Napoleon's theorem | Proof |

[@ThinkTwiceLtu]

Hey guys:) Sorry for the lack of uploads recently.. I was busy with my finals and other school work. Now that the winter break has started I should be able to post more frequently. ---- Recently I created an Instagram account where I'll be posting some short animations and pictures from my future works. Check it out if you're interested: @thinktwice_ltu Happy Holidays!

[@genericasianboi]

Happy holidays to you too!!!

[@mikedemchenko3513]

Your proof is incorrect. When you rotate around point a for 120 deg you imply that circles around point a and point c will intersect in point d, but it is not correct. This will only be true if it is known that ab == cd, but it is not given. So this visual proof actually is based on assumption that is derived from what we are trying to proof - this makes circular dependency.

[@davidb2885]

@@mikedemchenko3513 Just rethink it.

[@tahsintariq8757]

Could you please share the processing sketch

[@mindbend1128]

Think Twice Hi , which software u use to stimulate these graphics?

[@cuzeverynameistaken1283]

I think this is the wrong one. The actual one is to never try to conquer Russia in winter.

[@seaofscissors]

Yeah, no. By the winter he was already gone from Russia (14 of December marked the very last remnants of the Grande Armee leaving Russian territories, retreat itself started in October). Rather, the problem was in the (non-existent) supply lines and intensive guerilla warfare. (sorry for being an asshole)

[@cuzeverynameistaken1283]

@@seaofscissors Nah it's cool. I get educated about maths and history at the same time.

[@Kino-Imsureq]

lol

[@frisosmit8920]

Just never try to conquer Russia

[@fomorsataiwan4674]

Mongolian did, they need no math, but they did. Fuck communist

[@EmissaryOfSmeagol]

0:14 At this point I thought, 'well, which center?' Then I realized, all of them, since these auxiliary triangles are equilateral!

[@vijaysubramanian2037]

Same here... Though i only realized it after reading your comment

[@idk7016]

Holy fuck... and I thought I or someone else is gonna ask or complain about it in the comments... thanks

[@nerdporkspass1m1st78]

There is _no_ way the Napoleon I’m thinking of made this

[@HeroDarkStorn]

It is named after Bonaparte, though it is doubted he came up with it (and definitely was not first). If you are thinking of him, Napoleon was quite educated man and not all his "achievements" are from waging wars.

[@nerdporkspass1m1st78]

DarkStorn ohhh Thank you for telling me!

[@Gabtube252]

Napoleon Dynamite?

[@maartentheelen4805]

@@Gabtube252 Tina you fat lard!

[@adamxue6096]

Yes, and no, this theorem is named after Napoleon Bonaparte, but there are many doubts as of now regarding whether it was him or not. Either way, being a war chief doesn't mean he is nothing but that. In fact, concerning Napleon and his artillery usage, he must be at least somewhat good at math. He is well educated, so possibilities of him actually finding this out is still there. I wouldn't go as far as calling him *definitely* not the first one to come up with this proper theorem but as of now, it really doesn't seem like he was the one who did it. Especially concerning the ladies diary and all that jazz, but there are some very good chances of him did actually solve this out, just not the first, and potentially quite some years too late for being the first. Nonetheless, it is dubbed under his name, for now at least. Maybe one day when archaeologists manages to get this clear they will change it to who ever actually discovered it first. Or not, because it would probably cause confusion.

[@wingboy0]

I'm pretty young to understand this but man these theorems are so cool, my mind is blown by these small rules these people just discovered

[@redsalmon9966]

Good, stay curious

[@tharunmalayil2332]

Its wrong bytw...

[@samueldeandrade8535]

Are you old enough now to understand?

[@samueldeandrade8535]

​@@tharunmalayil2332what's wrong?

[@Mamedullin]

*

[@jakob_z]

@@enricobianchi4499 Says the one who can't even name the symbol correctly. This is a delta, ∆. ∠dab

[@enricobianchi4499]

@@jakob_z shut up i remembered it wrong

[@DiegoMathemagician]

hahaha

[@yaaryany]

@@enricobianchi4499 curb your edginess

[@TooHarshForYou]

@@enricobianchi4499 who hurt you today?

[@petermarsh4578]

I adore this channel. So simple, yet so refined and beautiful :D

[@junkalunk]

Wonderful, as always. Have a great new year!

