Make Your Own Hyperbolic Surface!

It's actually really easy and fun to make your own hyperbolic planes using crochet. I had many requests for these after the release of Hyperbolica, so here's a proper tutorial for them.
Crochet Simulator: codeparade.itch.io/crochet-si...
Perfect Sphere Pattern: avtanski.net/projects/crochet/
Cthulhu Pattern: www.supergurumi.com/amigurumi...
Daina Taimina: pi.math.cornell.edu/~dtaimina/
Wishlist 4D Golf: store.steampowered.com/app/21...
Support me and innovative projects like these!
Patreon: / codeparade
Ko-fi: ko-fi.com/codeparade
Merch: crowdmade.com/collections/cod...
Music (CC BY 4.0):
Lundstroem - The happpy en garde
Lundstroem - In the middle of the day
freemusicarchive.org/music/lu...

[@a99g]

As a crocheter, I recommend not cutting the tail because it could ruin the shape of your work if it gets pulled or something. Instead, you should leave enough tail to hide it between the stitches in the back of your work This is more important if you gonna use a regular yarn like cotton or wool

[@JohnDlugosz]

Yea, when he cut the tail I was thinking _no_ ! I like to hold it with the hook hand to control the position of the work when it's not large enough to grasp normally yet. Keeping it flat and under a little tension helps hook properly and with uniform size. I also winced at how much slack he has inside his stitches.

[@RainbowFacedCupCake]

it hurt to see him do that LOL

[@Asterism_Desmos]

I am actually thinking of learning to crochet because of this video, I will keep this tip in mind if I do decide to.

[@RainbowFacedCupCake]

@@Asterism_Desmos keep the starting tail long because you can sew it into your work and it'll have less chance of unraveling your project 👍

[@suphorg8597]

i had a physical reaction to the cutting as if the yarn was one of my limbs

[@DeenBoi]

I've never expected this channel to be making a crochet video

[@PunmasterSTP]

Me neither, but it's incredible!

[@DrakiniteOfficial]

I was gonna leave basically the exact same comment

[@cookiecan10]

It kinda reminds me of that time Derek Banas (Known for making tutorials on programming languages) suddenly did a "Learn Crochet" video. There were so many people in the comments who clicked on the video expecting a tutorial on a non-existent programming language called "crochet".

[@asheep7797]

@@cookiecan10 ready for someone to make a programming language called crochet

[@gollossalkitty]

Why is this an excellent comment? [✅️ Inspired me to watch] [✅️ Funny] [✅️ Relatable] [✅️ Informative] [✅️ Shows appreciation to video creator] [✅️ Interesting] [✅️ Other]

[@sashagornostay2188]

My mom was a businesswoman. She used crochet, knitting and sewing to make and sell toys. She had a brand, a shipping guy, an economist, but she was doing all of the toys for sell herself. Sometimes she would give crochet lessons to all our distant family relatives’ sons and daughters. They were always very excited. Two years ago her oncology got worst and she retired. I always believed she will come back. Everyone loved her. She died this year, in January. In a national saint holiday. Maybe I will continue crochet too. Some day. When it won’t be obstructed by my tears. Thank you.

[@singerofsongs468]

So sorry for your loss. I’m pretty active in crochet and knitting discussion spaces online, and I’ve seen so many stories from people who have taken up fiber arts to connect with their loved ones like this. Some learn the hobby to finish or repair a project that was left behind; others take it up to feel closer to their person or have a physical object to commemorate them. It is a slow, repetitive, almost meditative kind of craft, so it is a pretty good way to occupy your hands and mind through a difficult time. When you feel ready, I strongly recommend that you give it a try. Best wishes!

[@vampiresgrave]

my mom died when i was 10 and one of the only things i knew about her and kept is this really janky 9ft baby blanket she crocheted for me. i started crocheting because of that and it's one of the only hobbies i have had since. aka i have so much fucking yarn lmao

[@4.0.4]

Thanks for sharing such a bittersweet but wholesome story. I'm sure she was missed by many.

[@KerriEverlasting]

Don't delay, time is short. Hurry.

[@cheeseburgermonkey7104]

chad mom, she will never be forgotten

[@devmmmdoesstuff6429]

as a long time codeparade viewer and a crochet hobbyist, I see this video as an absolute win

[@Nobodyslittlebirb]

Ssssssssssssameeeeee

[@jacopo1farina]

Exactly!

