Magic Hexagon - Numberphile
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- čas přidán 25. 08. 2014
- Dr James Grime talking Magic Hexagons (and magic squares).
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At least it is not a Parker hexagon
too late?
Too soon
???
haha xD
lolololololololololololol
I just love James Grime
SpeeDim so do we!
There's just something about him, isn't there...
Andrew Cunningham perhaps its his little professor
maybe it's just because he's British and I'm not, but he seems like he'd make a great doctor who
Yes he conveys so much enthusiam
That size 1 magic hexagon blew my mind
Yeah,not to mention the rigorous proof that it is indeed magical
He didn't mention that an n=0 hexagon also works
@@yusuf-5531 diagonals in n=0 hexagon aren't well defined so it is way too hard of a proof for this video
??
His enthusiasm makes me so happy :D
me too
8:33 When you're a Maths teacher and your student asks you to prove why 1+1=2
Does anyone have wood?
I'll give you 2 wheat for 1 wood...
AlanKey86 yep, do you have 1 sheep? I’ll give you two wood.
Awkward for any guy to hear.... Odd glances everywhere
*rolls seven*
But I have all the ore....
I have wood for sheep
James Grime is so great. I always know it is going to be good when it is a video with him.
"Let's count that to make sure." Very difficult math I see it is to check the other 1 magic hexagon.
Thank you for being colorblind friendly in the animation because I had no idea what you were talking about with the shape grouping until that point.
What does it look like. You can only see... Gray? Ha?! No? :(
wolfiksk123 It he means that the red and blue ones look too similar
steinardarri Not exactly, it depends on what type of colorblindness he has, I myself am colorblind and found it difficult to distinguish the blue and the pink. Colorblindness is where you find it difficult to distinguish between certain colors
James: "What I have here is..." --- Me: "A poorly designed Settlers of Catan Board?"
YES THIS!
THE poorly designed Settlers of Catan board.
WeirdChamp
@@TriantalexmonkaW
1:44
Its the cutest "why" I have ever heard!
This guy has so much passion for what he loves and it shows in his videos
What's got 6 sides and isn't here any more?
A hexagone.
??
@@Triantalex A hexagon has six sides. But it's gone. So it's a hexa-gone.
Incredible! It looks like all the other Hexagons have Hexa... _Gone_!!!
I'm sorry for that.
+Bungis Albondigas shame
Sometimes I really wish there was a facepalm emoji. Just, so, so much.
that was a parker square. You still get a cookie :3
Numberphile2 would have been a nice place for the full solution :).
Chris O'Neil there are some small extras from this video coming to Numberphile2 - but not that solution I'm afraid.
Numberphile
Is the solution really that tedious?
EebstertheGreat Its just solving five variables system, nothing big...
João Melo
There's a lot more to it than that, though. That just tells you the sum of each color.
yes, that's my point, if haven't understood I was being sarcastic. A five equation system takes too much time for a video
Oh man I laugh out loud at 1:50 every time
i cant even understand what he's saying
"if you want to edit and cut to xxxxxx" ?
BattousaiHBr thats the point
Thank you Brady:) It's always great hearing Dr Grime talk about math. I did, however, notice a distinct lack of prime numbers in this video, and was wondering if there were any interesting mathematical things going on with geometric shapes that have a prime number of sides. I find it hard to imagine that there isn't.
Well; the regular pentagon has a prime number of sides (5); and its diagonals bisect each other in the golden ratio, which is very much related to the Fibonacci numbers; and the Fibonacci numbers seem to me to contain relatively more primes, than any old random sequence; which, I guess, makes sense, given that the golden ratio is kind of like the most irrational number there is; so, if I expected primes to show up anywhere, it’s definitely in the Fibonacci sequence 🤔.
Nice! I never paid attention to these magic n-gons! Thank you for raising my awareness!
1:52 can't stop laughing
awsomm
Lol
Exponentiation of each number in the hexagon leads to a magic multiplicative hexagon!
+Neel Modi please explain 0.0
+Auro Cords I believe what they meant is that if you had a magic hexagon (or a square, works there too) with any number to the power of numbers in the magic square (or a hexagon) and you multiplied them within rows, you'd get the same number! Observe:
For the usual 3x3 magic square, with rows of (6,7,2) (1,5,9) (8,3,4), if instead you had numbers like (2^6, 2^7, 2^2) (2^1, 2^5, 2^9) (2^8, 2^3, 2^4), which equals (64, 128, 4) (2, 32, 512) (256, 8, 16) and multiplied them (rows, columns, diagonals), they'd give you the same number! (2^15 or 32 768).
The reason this works is because of the way exponentiation works - if you multiply numbers, such as a^b and a^c, the result is a^(b+c), you get the sum of the powers! (Observe: 2^2*2^3 = 4*8 = 32 = 2^5.) This works for any base number (i.e. you can have 3^x, 10^x is especially nice because you only add 0s, e^x... it's up to you!).
