r x sin 15°). El area total es: 12 x [ 2 (r x sin 15°) x r cos 15°] x (1/2)... o sea 12 áreas del triangulo isósceles. Por identidad trigonométria y simplificando queda: 6 x [ (r x sin 30°) x r ] y finalmente resulta = 3 r r

[@ragnaoeynhausen898]

Get well soon! :)

[@ThinkTwiceLtu]

Kurumi Kaneko thank you:)

[@thatoneguy9582]

so how do you do it from knowing the side lengths

[@rochelimit55555]

Woooooowwwwwwww

[@murenkang2976]

The animation reminds me of Iron Man wearing his amour :) Will this work when treating other regular shapes like a 16 shaped one? Or maybe the volume of a 3D object?

[@yuyiya]

You've got a couple of intriguing questions there! Maybe you're a mathematician?

[@murenkang2976]

um wow my comment 2 years ago was replied now! btw I am not a mathematician, but extrememly interested in math. I wrote the question when I was 13 yrs old

[@identicalgd2446]

Woah

[@DowzerWTP72]

So if you had just 4 points, the area would be r², and with 12 it's 3r², so does that mean you take the number of points around the circle and divide by 4, and you'll get the amount to multiply r² by?

No, why do you think 4 points = r²?

[@pedronunes3063]

No because there a limit, that is πr^2, no figure has a area bigger than that.

[@DowzerWTP72]

Of course! I don't know what I was thinking! I don't know how I forgot πr^2!

[@pedronunes3063]

There a formula, r^2×sen(360°/n)×n/2 n is the number of verticies. And it's equal to 2r^2 when n=4

[@aleksandarprodanov4454]

Happy new year!

[@ThinkTwiceLtu]

Apple Productions Happy new year! hope you have a nice day.

[@aleksandarprodanov4454]

I really like your videos. Those simple visual explanations are just beautiful. I can't wait your next video. I wanted to ask you how did you make this video, i.e. what softwere did you use?

[@ThinkTwiceLtu]

Apple Productions thanks a lot! i really appreciate your support. I made this video with Cinema 4D, it's a 3D animation software. If you have any other questions, feel free to contact me anytime.

[@ThinkTwiceLtu]

Apple Productions honestly if you'd like to learn how to use this program I could help you out. Although I'm not that good at it myself

[@aleksandarprodanov4454]

Think Twice Think Twice I'll be thankful, but you are busy making other beautiful videos like this one and the other ones. So I don't want to interrupt your work. I really appreciate your offer though.

[@phroggy313]

Like: do this instead of homework Reply: do homework instead of this

[@offlinegaegt4429]

How do u even get the idea how to do that!?

[@warpromo6636]

Lol or you what you can do is connect a line to each point. Make triangles. Cut a triangle in half, rearrange it to form a rectangle Connect all the rectangles and yea

[@petrkdn8224]

NO FUCKING WAY ALMOST 30 K VIEWS 1 YEAR OLD VIDEO AND ONE DISLIKE?????

[@raghafazkamuhammad8576]

Dodecagon? Do you know that a regular dodecagon can be made of six squares, six equilateral triangles, and one hexagon?

[@anwarinianwarini2660]

(3/4)h^2

[@jmm1233]

radioactive symbol turns into 3 core symbol from homeworld

[@ayeariola]

This reminds of the game _PRISM.

[@maximkoneva6517]

I want to become a 69-sided dodecahedron

[@oliot4814]

You're actually doing so well! I can't believe you actually made this whilst in that soviet built piece of shit hospital! XD

[@ThinkTwiceLtu]

I can't believe that my video was approved by Oliot

[@EdwardNavu]

Liu Hui wants to: * Know your location

[@cybo_vampire9145]

0 dislikes... cool

[@carlostdied1184]

this is the first video i have seen with a 1000:1 like ratio: *my life is now complete*

[@cybo_vampire9145]

holy crap cool

[@carlostdied1184]

aaaaaaaaand, just as i say that..

[@carlostdied1184]

at least i got the screenie so thats pretty cool

[@cybo_vampire9145]

back to normal

[@0_-]

hey minecraft 1.13 is almpst a release (look at the time line)

[@carlostdied1184]

niec meme and edgy justin y. comment heres some loosely relevant quality content im deciding to promote for little reason kzbin.info/www/bejne/a5SVi5-NhZacrs0

[@yoavboaz1078]

π~3

[@volfarr2901]

Hate for the 1 unlike

[@insertcringename3931]

im to dumb to understand this😀

[@mdj3638]

Wtf

[@dejnol]

Very, very satisfying video. Get better soon!

[@ThinkTwiceLtu]

thanks :)