Magic Hexagon - Numberphile 

too late?

Too soon

???

haha xD

lolololololololololololol

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

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

??

me too

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

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

YES THIS!

THE poorly designed Settlers of Catan board.

WeirdChamp

@@TriantalexmonkaW

+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

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

??

@@Triantalex A hexagon has six sides. But it's gone. So it's a hexa-gone.

i cant even understand what he's saying "if you want to edit and cut to xxxxxx" ?

BattousaiHBr thats the point

+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!

Same

Me too.

+The Pip Man, I love that game.

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 🤔.

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.

You mean a Parker hexagon?

awsomm

Lol

My favourite part. XD

#HardcoreMaths

120 of them all got rejected at the end in the favour of the correct one 😂

Ven Weera It has to have all unique numbers

3:12

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.

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.

+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.

I think it says "sort of edit and cut to hoint (idk) with theee so..."