Romantic Mathematical Shape: möbius-loop hearts

Cutting a möbius loop in half is fun. Sticking two möbius loops together and cutting them both in half is romantic.
Much more on möbius loops and topology in my book Things to Make and Do in the Fourth Dimension:
mathsgear.co.uk...
Also on Maths Gear is the Cos I Love You card:
mathsgear.co.uk...
Think Maths parametric heart coordinates resources:
think-maths.co....
And here is my Royal Institution lecture:
• Four Dimensional Maths...
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
Music by Howard Carter
Design by Simon Wright

[@RobertRussellComposer]

I see a pair of handcuffs at 2:55. It could be argued that these are equally (if not even more) romantic than interlinking hearts!

[@aithne99]

+Robert Russell Composer naughty

[@theophrastushohenheim3251]

+Nóra B n*****y

[@JacobFelten]

+Theophrastus Hohenheim Hello Internet reference?

[@Ruminations09]

+Nóra B Watch your fucking language! Don't you know there are children here?

[@arqpal]

PokemonTom09 lol you asked him to watch his lenguage and you said "fucking"

[@kennethsizer6217]

"This is a boring cylinder! We can do *SO* much better!" Math with enthusiasm is one of the most sublime things in this or any universe.

[@STE6677]

If some told me you could make a square with two loops stuck together, I would have thought they where crazy until now.

[@standupmaths]

I still find it crazy.

[@STE6677]

+standupmaths I just love amazing maths things that I can try myself

[@durand95330]

+STE6677 I guess you can make two loops stuck together with a square ?

[@eagle3676]

pierre durand just go in reverse

[@beaclaster]

@@durand95330 with a full square that would be a torus (my guess)

[@guestuser2373]

Remarkable! You've finally squared the circle.

[@myknowledgemedia1080]

Guest User Quite the Parker Square.

[@kennethsizer6217]

I *LOVE* this comment!

[@einsteingonzalez4336]

No, it's not.

[@kimballchoo]

And I thought it’s impossible

[@rachelsimons2040]

Matt also gave that lecture at my sixth form one evening. He threw his hat at me, and let me keep both the square and interlocked hearts that he demonstrated. It was a truly fantastic moment.

[@standupmaths]

I hope you cherished them for weeks, minimum.

[@rachelsimons2040]

+standupmaths I think I still have them, stashed away safely. At home. Somewhere...

[@mata5724]

The nerdiest way to say your relationship is one-sided.

[@the-keymaker]

4ever al1

[@happypiano4810]

But two möbius loops make a Klein bottle when put together, so in reality, they are saying that their love is never ending.

[@morris1818]

That's some heart-core math you got there.

[@standupmaths]

I'm heart-core to the math.

[@NoriMori1992]

"And he was so proud of this shape, that he named himself after it."

[@aaron9828]

He obviously planned to say this, it wasn't a mistake.

[@sebastianespejoloyaga7603]

Parker Square ir Morbius loop?

[@CemCakrlar]

Did this right now for my wife. It is really über-romantic for an engineer couple. The story I told was made us have tears in eyes. Thanks for the idea Parker.

[@RickyCruzMedia]

Can't wait for that triangle.

[@kattparis6955]

Can’t believe how impressed I was with the square....... blown away by my reaction to the hearts. I love math!

[@paxpacis2]

Footguy from Numberphile already showed us this

[@standupmaths]

Whoops, I missed that Numberphile video. Thankfully I've been doing this paper demo for years. Not least of all for the Ri last February: kzbin.info/www/bejne/Z6ikknyVa8dsgKcm44s

[@dan339dan]

+paxpacis2 Foot guy was "Tadashi Tokeida"

[@paxpacis2]

+standupmaths No problem, was just surprised to see the möbius hearts again

[@Skadihehe]

+standupmaths I just watched that video yesterday. How very strange.

[@jjjjh4289]

+standupmaths No you didn't.

[@singingblueberry]

Okay okay, that's even more romantic than x^2+(y-cube root of x^2)^2=1 (Enter this in Wolfram alpha if you want to understand.)

[@standupmaths]

Ok, that is pretty romantic.

[@LazyMasterGamer]

+standupmaths how about this one: (x^2+y^2-1)^3-x^2y^3=0

[@theflaggeddragon9472]

+singingblueberry I really like this composition of 4 equations. y1=sqrt(2x-x^2) y2=sqrt(-2x-x^2) y3=arcsine(x-1)-pi/2 y4=-arcsine(1+x)-pi/2

[@AreyouReggae]

:D sneaky

[@NotJames1]

+The Flagged Dragon That doesn't produce a graph in Wolfram for me :( what is it supposed to be?