[@ThinkTwiceLtu]

Thank you! You too:)

[@ASLUHLUHC3]

Lol I can't seem to watch a single video nowadays without seeing the word Brilliant.org

[@connorcriss]

Hamzah Patel then stop watching videos. It works I tried it

[@vulgaraszleandrosz4105]

@@connorcriss How do you even comment?

[@connorcriss]

Vulgarasz Leandrosz I use my magical powers

[@TheDipperPinez27]

Vulgarasz Leandrosz never question his magical abilities, or face the power of r/whoosh

[@connorcriss]

TheDipperPinez27 r/woooosh

[@doornumb]

Thank you Think Twice, very cool!

[@debashismondal7536]

HOLY SHIT this is one of the most brilliant channels that I have come acris a.I really like how the vidoes are quite short but very informative and the animations are top notch. It's like daily dose of internet but for geometry

[@Zafarrrrrrrrr]

Now that is a proper New Year present!

[@aditya95sriram]

Yay!! This makes for a great Christmas gift (albeit delayed) Thank you

[@rcb3921]

What I really want at 1:50 is to fix two points of the "original" triangle, and watch the transformation of the whole tessellation (i think i'm using that right) as you shift the third point around.

[@NoNTr1v1aL]

He's back!!!

[@ahoy1014]

And you know what an equilateral triangle means? That's right, the Illuminati logo. With Napoleon's Theorem we can prove that every single possible triangle relates to the Illuminati.

[@chakra6666]

These videos are always absolutely incredible - smooth animation and clean presentation. Amazing work :D

[@ThinkTwiceLtu]

Chakra Thank you!

[@sirjohnnyg]

Is the last graphic implying that you can always tile the plane with this configuration?

[@TH-is8cf]

You can tile almost any kind of repeating pattern

[@ReaperUnreal]

Equilateral triangles tessellate perfectly, and so I think it's fairly easy to prove that this should tessellate perfectly.

[@stevethecatcouch6532]

@@ReaperUnreal Right. Just sketch in the congruent equilateral triangles the theorem gets you. Then show that tge triangular gaps in the resulting grid are all congruent to the Napoleon triangles.

[@stevethecatcouch6532]

Look at any one of the three configurations with the three equilateral triangles meeting at a point. Add the three copies of the original triangle. The resulting convex hexagon meets Conway's criteria for a tessellating hexagon.

[@Invalid571]

See M.C. Escher

[@rishabhdhiman9422]

Maths with lo-fi, sign me up

[@lok7396]

Yo the music is really trippy

[@ammyvl1]

the thumbnail immediately intrigued me and the video did not disappoint

[@HM-sc4to]

The tiling at the end is neat!

[@223breno]

As always, beautiful and fun video! Happy hollidays!

[@hpp6116]

Amazing theorem! Amazing visualization!

[@ジョルノ-d4w]

this theorem is beautiful.! I like this theorem's proof in complex plane.

[@Invalid571]

Your proofs/videos are always beautiful. Excellent! 👏 👏 ☺

[@ThinkTwiceLtu]

Invalid571 Thank you :)

[@ianprado1488]

I love your work

[@thingsfromspace]

At 1:15, how is it clear that ad and cd come together at a point?

[@alex.mojaki]

I wondered the same thing! Rotating the triangle b by 120º either way doesn't change it, and it has to still be joined at a vertex to a/c, so the two rotated triangles must coincide. Plus, the triangle only has one center which also doesn't move after rotation. Does that make sense?

[@thingsfromspace]

@@alex.mojaki Yes! Thanks so much!

[@dominiquefortin5345]

I think a better way to convince yourself that the triangle B' (the triangle that contained b before being rotated 120 deg. around c) is the same as B'' (the triangle that contained b before being rotated -120 deg. around a) is to put the angles inside the original random triangle (I'll call it T) then do the rotation around c and calculate the sum of the angles around the point where T and T' (T after the rotation around c) touches.

[@WayneKimRecords]

24/7 proofs to yeet/relax/ and leave as an exercise to readers

[@yossefbudagov8748]

this is beautiful great job

[@keppycs]

1:50 Am I the only one who finds the edges of the triangles looking a bit curvy?

[@xD-jm2ie]

I think it is because the triangles form circles. The brain is predispositioned to see patterns, so i wouldn't be surprised if the outer edges of the triangles appeared rounded.

