More Numberphile featuring Ayliean - kzread.info/dash/bejne/gnuptM-qoNWcf9I.html T-Shirts and merch based on the Kings Tours - numberphile.creator-spring.com/listing/symmetric-kings-tours-number

@AlSuChess

Ай бұрын

This is really cool when you see the pattern on the board like this! Thank you for sharing!

The Parker square still being referenced today is very funny

@volodyadykun6490

Ай бұрын

There was development in the story not so long ago

@aryst0krat

Ай бұрын

@@volodyadykun6490 Oh?

@racecarrik

Ай бұрын

Silly goose, why would a mathematical law not be referenced?

@eryqeryq

Ай бұрын

Poor Matt tho 😢

@cartatowegs5080

Ай бұрын

​@volodyadykun6490 you can't just leave us hanging.

"Who would call that a magic square?" That's savage 😂

I've been working on a Bishop's Tour that hits all 64 squares for 25 years, but haven't succeeded yet.

@shinobu5359

Ай бұрын

Anything's possible! Don't give up!

@JohnSmith-nx7zj

Ай бұрын

When you’ve cracked that I think you should work on the pawn’s tour.

@N.I.R.A.T.I.A.S.

Ай бұрын

😂 keep at it bro

@JustAnotherCommenter

Ай бұрын

Don't try Rook's tour. I think it's too straightforward.

@mathijs58

Ай бұрын

Did you try doing it on a Möbius board?

1:31 Parker Square spotted!

A Parker knight's tour on a Klein bottle that sums to -1/12. The ultimate Numberphile video.

@harmanpreetsingh7848

Ай бұрын

But the path is first passed through an Enigma

Thanks just upgraded my phones unlock pattern ! 📱🔓👍

9:04 Knight's Tours almost _have_ to be more awesome. There's nothing surprising about a piece that moves 1 space at a time being able to visit every square. The weird movement of the Knight is what makes it interesting.

@U014B

Ай бұрын

Exactly. It's the extra restriction on the Knight that makes it so much more impressive.

@TheArtOfBeingANerd

Ай бұрын

I think the fact the a magic square can be formed by each number adjacent to the previous is pretty amazing.

Massive shout out to Pete for the outstanding graphics!

Guy called Pete: "You rock".

@thenoobalmighty8790

Ай бұрын

Your mom rocks

Thanks Pete ❤ 11:18

I love her comment on obsessions of drawing these mathematical objects! I'm a postdoc in theoretical physics, and I definitely questioned myself multiple times in the past, "Do I actually like physics, or do I just like drawing shapes?". It's really nice to see someone who emphasizes the same sentiment!!

I absolutely adore Ayliean MacDonald! I sometimes sit for hours making art by methods she's shown on Numberphile and her own channel.

0:38 looks like a Nepo v Dubov game 😂

@prathamesh413

Ай бұрын

Waiting to see how many will get this reference

@Matthew-bu7fg

Ай бұрын

Hahaha wow very niche reference

@Filipnalepa

Ай бұрын

I know who are Jan and Danila, but I don't know which game itiis about.

@jeronbaxter

Ай бұрын

Imagine 3 fold repetition of knights tour.

@I_am_Itay

Ай бұрын

Knights go brrr ​@@Filipnalepa

Thanks Pete

I like how "tour" comes out as "tewer" in Ayliean's Scottish lilt. By the end of the video, Brady is also calling it a "tewer."

@TomDarlington

Ай бұрын

How do you pronounce it?!

@Nightriser271828

23 күн бұрын

I pronounce it "toor".

1:45 It's called Parker Square

That is super cool! Thanks for sharing! 👏

for someone who loves both maths and chess, this is a win video

chess, magic squares and beautiful art... lovely combination!

This is a visually beautiful video. Well done to the subject and the photographer.

"It's even cooler! If you look at the diagonals... April Fools!"

A knights tour on a Mobius Strip. That's it. That's the most perplexing thing I've ever seen.

Excited about the upcoming Parker Magic Tour

9:49 Look at them... they're having the time of their lives together... and you're just gonna have to learn to accept that.