[@Delemaroth]

This is the most hilarious twist to this channels story. Only you would go from math and development to crochet out of nowhere.

[@Waldbraut]

As someone who crochets for YEARS now, this is actually one of the best crochet tutorials I have seen

[@KerriEverlasting]

I was thinking the same thing 😂

[@lesbianaconda2971]

As someone who both crochets and has a mathematics minor, I feel like this video is made exactly for me. I crocheted a Klein bottle this year, which was really fun!

[@gabby222themoon]

Fellow crocheter here do you know of a pattern for it?

[@annasolovyeva1013]

BTW how?

[@urstrulyio]

Wait pattern please?

[@cole931]

Can somebody @ me if a pattern is found?

[@seymourbones]

​@@annasolovyeva1013i mean a mobius strip is easy enough to crochet, you could just crochet two of those and then crochet them together

[@bobbywilkinson5697]

As someone who has been crocheting for a while and has done some pretty advanced stuff, this is awesome, though you cutting tail off so short was hard to see, but I still love this. The math behind crochet isn’t talked about enough and it’s a tragedy.

[@bettercalldelta]

I'm curious, why is cutting the tail off bad?

[@a.johnson309]

Some prefer to keep the tail to help them hold onto their work until it's bigger and easier to grasp and to keep their work from easily unraveling. I find it also tends to give a much cleaner finish when you keep the tail and weave it into nearby stitches.

[@mattybrunolucaszeneresalas9072]

What math

[@bobbywilkinson5697]

@@bettercalldelta if you leave it really short, when you sew it back into your work it can come undone after enough time and then either you have to sew it in again or your work starts unraveling. You also need it long enough so that you can easily put the end through the needle and then be able to pull the needle back far enough to be able to actually put it back through the work roughly where the end originally comes out. Try sewing with thread that’s shorter than your needle and you’ll know what I mean.

[@bobbywilkinson5697]

@@mattybrunolucaszeneresalas9072 just the little bits of math that I think about when I’m working. If you want to keep the work straight, you have to make sure you use the same number of stitches per row, and some funky stitches you might want to do could take up slightly more or less space and you have to account for that. Also the size of your hook and the thickness of your yam could mean that the patterns that you’re following could end up bigger or smaller if you’re not using the intended size. If you want to correct for that, you have to make a swatch and count the rows and columns and then change the pattern slightly by adding or removing stitches so you do get the right size. There’s also the fact that single crochets and double crochets or half treble crochets or any other stitch has a different height and you can use them all in the one row but you’d need to make sure that the next row accounts for that so it ends up straight or ends up with the shape you want. One more example is figuring out how many stitches you’d need for each row if you’re making your own amigurumi so that the different shapes come out how you want. Honestly most of these don’t really ever come up when you’re following a pattern but I like to experiment and those are the things I think about - just about how what stitches I choose to put where and how that affects the work as a whole.

[@meenakshis4033]

In crochet, getting something like a hyperbolic surface is actually a happy little accident you'll make as a beginner. Some artists use these hyperboles to make appliques, or cool little decorative pieces. Some hyperbolic surfaces can be seen as a part of art pieces. Also those pentagons while increasing stitches can be imagined as little v stitches over a single stitch in the previous row, to visualise better in practical implementation. To keep track of counting, use little safety pins and pin them on the first stitches in the start of a row. ⚠️ Crocheting can be extremely addictive and you may end up hoarding yarn and making the first ever cardigan before you know it 😂 Stay safe!

[@awwkaw9996]

For another place in science where crochet turns up, check out the paper by Maria Feofilova: "Geometrical frustration of phase-separated domains in Coscinodiscus diatom frustules" (Tl;Dr: some organisms make weird shells, that can be explained by the math of crocheting)

[@hanniballecter1960]

thats awesome! thanks for the suggestion!

[@JohnDlugosz]

The thing about crochet that you won't have a machine is the open-ended creativity possible. You can insert the hook *anywhere* in the work, not just in the top loop of the next stitch in a row. You can go between stitches or in large holes created for that purpose; you can pick up just the back loop of the stitch. And that's still just going in rows. But you don't have to do that-- you can go sideways along the edge, or anything at all. When doing lace, you go off into the air sometimes connecting back to parts you already did, and finally bringing the whole thing back down to the main work.