[@greyfong8192]

1:50

[@whatisthis2809]

@@greyfong8192 the reason it didnt show is cause saying am/pm thinks its a time 1:50 1:50 Am 1:50 Pm 1:50

[@whatisthis2809]

@@greyfong8192 also nice name and icon

[@DynestiGTI]

1:44 what a nice tiled floor pattern.

[@mediter123]

One thing to tack on during your proof is that your taking advantage of parallelograms to show your sides are congruent in length! Very cool although not 100% intuitive. Great animation as always!!

[@alenandmuryelvlogs480]

My head hurts with the geometry class I’m glad I graduate from this already

[@ohboy1113]

This is my favorite channel.

[@atharvshendage4705]

This channel is underrated

[@yoavcarmel1245]

wow nice proof!

[@mac_3952]

I love this channel so much. Thank you!

[@GorjeCeleb]

Hi, I love your chanel and I have a question that my complex calculator couldn't specify it. The question is... Function i (n) = Log*i (i+n) (N starts being 1) Can you solve it for me? Thank you for your awesome videos.

[@sanath8483]

What do you mean by log*i? Also does i=sqrt(-1) or a function in this equation?

[@donegal79]

do you normally ask for free tuition?

[@avocadosauce6840]

Good as always But I still recommend a video on Leibniz formula

[@mathloverofallmath1890]

i love this stuff

[@ThePharphis]

awesome!

[@badhbhchadh]

Is that a delta Δ you used at 1:22 instead of the triangle △?

[@victorserras]

Great animation, though I’m curious: did Napoleon actually come up with this theorem or is it just named after him?

[@dainmeister]

Is it me or does pausing 1:45 make an optical illusion where the lines sometimes seem wavy

[@abhavishwakarma5035]

That music totally suits the content man...

[@alwysrite]

beautiful stuff

[@colonelstriker2519]

Trippy and cool

[@toolebukk]

I would love that wall paper

[@cavver3523]

I love these videos. That's really a good job. Do you make music by yourself?

[@ThinkTwiceLtu]

Thank you~ No the music wasn't made by me. Check out the description for more info about the artist^

[@cavver3523]

@@ThinkTwiceLtu oh, thanks. I really like it! :)

[@shilpimitra5342]

Wonderful

[@vegarsc]

I don't know what art is, but I know this is.

[@edwardsu764]

This video just left me with more questions please help

[@Eta_Carinae__]

It looks like the property is contingent on the fact that the equilateral triangles, in their pivot, will guarantee rotational symmetry. I imagine it should work for quadrilaterals and squares too, and any other shape or pairings of shapes which can tesselate under rotation... right?

[@farisakmal2722]

Me: * standing on a ledge * * crying * There's nothing left to live for. Fireman below: Dude, Think Twice uploaded a video. Me: * stops, rushes down the stairs, runs home and opens youtube *

[@ThinkTwiceLtu]

Faris Akmal

[@steffen5121]

This trippy music...

[@whooshwhoosh3094]

1:13 the dab angle

[@philippw4769]

very nice

[@melonbals5512]

i dont know but why does it look like each of the grey triangles look curved at the corners a 1:43

[@furkangogus]

Happy new year.

[@petardobrev5267]

Well, i am making a school project for this theorem but I am stuck. I am currently at 8th grade and I need to proof the theorem without using complex numbers, integrals or anything like that.. Is it possible to make the proof from the video to a proof on a paper? I will be very thankful if someone can answer me. :)

[@yaeldillies]

The proof I knew uses complex coordinates. It's as simple but not as visual!

[@bhaskarpandey8586]

Its somewhat like the ptolemy's theorem proof ! ( the easy one )

[@izakj5094]

A beautiful visualisation, but what exactly are the centers of those triangles?

[@atomiccompiler9495]

Liked before watching :D

[@vpambs1pt]

Love it (:

[@ThinkTwiceLtu]

Nuno Mateus Thanks man:)

[@ingilizcehazrlk9134]

Perfect

[@nightmare3711]

That music tho Love your channel tho

[@SkyFoxTale]

How do you make such animations?

[@mindbend1128]

Which software u used to stimulate these graphics?

[@osirisapex7483]

That music though...