[@spiffo5349]

2 möbius loops of the same type gives me a boat?! **runs off to find a pair of scissors*

[@DariusMo]

Well I already know that one from your lecture in the Royal Institution. Was a great lecture!

[@DariusMo]

+bl00dwork btw, what actually happens if you e.g. stick 3 loops or möbius loops together?

[@slendy9600]

+bl00dwork try it. im interested in seeing what happens too

[@DariusMo]

slendy9600 I will try :D

[@fluffyllama1505]

Any results yet? :P

[@DariusMo]

Fluffy Llama nope didn't have the time :C

[@proyc95]

Seen this demonstration on Royal Institution on KZbin, I think the title was "Things to See and Hear in the Fourth Dimension" :) Really enjoyed that video and I made some of them myself after the video as well - twas pretty cool. Your enthusiasm and curiosity are quite contagious Matt! Always enjoy the content on your videos and your sense of humor.

[@thatskap]

Never going to forget the wonders of the Mobius Loop. Loving the videos Matt! :)

[@crazydrummer4827]

Why didnt you show boat & thing?

[@NatsumiHinata]

+Crazy drummer It's on Numberphile video!

[@crazydrummer4827]

***** Thanks!

[@svge96]

+Crazy drummer they are easily imaginable after you saw the hearts.

[@NoriMori1992]

+Егор Свежинцев Maybe easily imaginable for you; not for everybody.

[@JackMaddock1]

A metaphor for my life: I attempt three times to make the hearts and instead got the weird boat thing, before giving up, watching the end of the video, and realising that I had ignored something essential.

[@carolinevenus7901]

I saw this already from Numberphile a while ago, but the way you presented this made it far more entertaining. Thank you!

[@standupmaths]

Thanks! Glad you enjoyed it.

[@IllidanS4]

You have cool music in your videos. Not that I watch them because of it, but it makes the maths even more cool.

[@standupmaths]

Everything gets better with cool music. Even maths.

[@stephaniecarroll1542]

+standupmaths And there was I thinking maths couldn't possibly get any better than it already was. Tut tut tut, so oblivious.

[@TheMrvidfreak]

"A boat...and a thing" I'm in tears

[@quendordoom]

Love your videos. I could be having a terrible day but your playful and curious approach to life always puts a smile on my face. Thanks!

[@standupmaths]

Glad I could help! I hope you have better days.

[@Rtcmanga_YouTube_Channel]

Wow, I would have never expected something like that coming out from pure math! :) Really cool!!

[@PC_Simo]

Gotta love, how the video is 7:22 long. 7:22 ≈ 1:π. 😅

[@bibekgautam512]

I knew this one from the a numberphile video with Tadashi Tokeida. Thanks for the remainder, matt.

[@physicsgoesbrrr1181]

The best plot twist at 1:13 (giving new meanings to plot and twist)

[@AndrewPitmanator]

"... Not even linked together. It is a world of disappointment." 😂

[@simoncunningham9231]

You, Sir, are a delight.

[@Garbaz]

Why is everybody commenting that "Numberphile already did this" or even "omg you copied numberphile, how lame"? 2) People made videos about this way before Numberphile or Matt Parker 3) Matt performed this "trick" on stage / in front of a camera before Numberphile did a video about it 5) Even if Matt would've watched the video on the topic by Numberphile and then decided to make his own about it, he has all rights to do so as long as he doesn't actually copy anything

[@connorcrowley3264]

You forgot one and four.

[@Garbaz]

Connor Crowley It's supposed to be a joke: p_1, p_2, p_3

[@connorcrowley3264]

+Garbaz I know.

[@johnydl]

+Garbaz 8) your sequence has confirmation bias, doesn't need to be prime to continue in a mathematical way ;)

[@celtgunn9775]

Garbaz you do know that Matt Parker IS from Numberphile right?

[@queenvictoria1802]

Briiliant entertaining explainer - you could probably explain the maths of the Einstein Field Equations and make it seem like great fun. Thank you

[@seancrane278]

I Literally geeked out over this idea yesterday when I watched your thing at the RI! It was wonderful and now it has it's own video!

[@standupmaths]

Yes, I thought it was a shame to leave it buried in the middle of a lecture. So I re-filmed this bit to give it its own video.

[@seancrane278]

And I am very happy you did so. I'm more amused at the timing.

[@martinowong]

That was some Parker Square!

[@all_time_Jelly_Fish]

Thanks Matt, I'll do this with my Wife on Valentine's day too! I imagine she will tell me something like, " I love you, nerd" when we're done.

[@3ckitani]

3:10 A SQUARE! A PARKER SQUARE!!

[@jashrox1998]

Matt PLEASE upload the theme song to Soundcloud. I LOVE it!