[@LeoStaley]

Was not expecting a crochet lesson from code parade

[@pyro-millie5533]

Dude as an engineer who loves 3D modeling robots in Solidworks and making then turning around to make adorable plushies with crochet… YES!!!! Ever since I heard about the lady who did the amazing hyperbolic models, I wanted to burn through some of my yarn stash to make some of my own! Can’t wait to learn!! So excited to see the fundamental topology mathematics connection too I am HERE FOR THIS!!!

[@atlasliet]

Depending on your family structure, crochet is probably the first hobby you see adults doing in your childhood, and yet few people (myself included) decide to try it... that's about to change, I just bought a crochet kit for beginners thanks to this video!

[@KerriEverlasting]

How you going? Addicted to crotchet or ptsd? There is no in between 😂

[@SamRMoyer]

@@KerriEverlastingwdym addicted to ptsd?

[@kg4484]

Hyperbolic space is such an Interesting form of geometry because of how different it is from our well-know Euclidean space

[@Kh-ik3de]

Not that different tbh, they’re both absolute geometry

[@NikZapp]

Man, I literally was just playing hyperbolic games and got recommended this, perfect timing!

[@foolish_edworm]

ive tried to learn how to crochet hundreds of times, and i honestly think this might be the tutorial that clicks for me

[@Arstynirp]

I never thought I would use crochet for math. Math isn't my best subject but one of my favorites is geometry. I'm doing a project where I study a mathmetician and create a scene with others. I suddenly dove in to hyperbolic geometry yesterday watching videos (including yours!) to understand how it works. My math teacher told me about hyperbolic crochet and now I'm here! I was thinking about explaining how it works using crochet models like this one. So thanks!

[@eliseosterbrink8000]

This was such a cool video! I've been crocheting for a decade now, and I never realize how closely tied to mathematics it was. The visualization of meshes was super interesting- thank you for the video!

[@draagsnuab6686]

This video got me into crocheting. Never thought I’d crochet more than some hyperbolic planes and now I have a poncho and several other smaller projects going on.

[@RoseVerdict]

When the hyperbolic space and gamedev youtuber activates the crochet/knitting part of your brain like a sleeper agent oh my gosh he knows what frogging is. HE'S TRULY ONE OF US!!!

[@mattsadventureswithart5764]

As someone who loves both maths and crochet, I was immediately *hooked*

[@gallium-gonzollium]

This is the video we didn’t deserve, but the one we needed

[@bettercalldelta]

no way it's the desmos keyboard guy

[@NikoHD203]

Well, that's certainly a tutorial that I didn't expect on your channel..

[@forsakengravity1738]

Omg I haven't thought about crochet being so connected to mathematical surfaces. Crochet is so fucking cool, I wanna do it myself !!

[@meenakshis4033]

As a Computer engineer and a crocheter, this feels like a personal win for me. I have always been curious why I was drawn to pick crochet as an hobby, and now I know why! 😂 We need a lot of ppl to appreciate the science and fun behind the hobby that some jump to cancel as un-cool.

[@dersps5905]

Today I learned crochet instructions are written in Assembly

[@JohnDlugosz]

They really are! There's even a notation for loops. Not really any standard for branching though; for variations the *if* statements are just ad-hoc and not so compact.

[@floresilla]

As a crocheter and programmer I never stopped to think about the relation between both, my eyes were opened now in ways unimaginable

[@realcygnus]

Well that was different & a 1st YT vid that both me & my girl could appreciate.

[@el_chivo99]

never thought i’d see the day where 3 of my biggest interests- math, crochet, and programming, all come together!!!