[@baconpancakes8899]

You give me lemmino/top10memes vibes

[@santoshuppal604]

Nice videos btw can u somehow geometrically prove the Cauchy schwarz inequality? The real proof is so difficult

[@ThinkTwiceLtu]

yes! I'll definitely make a video on that:)

[@volfarr2901]

Is it just me or the music seems a little depressing, distraught and has some weird unsettling vibe that is slowly dragging people down

[@electricity2703]

Which program do you use to make these animations?

[@ОльгаРомаскевич]

I am thinking, does the fact that there is a tiling like this give another proof of Napoleon's theorem ? I am not able to formalize it but maybe... there is some simpler proof, something along the lines of lattices ?...

[@sang459]

1:11 why

[@warrior5778]

Anyone help - this is intersection of which center (orthocenter , circum , centroid , incenter )???????

[@lucyluo497]

Whaaaa it was on my birthday!

[@ThinkTwiceLtu]

;)

[@lucyluo497]

@@ThinkTwiceLtu happy new year!

[@yimoawanardo]

Hmm. I'm thinking on the possible reasons one might dislike this video... Perhaps they hate that napoleon invaded their regions in the past ? Hmm.... Perhaps they find the name of the theorem extremely silly ( I do ) ... They hate visual proofs ? ... .....

[@macronencer]

Why would you DO that to music?

[@FearTheImpaler]

whats the use for this? seems straight forward, using equilateral triangles to make other ones...

[@columbus8myhw]

Oww the music

[@dominiquefortin5345]

This proof lacks an explanation why B' (the triangle that contained b before being rotated 120 deg. around c) is the same as B'' (the triangle that contained b before being rotated -120 deg. around a). This could easily be done by showing the angles of the random triangle (as Greek letters) and on the 2 rotated versions, then by calculating the sum of all the angles around the point where the original random triangle and the 2 rotated versions touches.

[@luizfelipegarcia4676]

Dope

[@sebastianzaczek]

The music... microtonal, cool, but confusing

[@martin-rs2gf]

1:16 Dab

[@robertlembo]

Neat :)

[@xyphinon8544]

1:13 Dab

[@qinyuping2823]

genius

[@harjeck9518]

Great animation, great explanation.. just the soundtrack I don't think it fits in there.

[@johnpaterson6112]

Always be deeply suspicious of any video which distracts from serious argument by including needless music. This video is an amusing illustration of the misnamed theorem, but no proof to me. However it helped me to spot a simple proof, which depends on the tiling effect shown at the end. There are symmetries which show that bc equals cd, and you can imagine a third red line heading south-east fom c and constructed from a continuation of the tiling. The symmetry will show that the 3 angles at c are equal, so are all 120 degrees. Likewise da = ab, and the angle at a. The rest follows simply from the qualities of the kite abcd.

[@cl1ckdanny]

Wow I love your videos man!

[@ThinkTwiceLtu]

desk8ers thanks. sure where you at?

[@greyfong8192]

1:14 DAB

[@petardobrev5267]

How can we proof that after the 60 degree rotation there will be a 120 degree angle?

[@dominiquefortin5345]

There is no 60 deg rotation. The rotation of an equilateral triangle on it's center will show the original triangle for 3 angles because of the symmetry of the shape : at 1/3 * 360 (=120), at 2/3 * 360 (=240) and at 3/3 * 360 (=360). So for 1 rotation on the center, any segment with one end on the center of the equilateral triangle and that moves with the triangle will have rotated 120 deg.

[@petardobrev5267]

@@dominiquefortin5345 I needed that for a school project, just a little bit late but thank you :D

[@suup4k75]

Would you ever consider making tutorials for cinema 4D and processing? I'd like to creature videos similar to yours and it'd be cool to see how you do them

[@ThinkTwiceLtu]

Yes I was thinking about making a tutorial someday. Not sure how many people would be interested though. Or I might just do a live stream while I work on some new video.

[@TechToppers]

Now, this is called homothety! I'm thinking, *Was I the only fool who bashed this stuff with law of cosines?*

[@JoeMansley]

I used complex numbers.

[@ashes2ashes3333]

Why does ac intersect angle DAB?

[@ArdourXL]

Why is it always true that ab=ad?

[@skeletonrowdie1768]

pretty sure napoleons theorem is about a meter being one meter