@BooleanDisorder

Ай бұрын

I do accept and love them both. Harmony. ❤

@LimeGreenTeknii

Ай бұрын

Relationship goals: me and my partner hopping wildly on an 8x8 grid in L shapes.

This episode was extra magical, thank you!

I know this wouldn't be a magic square, but the most obvious king's tour in the first place is the "snake path."

Some nice potential tattoo designs for Ayliean here! Love the 3D ones at the end!

Loved this.

I love these math videos that are creating beautiful shapes, like this one and the one tile discovery

Thanks for the animations Pete :)

I saw Ayliean, I clicked ASAP

@Ayliean

Ай бұрын

Aww thanks 🥰

@lessgoofyone

Ай бұрын

This channel's maths crush! 😅​@@Ayliean

Surely the room with those patterns on the walls was deliberately chosen. ❤ Ayliean

More than 25 years ago, I became somewhat entranced with knight's tours, and composed a few dozen of them that were very beautiful. I concentrated on the symmetrical ones, because I was looking for beauty. I even made a chessboard of knight's tours, which used 32 tours twice, mirroring each other. Each square of the chessboard was 2 inches, so the whole thing was 16 square inches. And it was a closed tour. I also made what I called modular tours, dividing the board into sections and then connecting the sections. It was loads of fun to play with something I had read about 50 years ago! 🐴

Matt Parker tries every year different method to calculate Pi, still he will be remembered for Parker Square 🤷‍♂️

On the sponsor screen before the video recommendations i heard Neil's beautiful voice. I miss his sequence videos so much. Hope he return some day

Anyone else notice that the 12x12 magic and semimagic knight's tours follow space filling curves? Super cool the fully magic one is a Hilbert curve, and that's why it translates up.

That rebelious squint smirk is my favorite

I bet these tours would look especially nice as Bezier curves.

Love that flash of the Parker Square

That's just fascinating.

Nice bit of -sunshade- fun shade thrown at Matt 1:32 LOL

3:05 I immediately thought of tiling in the pattern of a Hilbert curve

I chatted with Ayliean for 42 seconds in London last year. Highlight of my vacation.

Ayliean is a gem!

B2 looks great.

I've been watching since the original Parker Square. It was very funny to see it referenced again.

I think it's funny that you gave an example of a closed one before an open one, given that the closed one IS an open one 1 move before you close it.

1:30 catching strays 😂

7:10 was gonna say, that looks exactly like something you'd find in the Book of Kells, a very old church, or weaved into an aran jumper.

9:49 this I find very similar to that 'synchronously dancing bears' gif. Probably cuz they both have the same pace of movements and also the angle of view.

Now I want to make a belt and some border wallpaper with King's tour patterns.

Cool thing 😎 these Celtic patterns had some mathematical connection

The math speaks for itself.

Your makeup looks so nice! Also thanks for the cool math knowledge

@Ayliean

Ай бұрын

Thank you ☺️✨

Are any of the magic, symmetric King's tours pan diagonally magic? Also, I find myself wondering about Queen's tours where you forbid King's moves and require alternation between Bishop and rook moves. Are any magic and symmetric... and how big can one make the smallest step and still complete a queen's tour? And what about tours using non-standard chess pieces or on a hex or triangular grid?

IDK, seems like king's tours & Celtic knots naturally divide a space with a line of connections. Sounds like a way to encrypt with complexity.

I have collected these patterns as knots

Just wanted to throw out there that these tours can be represented as a Hamiltonian path. Finding new tours could be done by changing which 2 vertexes connect to each other and then working to remake a new Hamiltonian path from that.

Ayliean and chess? Oh this will be an amazing episode!

Obviously you can start a closed tour from any square (you can start it at any point on the entire loop) but are there open tours that start at any given square? For a knight's tour, you obviously have to alternate colours, but if you pick any white square and any black square, is there always a tour that starts at one and ends at the other? I'm sure the answers are known, but they're still obvious questions to ask :)

It took a while but I eventually managed to successfully achieve a tour for every type of chess piece on a 1x1 board!

Big fan of the intersection of numberphile videos and puzzles from professor layton games that traumatised me as a kid. Eight queens next?

@numberphile

Ай бұрын

I think we’ve done that.