[@KayJ268]

I’ve been crocheting for years and was searching for new scrap yarn project ideas and stumbled across this video. I’m minoring in computer science and enjoy mathematics and this makes my nerdy crafty brain so happy. I think about how math is interconnected with crochet often, but I agree it’s not talked about as much as I think it should be, it’s just so cool! It took me years to really understand crochet and understanding the math of it helps and I think it could help other crocheters! I’m always learning more. Thanks for this video! Gonna go make a bunch of these now! :)

[@elliwesishawkins4799]

As somone who was taught to crochet growing up and still does from time to time, I love this little cross over episode. I’ve been seeing a few of your dev logs and was mainly just here for the space distortion since I’m not a programmer. But now I get to see hyperbolic space in a more familiar setting and I think that’s really cool Edit for additional thought: usually increases and decrease are made to make different shapes like circles, but in my experience those shapes are meant to be flat like if you’re making a coaster. Or you make hexagon shaped tiles to join into a blanket same way you would with granny squares. Also, most 3-D aspects of crochet is texture on a flat surface like a front post double crochet stitches that connect to make a line of Vs across the rows of a scarf. The purposeful increasing to break the flat plane and just keeping doing it in a pattern is really cool.

[@icannotbeseen]

That was the coolest crochet tutorial I’ve ever seen. I guess this is the logical result of watching only computer stuff and crochet videos

[@tafellappen8551]

I was gonna say this is the ultimate crossover episode but then i realized this is the ultimate yarnover episode

[@Nobodyslittlebirb]

I love it when KZbinrs I watch a lot combine my favorite things😊

[@milkymoo1525]

Thank you for touching on the uniqueness of crochet and how if cannot be replicated with a machine! As it’s become more and more fashionable lately, I’ve seen pieces at big box stores for chump change and it breaks my heart

[@elendiastarman]

I literally *just* learned how to crochet over last winter break (from my mom) and I have been enjoying it immensely. I had the same realization, not long after I learned, that crochet allows me to make meshes / surfaces, especially those that are hard to make any other way (like hyperbolic surfaces!). That quip about the beginning few crochets being the hardest part is 100% true - there's very little to hold on for generating tension in the right way and once you have something substantial to hold on to, it becomes more about doing quadrillions of crochets until you're done.

[@drawingmomentum]

I'm a nerdy artist looking for inspiration. My 15 yo son went away to a summer college STEM class and is learning discrete math, etc... I miss him. 😢 I think making this might be something to help me and have a fun fidget gift for him when he comes home. ❤ Thank u!

[@somelaser5906]

Never thought I'd willingly sit through a crochet tutorial lol

[@Twiddle_things]

Gosh I never thought to be taught how to crochet. The schools, PLURAL, I went to made it so complicated and hard to understand, _somehow._ This video doesn't just satisfy the nerd part of me, but also the crochet part of me!

[@Jay-ko2ql]

as a cs major who crochets, you just changed my view on crocheting in a good way lol this was so cool thank you for sharing!

[@Coffee_Toffee]

Daina is lovely! She gave a talk at my uni recently, so it's lovely seeing her get the recognition she deserves!!

[@johnydl]

I once made a hyperbolic surface that followed a Pi pattern, single single double, double, single single single double, double etc so yeah 'really forgiving' is an understatement XD

[@joda7697]

Wait so you used the binary representation of pi to decide wether to single or increase? That's fun. Though now i wonder how it'd look with a balanced ternary representation, where -1 is a decrease, 0 a regular and +1 an increase.

[@hexagon8899]

@@joda7697 no i think its base 10. just look single single double (3) double (1) single single single double (4) double (1)

[@Not_mera]

I've always loved maths. And I've always loved textile art (sewing, knitting, crochet, bobbin lace etc.) And I've always loved making the patterns for my sewing bc it felt just like applied geometry. (Edit) I think I love Mrs codeparade

[@DoNotPutMeInABox]

As someone in the video game industry who crochets, this was fascinating! I'll have to make one of these soon, and maybe check out some more of your videos!

[@bafflingjerboa]

the way i physically flinched when he cut off the tail 4:14

[@Manuel-in1vt]

My friend tried reaching me crochet awhile back and I couldn’t understand. But relating it to linear space and hyperbolic space, it makes so much more sense

[@stickguy9109]

Bro Sebastian and Code Parade both upload at the same day? Man today is my favorite

[@dit-zy]

I have done some crochet, but keep getting confused and frustrated by the effects of added or skipped stitches. Your mathematical explanation of the effect, and showing it in blender, finally made it make sense for me! Thank you! :D

[@YandiBanyu]

You see, this channel see crocheting from programmers perspective. This is why it is easier for my brains to wrap around it lol

[@violetviverson8340]

As someone who is wanting to learn crochet, I have never seen a description and visual of decreases and increases that I actually understand until this video!