[@standupmaths]

Yes, once Howard and I get organised we'll put it out somewhere.

[@solarmaster3405]

So what your saying is 2 Parker Circles divided by 2 = a Parker Square? That makes total sense!

[@sagiksp4979]

I saw this on your lecture at the Royal Institution already

[@seanpuchaty1901]

This was just beautiful!

[@jetstreamjackie3437]

Consistent video corruption at 2:18

[@AltarenGalil]

haha that blew me away, you cant cut it in half!

[@AltarenGalil]

+Jan Šinkovec a square?? this is just a rollercoaster of a video

[@emmey8865]

Finally this trick gets its own video.

[@nerdbot4446]

What's that chiptune music in the outro of your videos? The description says "Music by Howard Carter", but it's impossible to search for this artist. I really like the 8bit music style and this track is amazing

[@MrHSX]

+Patrick Star Apparently they haven't released the music yet. :( There is a comment from Matt on this video saying that...It's like the 15th comment

[@johnvictor9071]

My wife and I did this during our wedding ceremony.

[@WarpedWartWars]

(really late here, but...) I was waiting for you to drop the Möbius Hearts at the end!

[@clumsycuber3254]

THIS MAN IS A WIZARD!!!!

[@half_pixel]

Not sure why everyone's complaining that Numberphile has a video on this already. Two different channels are allowed to cover the same bit of mathematics...

[@DowzerWTP72]

You know what... I will subscribe! This video genuinely made me smile about a subject I've always found pretty confusing!!

[@eulerpie]

what a twist!

[@alexshmalex455]

I did cut the moebius strip the second time and it blew my mind. The result is three independent 8's bond together...

[@ecstasyofgold888]

I tried this when I read your book. I must not have done it right. I remember I got the "thing" result.

[@unknow210]

awesome!! nice mobius loop!!

[@maddoxMw3]

best math teacher

[@james0xaf]

What I want to know is why you end up with a boat and a thing, instead of two boats or two things? What determines which piece is the boat and which is the thing? Hearts are great for showing off, but the "disappointing" result is the one that keeps me awake at night.

[@JosephParker_Nottheboxer]

I did this for a girl and she was amazed... sadly I didn't do my research and had nothing to follow it up with. I got a smile and a giggle but when I tried to explain the math she really didn't care. :(

[@TallMoose]

I'm currently reading your book, and im right past the part where you urge the reader to cut the stuck together cylinders in half. Really glad i dont actually have to now.

[@JackDrewitt]

our 6th maths teacher abused us as a labour-force, and made us do a tonne of weird star things out of paper for xmas, i broke the mold however and did a couple of mobius-hearts. id learnt it from ur ri video way back when

[@standupmaths]

That's the spirit!

[@JanickGers0]

Holy shit I did not expect that to happen. Best pick up line EVER.

[@lin4cba]

I is not as romantic unless you use your foot to help with cutting. :\

[@slendy9600]

XD

[@emilysofiadelatorremartin524]

oh god! XD

[@danlurny4129]

+lin4cba u've watched that vid

[@animeshsarkar3437]

He named himself after this! 😂

[@lawrencecalablaster568]

I love this! :) Same wonderful Möbius stuff as your talk Things to See & Hear in the Fourth Dimension.

[@fortheloveofit5317]

Dude! In your book you talk about the tesseract, and its appearance in marvel movies. Well, the mobius loop appears in Avengers Endgame! It's the shape of the band Iron Man uses for time travel! Check out the movie if you haven't noticed.

[@inkpanther]

Next video should show "a boat... and a thing". ;) I've already seen Numberphile video but I did enjoy yours as well!

[@fx4d]

Wait for the twist!

[@Zalaniar]

I actually just watched your video from the RI channel of you doing this exact same thing. Let's just say I got deja vu while watching this one :P Neat trick anyway :)

[@itaialter]

I don't see anyone saying "August Ferdinand already did that"... People just like to make it well known that they watch additional math channels...

[@standupmaths]

I fully support that watching of many math channels! And it was a Martin Gardner book where I first saw a möbius loop cut in half. These things go way back!

[@itaialter]

standupmaths Hehe, I fully support that too, of course. I was just a bit annoyed with all the "they already did it" comments just to promote that fact about themselves. Keep doing what you're doing!

[@humpingdumplings]

Matt, I absolutely LOVE your content. Such a great idea in time for Valentine's. But I feel some of your standupmaths sessions are a bit too slow-paced and scripted compared to your numberphile sessions, which have your natural flow of quick wit. Anyways, it may be just me.. it could be something for you to think about. Having said that, I'm enjoying seeing your channel grow! Best of luck :)

[@avaaaaavva]

'This blew my mind'

[@DanDart]

seen it already in your 4d lecture and from someone else on numberphile!

