![GrapefruitGecko](/img/default-banner.jpg)
- 29
- 56 425
GrapefruitGecko
United States
เข้าร่วมเมื่อ 20 มิ.ย. 2019
Welcome! Here you will find some dazzling gems of mathematics explained through artistic and tangible means. I particularly love all things geometric and topological, as well as any piece of mathematics with a beautiful picture. I would love to hear from you about the channel or any mathematical topic! You can reach me by email [geckograpefruit@gmail.com] or on Twitter [@fran_tastic44].
Channel by Fran Herr. franherr.weebly.com
Channel by Fran Herr. franherr.weebly.com
From Points to Braids: Unraveling the Configuration Space
Hi Everyone!
This video serves as an introductory lecture to the configuration space of points in the plane. To learn more about configuration spaces and braid groups, a good source is _Braids, Links, and Mapping Class Groups_ by Birman.
Go check out my dance film on the same topic if you have not seen it yet! th-cam.com/video/pSdeWTqz4yg/w-d-xo.html
Thanks for watching!
----------------------------------------------------------------------------------------
0:00 - What is the configuration space?
6:23 - Some applications
9:58 - Defining the fundamental group
17:50 - The fundamental group of the configuration space
21:16 - The braid group
26:28 - Tying it together
----------------------------------------------------------------------------------------
This video serves as an introductory lecture to the configuration space of points in the plane. To learn more about configuration spaces and braid groups, a good source is _Braids, Links, and Mapping Class Groups_ by Birman.
Go check out my dance film on the same topic if you have not seen it yet! th-cam.com/video/pSdeWTqz4yg/w-d-xo.html
Thanks for watching!
----------------------------------------------------------------------------------------
0:00 - What is the configuration space?
6:23 - Some applications
9:58 - Defining the fundamental group
17:50 - The fundamental group of the configuration space
21:16 - The braid group
26:28 - Tying it together
----------------------------------------------------------------------------------------
มุมมอง: 299
วีดีโอ
Braiding Through Time -- a dance film
มุมมอง 3284 หลายเดือนก่อน
How can you record a dance? By thinking of dancers as points in a two-dimensional plane, we can begin to answer this question. We use dance as an entry point to learn about the configuration space of points in the plane and its fundamental group. A more traditional explanation of the math content can be found here: th-cam.com/video/-DEP100D8n4/w-d-xo.html made for Bridges 2024 short film festiv...
A crochet announcement (and how to make your own patterns!)
มุมมอง 6784 หลายเดือนก่อน
Hi Everyone! I hope you will check you Shiying's channel and learn how to make more of her awesome models! www.youtube.com/@epimono If you will be in Richmond the weekend of August 3-4 and you have not registered for the conference, you still have an opportunity to participate! There will be a "family day" at the science museum of Virginia which is free and open to the public! www.bridgesmathar...
The Dynamic Doubling Map
มุมมอง 2.6Kปีที่แล้ว
Hello everyone! We hope that you had as much fun learning about this little dynamical system as we had making this video! It was amazing to explore how this simple idea connects to so many other mathematical gemstones planetary orbits, modular multiplication tables, and, of course, the Mandelbrot set (and more to the point Julia sets). The poem read at the beginning of the film and mentioned is...
Crocheting a Seifert surface | a math-y crochet project
มุมมอง 9Kปีที่แล้ว
Hello everyone! I met Shiying this year and I was amazed at her beautiful crochet pieces! Being a beginner crochet artist myself, I've worked through a few of her designs and learned a lot along the way (though many many failed projects :)). We both thought that more people should learn how to make this beautiful model and thus this video was born. *Here is now the list of things:* - The compan...
Knots, Surfaces, and Crochet with Shiying Dong
มุมมอง 4.4Kปีที่แล้ว
Hi Everyone! Shiying and I had so much fun filming this video. I wanted to share with you all her amazing work and the interesting mathematical principles behind it. If you would like to learn in detail how to make this project, go check out the companion video here: th-cam.com/video/UgoGGRhlhPU/w-d-xo.html Also, make sure to follow Shiying on instagram to keep updated on her work! @clay_mushi ...
The Light Bulb Lemma (how to untangle knots)
มุมมอง 475ปีที่แล้ว
Hi everyone! I hope you enjoy this cute little lemma! With Summer beginning, my schedule is opening up and I will have more time to devote to this channel. So keep your eyes out for upcoming projects! If you'd like to check out Gabai's paper, it can be found here: arxiv.org/abs/1705.09989 If any of you all know more about the Light Bulb Lemma, I would love to hear about it in the comments! Than...