[@coolbeanschannel]

Gonna send this to my grandma. She’s going to have one heck of a time…

[@wasababi]

As a crocheter its fun to see it put into a mathematical situation

[@izurdeaOdyssey]

Dude,, you single-handedly explained how to crochet a magic circle/cast-on perfectly for it to finally click for me, and way better than other KZbin videos of full time crochet hobbyists 😭 Thank you for this. Best part, I got a new crochet project to work on now. Truly a great video my guy.

[@a99g]

8:10 And that's why i love it Also you can literally make anything with it !

[@noahnaugler7611]

It's funny because I just taught myself how to crochet last fall, and this was one of the reasons

[@trymbruset3868]

So fun to see these random blasts from the past, I bought the hyperbolic crochet book and made a bunch of math crochet things during my undergrad more than 10 years ago now. Something super fun and easy to do as well is to crochet different knots and links.

[@shayforrest6880]

Literally never crocheted a day in my life, learned how from this video, thanks for the skill up ✅

[@Nulley0]

this episode of crochetparade is epic

[@e_cube4631]

liking this implicitly bc i love making these things i love your explanations of this stuff with the 3d models! its such a delight to see someone primarily known for their mathematical content talk about crochet... my two great loves and they combine in such a lovely way but people don't talk about it enough. if anyone (CodeParade included) wants to see more of this stuff in an artistic and environmental sense, please please look into the Crochet Coral reef project! the way coral is formed looks very similar to these hyperbolic surfaces and the project is just incredible

[@MidasKeyboard]

I’ve been crocheting for about 6 months, and watching your channel for quite some time, honestly I never thought you’d make a crochet video! And my brain cannot comprehend this whatsoever! However your explanation of crochet is mesmerizing and really grabs my attention

[@honeybun3596]

THIS INSPIRED ME TO MAKE A HYPERBOLIC BUCKET HAT IM SO HAPPY

[@TC-rv6sz]

Omg this is the best beginner crochet vid because it immediately shows people the vast volumetric/creative possibilities of crochet! Thank you for making this! I've been looking for something I could share with people just getting into freeform crochet ❤

[@pyro-millie5533]

And your crochet tutorial is so wonderful too lol! You get it. You get the community! I love that you mentioned “frogging” lol! We call it that because you take the yarn and “Ribbit Out”. Also I can’t believe I’ve made so many beanies and plushie heads in the round without realizing that spheres count as making a hyperbolic plane haha

[@JohnDlugosz]

The sphere is the opposite of the hyperbolic plane. It has positive curvature. You probably have done something like this, to make a bouncy edge around a finished work. And of course, you always do increases when doing anything in the round (rather than back-and-forth) and that includes Granny Squares. Sometimes a placemat becomes a little hyperbolic by accident, if the increases aren't exactly right.

[@anthropomorphicpeanut6160]

Damn crochet sounds fun 🥺 I'd love to try it out but I've already spent too much on embroidery thread lol

[@sorek__]

Today is Polish mothers day. My mom loves crocheting. She loved the video, so did I. Thank you!

[@obsidiandragon6983]

Oooh, I do a lot of homebrew amigurumi patterns, pretty curious and excited to try out the simulator as a tool for approximating pattern decisions.

[@rj6116]

I always approach crochet with some little math so I'm happy to come upon this video 😊

[@cibby-kun8088]

this was the best crochet tutorial video ive seen and it wasnt even on a crochet channel

[@lewismassie]

This was unexpected and also delightful to watch

[@PunmasterSTP]

This video (and whole channel) is just crochetcredible!

[@_elioneli]

Bruh, i was LITERALLY looking for how to do this

[@Uni_974]

Same

[@SianaGearz]

Well it's a lucky day for you lot then. Get a lottery ticket or something.

[@unnamed7225]

got a final project due today, it's 2 am, and I'm watching this

[@milk-sharks]

YES this is why i love crochet!! it’s all math!!!!!

[@irregularstuff5290]

This video is the reason i even managed to get into crochet.

[@Lavamar]

I've never crocheted before but this video was really cool. Love seeing math connect to things like this

[@moth5799]

I remember reading about this in one of Alex Bellos' books when I was quite young. I didn't fully understand it at the time but now I've got a much better grasp on it thanks to your video! It's awesome how intertwined crotchet is with topology.