Hope that helps and answers your question!
Amazing!
I had forgotten about that property, I guess the original comment should have said "Exponentiation *to* each number in the hexagon..."
I didn't quite get the last part of what you said: " (i.e. you can have 3^x, 10^x is especially nice because you only add 0s, e^x... it's up to you!)."
Thank you =]
+Auro Cords You're welcome! What I meant by that part is that it doesn't need to be powers of 2 like I showed you, but it can also be powers of 3, powers of 10 (especially nice because then you're only adding 0s to the numbers, i.e. you get (100,1000000000,10000) (10000000,100000,1000) (1000000,10,100000000) I think), it can be powers of e - that is totally up to you! The sum of exponents during multiplication applies to any number. :)
Ah yes, that's what I understood but wasn't sure.
This is why I love maths, gotta get some practice tho to keep the brain slick. tx again!
Brilliant video! Brilliant explanation, brilliant subject, brilliant professor. Simply intelligent.
8:35 to 8:44
My favourite part. XD
#HardcoreMaths
10:00 are Grime's birthmarks the vertices and center of an equilateral triangle?
Illuminati confirmed.
***** if it was an equilateral triangle, it would be all of them! (I loved that one video)
+Daggawaggaboof It looks like it _is_ an equilateral triangle!
What an awesome birth mark
3 zeros in the time stamp. 3 side in a triangle. Illuminati confirmed.
Numbers that can't be in the same row in a 3x3 magic square:
1,2
1,3
2,3
7,8
7,9
8,9
7,4
3,6
Also, 4 needs to be in a row with 5 or 6. 5 with 4 or 6. 6 with 4 or 5.
There are probably other numbers that can't be together or have to be together, but this is what I've found so far.
Sorry, let me correct that. (I am on mobile so I can't edit it.)
A 3x3 magic square where you can only use numbers 1-9 and the answer needs to be 15.
Another correction! You can only use each number once.
Now I want to play the settlers of catan
Same
Me too.
+The Pip
Man, I love that game.
I'm sure Matt Parker will create another magic hexagon that *almost* works. You've always got to give things a go!
You mean a Parker hexagon?
Another James Grime classic!
I love the way counting the sum of all numbers in one hexagon.
Very nice video. I like your way of clearing up things.
Thank you.
Thank you! Also, will there be a Mandelbrot Set continuation? It's been more than a month. :)
Keep up the good work!
Any Parker hexagons?
120 of them
all got rejected at the end in the favour of the correct one 😂
While I enjoy numberphile videos they usually go right over my head! I actually understood this video and followed his thinking all the way through so I really liked it.
Very nice and not too hard either!
You should do more videos, I love them, James :)
James you are awesome! Keep up the good work!
The magic hexagon is in the shape of the flower of life.
Having Dr Grime must be such a fun lecturer to have
@8:33 there is a slight addition error, happens to the best of us
Ven Weera It has to have all unique numbers
3:12
I get the same feeling as reading a chapter by Martin Gardner.
thanks Brady, thanks James for the wonderful content!
ND
8:22 That Smile!!! LOL! This guy loves numbers clearly
You're my magic hexagon James...
he`s so happy about it! :D
"And the diagonals too!"
Matt Parker: what.
Really good video. Great chromakeying with the blue writing too, and very interesting to watch. Love it! :-)
Dr James Grime is my favorite :)
Love your show, Numberphile.
I want a t-shirt with a magic hexagon on it
James' videos are my favorite tbh.
Poor empty hexagon, he didn't even get mentioned :'(
Yeah! And what about n=-3! :(
Zardo Schneckmag n = -3 would make the denominator 0; better make it n = -2.
louisng114
n=-3 would make a denominator of -5. A denominator of zero never appears.
Zardo Schneckmag Oops, I mean "makes the denominator -7."
louisng114
Yeah, whatever! :D I'm used to calculate with 2n+1 more than 2n-1.
Dr. Grime is so fun to listen to... I wish I could do my whole undergrad over again where he teaches every class.
This is Amazing, I find this so interesting! Thank you for teaching me something new!
I love the singing banana
0:58 NICE! :D
Thank you for blowing my mind once again.
Beautiful video!
I'M CRYING AT BRADY'S EDITING
8:31 The Highlander magic hexagon
when he checked the magic hexagon of n=1 I died.
Reminds me of a game we used to play in maths class called 'Nubble'. The maths of the game has nothing in common with the video but there were numbers in hexagons which formed a large hexagon.
Not going to lie. My interest in watching this was to get better at settlers @numberphile
This is entirely based on the fact that it has to use every single number from one to the number of hexagons (19 in this case), which is not a condition for a magic shape.
Could you perhaps do a video on slide puzzles? I've been doing lots recently and can never do a scrambled 4x4 in less than around 60 moves, is there a number of moves all can be completed in like Gods Number, and how about for a nxn puzzle? Love the videos!