Crocheted hyperbolic friends
มุมมอง 1.2Kปีที่แล้ว
Hello! I wanted to show you all some of the crochet pieces that I have made! If you want to learn about hyperbolic geometry, you can watch my other video on this topic here: th-cam.com/video/Bx6gqLw3W8E/w-d-xo.html Make sure you check out Daina Taimina's book: "Crocheting Adventures with Hyperbolic Planes"! If you end up making any pieces of your own, I would love to see them! You can email me ...
A cozy history of hyperbolic geometry
มุมมอง 782ปีที่แล้ว
Hello everyone! I hope you all enjoy this exploration of hyperbolic geometry through crochet! Most of the historical information is from "Crocheting Adventures with Hyperbolic Planes" by Daina Taimina. You all should absolutely procure a copy and read the book! It is interesting and approachable for mathematicians and non-mathematicians alike. If you end up making any hyperbolic creations of yo...
The Gauss-Bonnet theorem | Folding up Surfaces (3/3)
มุมมอง 3.6K2 ปีที่แล้ว
Hello everyone! This is the final installment of our investigation of the Gauss-Bonnet theorem! The proof given in this video and the inspiration of the series is from Richard Schwartz' book Mostly Surfaces (PDF here: www.math.brown.edu/reschwar/Papers/surfacebook.pdf). I highly encourage you to check out the section on the Gauss-Bonnet theorem as well as the rest of the book because it is very...
Euler Characteristic and Angle Deficiencies | Folding up Surfaces (2/3)
มุมมอง 8152 ปีที่แล้ว
Hi Everyone! I hope you enjoy the second installment in the Gauss-Bonnet Theorem series! The third video is on its way along with a special "extra content" video. See you all soon! music: bensound.com
Angles of Polygons | Folding up Surfaces (1/3)
มุมมอง 6832 ปีที่แล้ว
Hello everyone! I hope that you enjoy this first installment of a three part series covering the (combinatorial) Gauss-Bonnet theorem! The good news is that parts 2 and 3 are on their way out very soon, so there won't be much waiting time! This is one of my favorite theorems and I hope after these videos it will become one of yours, too :) music: bensound.com
Plato's Elements -- a dance film
มุมมอง 4303 ปีที่แล้ว
A dance film inspired by the five platonic solids. Created by Fran Herr Dancers: Joshua Chong, Elsa Herr, Gio Mangione, Raquel Gordon, Fernando Eizaguirre Music: Kim Duk Soo, 푸살 th-cam.com/video/fE873BITbes/w-d-xo.html Qinyuan Chinese Orchestra, th-cam.com/video/sKgw8x2nldA/w-d-xo.html Oscar Graae Madsen, Dance of the Demons th-cam.com/video/POMrW2uwDKY/w-d-xo.html Debussy, Deux Arabesques, Hél...
Types of Impossible | Impossible Rubik's Cubes (3/3)
มุมมอง 2463 ปีที่แล้ว
Hello Everyone! This is the third and final video of my Rubik's cube series. I hope you find the connection to quotient groups as fascinating as I do! As in the last video, most of the content is from Jamie Mulholland's book on permutation puzzles: www.sfu.ca/~jtmulhol/math302/notes/permutation-puzzles-book.pdf If you'd like to learn more about group theory, here are the two series that I would...
What makes a cube impossible? | Impossible Rubik's Cubes (2/3)
มุมมอง 2843 ปีที่แล้ว
What makes a cube impossible? | Impossible Rubik's Cubes (2/3)
Permutations | Impossible Rubik's Cubes (1/3)
มุมมอง 7643 ปีที่แล้ว
Permutations | Impossible Rubik's Cubes (1/3)
Math Crafts: Making the Five Intersecting Tetrahedra
มุมมอง 3.9K3 ปีที่แล้ว
Math Crafts: Making the Five Intersecting Tetrahedra
Patterns in Modular Multiplication Tables (2/2)
มุมมอง 2.2K4 ปีที่แล้ว
Patterns in Modular Multiplication Tables (2/2)
Understanding Modular Multiplication Tables (1/2)
มุมมอง 10K5 ปีที่แล้ว
Understanding Modular Multiplication Tables (1/2)
Solving Modular congruences with Inverses (2/3)
มุมมอง 6K5 ปีที่แล้ว
Solving Modular congruences with Inverses (2/3)
Very cool!
Underrated!
wonderful :)
I've now done a couple of trefoils. Started using the softball as help to position the initial chain but I found that wasn't helpful and used my left-hand fingers instead. Locking in the twists requires a lot of checking and re-checking but in the end all flows very well if you set it right. As I haven't really grasped knot theory, I'm not sure how to use crochet to make 3d versions of other knots.