The patterns made by the magic king's tours make me think of knot theory. Also, I wonder if the fact that magic tours are possible on 8x8 with a king but not a knight has anything directly to do with the fact that a knight is strictly color-switching and a king isn't? Would you get the same results as the king with a piece with the same number of possible moves that is similarly divided between colorbound and color-switching, like a wazir+alfil?

Are there any underlying properties with the knot being made with this method?

Is there someplace online where we can view pictures of all the Knight's Tours and King's Tours?

I want those knight tour bracelets!

It's a Magical Chivalry Tour! (Roll up!)

I wish there was an option to see a pawn's tour... which promotes to a knight when it reaches the end of the board 😅

What are the RL applications to these tours besides it's pleasing to look at?

@theguyshetellsunottoworryabout

Ай бұрын

Nothing more for the moment I think Centuries ago mathematicians were playing with numbers developing what we call number theory today, ignoring that few centuries later we would use them for the security and cryptography of your credit card, or write the code source of your mobile phone or computer Soooooooo nothing for the moment I think, maybe one day it will have some And if not that's still beautiful enough to be published in my opinion

@nekrataali

Ай бұрын

Chess is still unsolved. Specific board states of chess have been solved, but starting from White's turn 1, we're still mostly in the dark. Given there are more possible games of chess than there are atoms in the observable universe, chess is excellent for training computers and testing their limits. Research into topics like this could help us eventually solve chess, which would also result in solving problems using large or infinite numbers. If you can prove specific moves always leads to a win, you'd also be proving stuff about 10⁷⁸. It'd be like proving the last 10 digits of pi.

I personally like "dizzy king tour": where king not allowed make move in the same direction twice in the row.

How about a double bishops' tour?

@jiaan100

Ай бұрын

Kinda boring I think

⏺ graphic design/animation appreciation button!

Yay, Pete!

This is mathematical wizardry 🧙

She shared the secret quite early on in the video! Is she sure we are her favorite kind of people????

2:54 In fact, there are no knight's tours _at all_ on a 4x4 board, let alone magic knight's tours. In general, there are clearly no knight's tours on 1xn or 2xn boards (except 1x1), and it turns out there are also no tours on 3x3, 3x5, 3x6, or 4x4 boards.

The magic knights tours seem to me to resemble a Hilbert curve shape. I wonder if this is a mathematical connection there. Both space filling curves?

Could we invent other moves? Could it work? Moves you don't find in chess, like 3-1. Fascinating as usual!

Parker Knight Tour

❤

Nice house Ayliean has got! 😉

Parker Square spotted in the wild 😂

I wonder if they noticed the kings tours-like patterns on the wooden wall behind them…

Doesn't make a lot of difference in this context (though it definitely does in chess), but the bottom right square should be a light square if the board is set up correctly.

nepo and dubov likes this video...

Fyi this video is an April fool, but it's a secret which part.

@robadkerson

Ай бұрын

You are an agent of chaos. Seeding doubt in the the minds of the masses.

Could you invent a new 10x10 chess game with a special figurine (x4 + 4 extra pawns) with a special movement as well?

@landsgevaer

Ай бұрын

Fairy chess has plenty...

Gonna assume the maths behind pawn's tours is pretty dull ;)

@bluerizlagirl

Ай бұрын

Only till it becomes a queen, and then it just zips around the rest of the board.

My tours with other pieces ran into problems when I got to bishops.

1026W 7182D

I’ve been working on the Pawn’s Tour for the last 30 years. What the heck? 😂😂☠️☠️

@bluerizlagirl

Ай бұрын

It speeds up a lot after the seventh move .....

@iabervon

Ай бұрын

You should try a bishop's tour. I've been working on that, and it's going great! I'm almost half done, and no problems so far...

Do the diagonals really all have to look like that? Why not just have a big Snake-style squiggle? Just go horizontally over each row.

1×1 works.

Satte ke number kaise nikale uski math bataiye

Remember kids, it's 'white on the right'. 😊

Will we ever get to meet Pete? (It's not me by the way)

Magical girls rise up 🔥🔥

@MichaelOfRohan

Ай бұрын

Woof..

Wait, there's another Perth??

What about the bishop? Does he get a magic tour?