This went whoosh, over my head. But I love his dimple
Not sure if editing humor at 1:52... or just mistake during editing...
I think it says "sort of edit and cut to hoint (idk) with theee so..."
Sorry, James! That's not the only magic hexagon. I have one just like it here!
Wow, grats on 1m subs!
In the video you never mentioned that the Magic Hexagon must be made of consecutive numbers. Since you can just multiply all of the Numbers in the Hexagon shown in this video by 2 and get a new Hexagon that Works. (MAGIC NUMBER: 76)
If you want a Magic Hexagon in it's simplest form, you can take the Hexagon shown in the video and Add 8 to the Pink, then Add 16 to the Blue and Center. This will give you a new Magic Hexagon in it's simplest form. (MAGIC NUMBER: 70)
Thanks for the explanation. I couldn't figure out what was going on at 2:34
Magic number 76 works as well as other multiples of 38 . The array of numbers for M 76 are consecutive even numbers! These magic hexagon 1-19 numbers x3 =114 should work but they r not consecutive numbers..
and for 70, I tried but it’s not working for all rows..
@@yatra6110 Add 16 to the center instead of 8, that's mb
Very interesting. I have to say though, I only really watch when James is in the videos.
Good work !!
Welcome back James
Kept seeing the "Settlers of Katan" board when I saw the Hexagons, haha.
Fantastic. Thanks a lot.
Great one!
Amazing! Great video. Seems a bit miraculous that even the 3-layer hexagon works.
+Ace Diamond theres nothing miraculous about it, its just a coincidence, things would be different if the numbers used is base 6 not base 10
Well yeah, that's kinda what I meant, not a literal miracle, lol.
But, besides the point, this concept is base-independent.
Dr James Grime said "There can be only one..." He's my new hero. The Highlander of Hexagons!
Great videos watching from Serbia!
This is great! I really love proofs like this. Has it been used for anything practical yet or is it still just in the realm of recreational mathematics?
5:24 and then James Grime sets the hexagons on fire
I like how Numberphile finally touched on Magic Squares :)
Also, every comment (except Brady's) below me has nothing to do with the video. Lol.
boilpoil we've done magic squares before!!!
Numberphile Really? I only subscribed a few months ago, at the video about -1/12 xD
boilpoil better get into the back catalog!!!!
boilpoil boy got you some work ahead of you
There already is another video about magic squares.
its cool how you just added his handwriting instead of a preset font :)
Great video! Thanx, im now thinking aboyt it in dozenal would be the formula nicer
No one tell Matt this is the only one and let him "have a go at it" XD
Awesome video! Will there be anything on Klein bottles?
For a moment, when James started adding the numbers 1 + 2 + ... + nn, I was lost. But then I remembered that a magic square must be made of all the numbers up to and including nn.
Also, are there any other magic hexagons if we remove the constraint that the numbers have to be from the set {1, 2, 3, ..., 3n(n -1) + 1} only? Like, could we use distinct whole numbers not necessarily from that set to fill out the honeycomb, and still get this effect?
It seems to me that that problem would have a much more involved and non-elementary solution than this one.
This is a beautiful proof!
Very cool! I'll have to give this a go in my spare time =p
Numberphile If I get this right, the definition of a magic hexagon is to use each number once. If you allowed that rule, you could create infinite magic hexagons by simply adding 2 to all outer numbers, 1 to all middle ring numbers and 0 to the central number (in this example they all add up to 44 then (you take 3x the number you added to the outer ring)), however in my workings you do get the number 5 three times.
Perhaps it would have been a little clearer if the coloured hexagons were turned over during the section from about 9:00, to make it clear that we don't know where all the numbers should be yet. Just a suggestion in case you do a similar video in the future, great work as always!
YES!
Amazing！
Awesome!
YOU ARE THE BEST
At the end, I have checked why it is the only magic hexagon, and I didn't understand why Y is even, smallest possible
Numberphile should get a show on PBS. Preferably PBS, because it's too smart for cable TV. I'd love watch it.
Question, you have a 8 1 6 | 3 5 7 | 4 9 2 magic square as mentioned in the video, it would seem to me that if the magic hexagon has to be able to work from any angle with any number of hexagons then why doesn't the magic square have to say add up to the magic number when you take say 1 from the top row middle column and 7 from the middle row right column?
I do love that this mathematical phenomenon created the entire genre of “hex bingo”
What if you remove the requirement that the numbers in the cells have to be 1 through n?
FYI, this fucking ROCKS!
Sitting here watching videos about magic squares, and just noticed Matt Parker's "Magic Square Party Trick" for the 34 magic square! Oh, you guys.
That was really fun. :D
That's great. Magic Squares are to mainstream, so it's good to have this. Very interesting that there's only one possible way to do it.
Lol, when Brady edited. That was hilarious