[@alisonjay5522]

Absolute slay to learn crochet to do math videos, keep it up babes

[@daometh]

always impressed with how creative you are at coding. i really wish i knew how to code like that. coding just feel so boring for me and i dont really tend to experiment that much because im too confuse by the basic

[@dexterrity]

one must learn to walk before they can parkour

[@2fifty533]

well people aren't just born with knowledge, you need to actually start learning yourself, thats the only way you cant just sit there doing nothing then wonder why others are more successful than you

[@nonyobisniss7928]

i have the same issue. i'd probably be good at the creative aspect if only i knew the boring basics. it's just very hard to feel motivated to improve when there's a million road blocks and it seems to take hours to solve even one in an unsatisfying way.

[@2fifty533]

@@nonyobisniss7928 road blocks such as?

[@2fifty533]

@@nonyobisniss7928 and how are the basics "boring"? they are usually quite simple and give you a fundamental understanding of how things work, you need to start somewhere lol that's the same as saying that you can't get into art, because learning how to use a paint brush and a pencil is too boring for you

[@srjskam]

"Either for fun or in a sweat shop". Well there's a sentence.

[@Sardiniastan]

Ngl, this is the best crochet tutorial I've watched

[@Flare03l]

This looks like so much fun, I will give it a try

[@tobywyman6843]

ahhh this is how i make all my ponchos extra frilly !!!

[@jam2390]

This is so cool! I love looking at crochet through a mathematical lens. I feel like since math has always been my favorite subject in school, it has helped me understand crochet and I fully agree that the links between crochet and math should be talked about and explored more :)

[@martianpudding9522]

You can make a fun fidget toy by using a mobius strip as a base instead of a circle. Basically just keep increasing until you fill the hole of the mobius strip

[@dumpygirl6736]

I’m a physician and math guy, I’ve been crocheting for years. So easy to enter flow state.

[@ejsafara456]

as an avid crocheter of several years, i must say your technique and explanations are very good :3 i never thought about this application of crochet, so much creativity! :D

[@GOLD4DJ]

I gotta say, I never expected to see crochet on this channel :)

[@mattybrunolucaszeneresalas9072]

?

[@SotraEngine4]

I can finally really connect to my mother!

[@xMightyTinfoilx]

my partner has been trying to get me into crocheting and i did not expect codeparade to be helping her with that task of hers haha.

[@thistle_ish]

i'm actually losing my mind!! this video combines two of my favorite things: crochet and topology! i can't wait to make my own hyperbolic plane :)

[@nianyiwang]

codeparade: those demonstrations are confusing also codeparade: hey let's make a real confusement

[@nianyiwang]

oh shoot confusion*

[@abegley6588]

I just bought 4 skeins of yarn from dollar tree because it was a pretty color and now I need to find a project for it. It just so happens I was curious what it would look like of you increased every round and I just got my question answered! It looks so cool! Might make one of these

[@AceOfStars0]

dang, i didnt know my hobby that i do daily could make a scientific phenomenon

[@glowingseal]

Finally I find a video explaining how much crocheting and geometry are linked! I've always been enthusiastic about that connection and wanted to see it be talked about more. I also always wanted to see some program to simulate crochet patterns and show an approximation of the final shape, this is awesome! I'm definitely trying out your simulator later today 😄

[@truckerbouchard1389]

I watched a lot of videos to learn how to crochet but I wish I had this to learn

[@PatheticRobot]

As someone that just started doing Crochet I really want to do this even if takes a lot of time andy hands hurts.

[@Mariorox1956]

I do love it when my love for recreational mathematics and arts and crafts come together! Time to find some crochet hooks

[@eilo7400]

As a crocheter I’d like to add that if you don’t want a small hole in the middle, you could use a magic circle. It’s a little more complicated but is one of my personal favorite techniques!

[@jocelyngray6306]

The expansion and contraction system in crochet is similar to weaving chainmail. That makes me want to try weaving a hyperbolic chainmail sheet.

[@fntthesmth423]

It's funny, i started doing a bit of crochet myself in the past month! Funny how you were also inspired, mr parade :)

[@Skylars_Dead]

The only reason I know how to crochet today