That's great that you've had success! This is the kind of project you need to try many times to get it right! If you're interested in making more surfaces like this, I made a video giving a generalized algorithm to make these patterns: th-cam.com/video/cas01tsYeHo/w-d-xo.html Also, Shiying has her own channel where she gives tutorials on a couple more designs: www.youtube.com/@epimono/videos Happy crocheting!
It reminded me of the maypole dance (en.wikipedia.org/wiki/Maypole) A nice example can be seen in The Wicker Man : th-cam.com/video/cYLRRrfPJ1s/w-d-xo.html Or in The Safety Dance by Men without hats (1:37) : th-cam.com/video/1p_BvaHsgGg/w-d-xo.html Now I'd be curious to see their paths in the space configuration! Thanks for those two videos! And the links you made with crochet on other ones! I'm a big fan!! :) And also of Kiya Tabassian!
I made hiperbolic jewelry =)
love it....
26:30 "Tying it together" funny xD. Finally watched this video! have encountered braid groups many times but saw them properly here for the first time! I have a few questions, math and technical: 1. Correct me if I am wrong as I might be confusing concepts here - the braid group is defined by the presented generators and the braid relations right? The way it was presented, I initially thought it was a freely generated group 2. (I could look this up but why :P) what are the generators of the pure braid group? 3. Conf_k is a bigger space than UConf_k as each point in UConf_k splits into k! many points in Conf_k, but the corresponding group of Conf_k is smaller. Is there a Galois correspondence for configuration spaces? 4. I make math videos on a different channel and was really curious: is the mic on the table your main audio input? The audio is pretty clear and I am surprised the mic is picking all of it up. What is your recording setup like?
Hello! So glad that you enjoyed the video! Here are my best answers to your questions: 1. Yes, the braid group is generated by σ_1, ..., σ_{n-1} with the braid relation and the relation σ_i σ_j = σ_j σ_i for |i-j| >= 2. You can see the explicit presentation on the wikipedia page: en.wikipedia.org/wiki/Braid_group But I prefer to introduce it with the physical understanding of literally braiding strings and then "untangling" with the ends fixed (ambient isotopy). All the relations in the presentation can be found with this physical intuition. 2. The generators of the pure braid group are "twists" where you wrap two strands around each other. You can find a good explanation and pictures on page 3 of this document: dept.math.lsa.umich.edu/~jchw/RTG-Braids.pdf 3. Yes, you are totally hitting the mark here! What you are noticing is actually a correspondence with covering spaces. Conf is a k!-sheeted cover of UConf and so π_1(Conf) is a subgroup of π_1(UConf). This is just like how R^2 covers the torus and π_1(R^2) = {1} is a subgroup of π_1(T) = Z^2. The inverse relation of covering spaces and fundamental group is a Galois correspondence! 4. Yes, the mic on the table is my source of audio. It is a Yeti nano. Although, I am looking to get another mic for this sort of video because of the background noise. I am looking at the Rode lapel mics. Thanks for your questions and I'm so glad this video was interesting/useful for you :)
Úžasné! To musím zkusit. Budu mít dárky pro všechny matematiky v rodině a mezi kamarády. :)
I HAVE BEEN MEANING TO LEARN ABOUT CONFIGURATION SPACES. THIS VIDEO IS A GODSEND
Awesome! So glad it is useful for you!! :)
Interesting. :)
Fascinating! :)
Welcome back! :)
Hello! I have been interested in mathematics in crochet for a long time. I've been searching for videos on TH-cam, for something like your channel but could not find anything. I only found you through the reference page of one of the studies. If I had found you earlier, it would have meant so much to me. So, I think some people think the same way, who want to find your content but don't know how. Maybe using hashtags would be helpful?
Thank you for the great feedback! I am glad that you found my channel :) I am learning now that "youtube tags" and hashtags are actually different things, so I will definitely include hashtags in the future.
@GrapefruitGecko I did not want to be smart pants, and I honestly do not even know the difference between hashtags and TH-cam tags 😂😅 I was just so happy to come across your channel and wanted to say that you are needed! 🥹
@@lisamarkelova7457 Thank you! That is so sweet <3
Thank you! You are a blessing!
I do not quite understand but boy is it beautiful! 😊
Unfortunately not so good explanation! The most important row is row no. 1 and she didn't make it quite clear! Don't know where to put the hook , is it through all marked stitches or just the first chain ?
Hello, I'm sorry that this wasn't clear for you! Yes row 1 is the most important, and setting up the chain correctly is the main challenge of the project. When you put stitch markers through several chains, you will treat those as one chain. So you put the hook through all the marked chains together. Let me know if you have any other questions I can answer!
