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!
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.
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)
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.
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.
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
@@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.
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.
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.
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.
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.
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!!
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?
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.
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.
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?
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. :)
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 ?...
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.
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.
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 *
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.
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.
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 ? ... .....
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.
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
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.
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.
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!
Happy holidays to you too!!!
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.
@@mikedemchenko3513 Just rethink it.
Could you please share the processing sketch
Think Twice Hi , which software u use to stimulate these graphics?
I think this is the wrong one. The actual one is to never try to conquer Russia in winter.
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)
@@seaofscissors Nah it's cool. I get educated about maths and history at the same time.
lol
Just never try to conquer Russia
Mongolian did, they need no math, but they did. Fuck communist
0:14
At this point I thought, 'well, which center?' Then I realized, all of them, since these auxiliary triangles are equilateral!
Same here... Though i only realized it after reading your comment
Holy fuck... and I thought I or someone else is gonna ask or complain about it in the comments... thanks
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
Good, stay curious
Its wrong bytw...
Are you old enough now to understand?
@@tharunmalayil2332what's wrong?
There is _no_ way the Napoleon I’m thinking of made this
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.
DarkStorn ohhh
Thank you for telling me!
Napoleon Dynamite?
@@Gabtube252 Tina you fat lard!
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.
I adore this channel. So simple, yet so refined and beautiful :D
*
@@enricobianchi4499 Says the one who can't even name the symbol correctly. This is a delta, ∆.
∠dab
@@jakob_z shut up i remembered it wrong
hahaha
@@enricobianchi4499 curb your edginess
@@enricobianchi4499 who hurt you today?
Wonderful, as always. Have a great new year!
Thank you! You too:)
Yay!! This makes for a great Christmas gift (albeit delayed) Thank you
Thank you Think Twice, very cool!
Now that is a proper New Year present!
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
Lol I can't seem to watch a single video nowadays without seeing the word Brilliant.org
Hamzah Patel then stop watching videos. It works I tried it
@@connorcriss How do you even comment?
Vulgarasz Leandrosz I use my magical powers
Vulgarasz Leandrosz
never question his magical abilities, or face the power of r/whoosh
TheDipperPinez27 r/woooosh
These videos are always absolutely incredible - smooth animation and clean presentation. Amazing work :D
Chakra Thank you!
Is the last graphic implying that you can always tile the plane with this configuration?
You can tile almost any kind of repeating pattern
Equilateral triangles tessellate perfectly, and so I think it's fairly easy to prove that this should tessellate perfectly.
@@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.
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.
See M.C. Escher
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.
He's back!!!
Your proofs/videos are always beautiful.
Excellent!
👏 👏 ☺
Invalid571 Thank you :)
the thumbnail immediately intrigued me and the video did not disappoint
Amazing theorem! Amazing visualization!
The tiling at the end is neat!
As always, beautiful and fun video! Happy hollidays!
Yo the music is really trippy
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.
1:50 Am I the only one who finds the edges of the triangles looking a bit curvy?
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.
1:50
@@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
@@greyfong8192 also nice name and icon
this theorem is beautiful.!
I like this theorem's proof in complex plane.
This is my favorite channel.
this is beautiful great job
This channel is underrated
I love your work
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!!
At 1:15, how is it clear that ad and cd come together at a point?
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?
@@alex.mojaki Yes! Thanks so much!
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.
24/7 proofs to yeet/relax/ and leave as an exercise to readers
wow nice proof!
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.
What do you mean by log*i? Also does i=sqrt(-1) or a function in this equation?
do you normally ask for free tuition?
My head hurts with the geometry class I’m glad I graduate from this already
Good as always
But I still recommend a video on Leibniz formula
Great animation, though I’m curious: did Napoleon actually come up with this theorem or is it just named after him?
I love this channel so much. Thank you!
1:44 what a nice tiled floor pattern.
That music totally suits the content man...
A beautiful visualisation, but what exactly are the centers of those triangles?
Is it me or does pausing 1:45 make an optical illusion where the lines sometimes seem wavy
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?
Maths with lo-fi, sign me up
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. :)
beautiful stuff
I would love that wall paper
i love this stuff
whats the use for this? seems straight forward, using equilateral triangles to make other ones...
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 ?...
Nice videos btw can u somehow geometrically prove the Cauchy schwarz inequality? The real proof is so difficult
yes! I'll definitely make a video on that:)
Anyone help - this is intersection of which center (orthocenter , circum , centroid , incenter )???????
Is that a delta Δ you used at 1:22 instead of the triangle △?
Trippy and cool
I love these videos. That's really a good job. Do you make music by yourself?
Thank you~ No the music wasn't made by me. Check out the description for more info about the artist^
@@ThinkTwiceLtu oh, thanks. I really like it! :)
Which program do you use to make these animations?
awesome!
Which software u used to stimulate these graphics?
Liked before watching :D
Wonderful
That music tho
Love your channel tho
How do you make such animations?
i dont know but why does it look like each of the grey triangles look curved at the corners a 1:43
Happy new year.
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.
I don't know what art is, but I know this is.
This video just left me with more questions please help
How can we proof that after the 60 degree rotation there will be a 120 degree angle?
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.
@@dominiquefortin5345 I needed that for a school project, just a little bit late but thank you :D
Why does ac intersect angle DAB?
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 *
Faris Akmal
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.
very nice
The proof I knew uses complex coordinates. It's as simple but not as visual!
This trippy music...
Why is it always true that ab=ad?
Why is the initial angle 120°
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.
Its somewhat like the ptolemy's theorem proof ! ( the easy one )
Is it just me or the music seems a little depressing, distraught and has some weird unsettling vibe that is slowly dragging people down
Great animation, great explanation.. just the soundtrack I don't think it fits in there.
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 ?
...
.....
A nice graphic but not a proof. You have not shown that phi=120 gets you to the triangles constructed on the alternate face.
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.
You give me lemmino/top10memes vibes
That music though...
Whaaaa it was on my birthday!
;)
@@ThinkTwiceLtu happy new year!
The music... microtonal, cool, but confusing
Love it (:
Nuno Mateus Thanks man:)
Oww the music
1:13 the dab angle
Perfect
1:11 why
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
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.
Why would you DO that to music?
You can't just say It's 120° without any explaining. It wouldn't be accepted as a "proof"
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.
pretty sure napoleons theorem is about a meter being one meter
Dope
Wow I love your videos man!
desk8ers thanks. sure where you at?
This background music is strange and I hate it. Where can I find more?
Neat :)
genius