[@JupitersDancer]

I saw just hours before you uploaded this video, your talk at the Royal Institute where you do this trick :P

[@traktortarik8224]

1:10 that gets me every. Damn. Time.

[@adnamamedia]

I am definitely doing this

[@MrNudeMonkey]

I found the square much more exciting than the hearts tbh

[@p.h.shabanabegum615]

Superb sir

[@whuspr]

I now know how to make a square out of hand cuffs. @2:57

[@nickcline3792]

I just watched this on the Royal Institute two days ago lol. Awesome trick!

[@danielbil710]

If you can say these 4 words fast without getting tongue tied, you are a genius 1)Eye 2)Yam 3)Stew 4)Peed

[@leungclj]

even the same jokes as you gave during the lecture in royal institute

[@standupmaths]

I'm an efficient man.

[@leungclj]

+standupmaths I agree! 😂😂😂😂

[@chrisg3030]

As Feb 14 has been and gone this year, I want to move on to another Mobius matter. I notice Matt used quite a wide strip to make his Mobius loop, so how wide can you go? Go wide enough, if you carefully squash it flat it makes a hexagon. But what happens if you go even wider? Use an A4 sheet for example? I just got a crumpled mess with paper, but by using a nice floppy cloth towel of the same proportions (more or less), and making the same moves as for a paper strip, and after smoothing and shaking out some extraneous folds, I got something that looks like the silhouette of a bungalow with a big pitched roof. It passed the ant crawling test for a single surface. I then built that same shape by creasing an A4 paper sheet in exactly the same way. So you can make paper A4 Mobius, or at least a flattened version. But here's the crunch (or crumple): is it possible to make a Mobius loop by bringing together the long (rather than the short edges) and twisting them round. Or can this only be done in 4 dimensions?

[@kennethsizer6217]

"A boat and... a thing. It is a world of disappointment" I'm dying over here!!!!!!!

[@SteelSkin667]

If you give that card to someone that isn't into mathematics, they might not be thrilled by the "I shart you" message.

[@denummer1893]

"He was so proud of this shape, he named himself after it" hmmmmm

[@m1lkweed]

I remember this from your comedy routine where you spilled water on Faraday's desk.

[@RaccoonSnunkWolf1011]

this reminds me of high school lol i did this is junior year with my ap calculus teacher mr. goodrich.

[@mytubepleasure]

Hoo,Hoo, now I know what had happened when I last time tried to cut the hearts, I have failed and failed and failed, because I did not know the secret hint, one twisted right, the other twisted left. Thanks for the tips.

[@BBAFER]

I did not know KZbin had heaven in it!

[@nalingoel6971]

He named himself after it. 🤣😂

[@Pilbaran00b]

Whoah! A SQUARE!!!! This was awesome :)

[@wilkmarton]

Done this a few times since I watched the RI video. Took me a few goes to get it right. Still never found the boat and the thing though.

[@swedneck]

So wait how do you actually cut a mobious strip in half? There has to be a way right?

[@maliwulis]

In the third grade of the middle school, it wasn’t all that surprising, but you can still cut a $ 100 dollar bill in such a way that an average citizen can easily get into it

[@loreleihillard5078]

he just squared the circle!

[@lawrencecalablaster568]

Even though you did this exact same joke in your lecture, it is still brilliant :)

[@standupmaths]

Thanks. Writing new jokes is over-rated.

[@lawrencecalablaster568]

standupmaths :) There are no new jokes, just old jokes told to new people.

[@themrfj]

Don't worry thing and boat, I sitll like you * pats boat and thing *

[@kennethsizer6217]

"...and instructions" 🤣😂😜

[@MiahooJunk]

What would a two 4d möbius-loops connected to each other cut in the middle will look like?

[@standupmaths]

If you cut a single Klein Bottle in half you can get two möbius loops.

[@RoderickEtheria]

@@standupmaths but he specified two, not just one.

[@Niker107]

Is there actually a way to download or buy the amazing music used on this channel? Googling 'Howard Carter' doesn't help in finding it.

[@standupmaths]

We have not released it yet. One day!

[@MrHSX]

+standupmaths There goes a half hour of googling to waste... Please release it soon!

[@Karlavaegen]

It's so amazing! From all the tricks I think this is one of the best! Well not the hearts, but the square :) That's beautiful! As a long-time-ago-origami-master-wannabe, I still remember my best moves. Matt, I challenge you to fold a dinosaur from a square piece of paper :) I will upload a video if I think mine will be better looking :p

[@IcepickL]

That's exactly how I would have described it: a boat and a thing.

[@zachjensen4555]

He named himself after it Nice