@@GrapefruitGecko Thank you so much for the reply, the second row is more difficult! Anyway , I work on an experienced level in crochet , amigurumi in particular, but I loved this project! Alas , couldn't make it due to the lack of so much information in this tutorial, especially the 2 row .. Many thanks
Wow!!! Amazing work!! Thank you for sharing.
this is amazing! thank you for this video, from a lover of crochet and mathematics
So glad you enjoyed it :)
Thank you 🤍
Glad you enjoyed the video :)
This was so fun....Now I want to have a bunch of her Einstein hats to play with.
Congratulations on being in the NYT on Einstien shapes.
What a beutiful math girl with some weird elements in hand... Awesome!
The tetrahedron is self dual. The cube is dual to the octahedron synthesizes homeomorphism (sphere). "Always two there are" -- Yoda.
3:40 its definitely cardiod and parabola, not what you thought, pervert)))
Every dialogue of jeff in the beginning gave me goosebumps. Literally the beginning extract and the realisation that it's about dynamical systems is soooooooo good. Thanks for the video. Appreciated.
I’m so glad you enjoyed it! It’s really good to know that our intention came across! :))
Incredible crochet!!! ☺️
I stumbled across this because I saw the event at the Museum of Math that Shiying is hosting! I live in Canada so can't attend but I am so glad I was able to find a video with at least one of her patterns! If there's any way to attend some other way or learn more from her, I would be SO interested! You're both awesome :)
I’m so glad this video was helpful for you! I know that Shiying has a few more of her patterns written up, I will see if I can share them with you! If you email me at geckograpefruit@gmail.com I can put you in contact!
@@GrapefruitGecko just responded, thanks so much!!
hello! I watch your videos and it's easier for me to live. thank you!!11!
Same here 😂😂😂❤❤❤
Great video! The conversational style reminds me of the classic math video "How to turn a sphere inside out"
Absolutely nailed it! That was a key inspiration for this video!
Do you know where one could find a proof of the 3 dimensional version shown in the video? I can't find anything other than the 4 dimensional variant.
I also had a hard time finding concrete writing about this... which is one reason I made this video! But here is blog post that talks about it: jde27.uk/blog/lightbulb.html
good vid 💯
great video! the comedic moments (JEFF!!!) really elevate it in my opinion and the reasoning is very clear and engaging throughout :)
Thanks so much! We had fun with the comedy aspect haha :D
Your animation style is amazing.
Thank you!
Beautiful video. Really enjoyed it. Very artsy, clear, and beautiful visualizations. Maybe a bit of background music would have been nice, I don't know.
Thanks so much for the feedback! I’m glad you enjoyed the video :))
@@GrapefruitGecko I agree with everything they say!
Sublime!
<3
Cannot wait for the autumn to arrive, being so poetic about falling leaves, huh? One more month of Summer... That was a really nice collaboration, thank you for making and sharing this. :)
True, we are being a bit preemptive ;) I’m so glad you enjoyed the video!! Thanks for watching <3
@@GrapefruitGecko no problem, I cannot wait for the fall/Halloween season either, :)
excellent video!
So glad you enjoyed it!!
let's make cool stuff!! inspiring
:D
that is a beautiful crochet :o
❤️❤️
I need a basic crochet tutorial, help me PLEASE!
I love this video so much!! The animations are so cool. By the way, I think it would help to normalize your audio. Hopefully, your editing software has the audio levels visible, and you can adjust the gain so that it's easy for everyone to hear :)
Glad you liked the video!! I will definitely pay attention to the audio next time, thanks for bringing it to my attention
New video drop!!!
!!!!
Woah, I didn't know knots cannot exist in 4D space, you blew my mind! o_O So if knots are made from 1D lines and can exist in 3D space, does that mean that in 4D space knots of 2D sheets can exist? Could like for example the Klein bottle be considered a 4D knot?
You're thinking on totally the right track! In 4D, mathematicians study knotted 2-dimensional spheres... and in general, in 'nD' mathematicians study knots in (n-2)-dimensional spheres. Since the Klein bottle is not homeomorphic to a sphere, it's not a typical 4D knot. However, knots in other non-sphere closed 2-manifolds (without boundary) might be studied too... that's a good question that I don't know the answer to!
Great video! just a bit of feedback, the sound was very weak
Thanks for letting me know! I don't think there is anything I can do at this point but I will make sure to do more thorough checks in the future
This is a really great video, love your mixture of animations over the video!
Thank you so much! I'm so glad you liked it :)
i just want to experience one day as a four dimensional creature
What an experience that would be haha!
This is really cool! Thanks
Glad you liked it! Thanks for watching :)
cozy indeed … i am amazed