Name: Emma Busch

Major: Mathematics

Minor: Spanish

Advisor: Dr. Pamela Pierce

The purpose of this IS was to look at the relationship between math and knitting, specifically how knitting can be used to represent the symmetries that can occur in math such as the frieze patterns. The project begins with an introduction into group theory, looking at what exactly is a group and what are various properties that they can have. Next, the focus moves onto the frieze and wallpaper patterns. These patterns, made up of transforming motifs to create designs, have been featured in the work of famous mathematician and artist, M. C. Escher. We look at how to classify various frieze and wallpaper patterns and what makes these two symmetry groups special. The next chapter looks at the relationship between math and knitting and how the two fields benefit each other; whether that is through knitting mathematical objects for better visualization, or using knitting projects to teach mathematics to students in an accessible and exciting way. Finally, the project concludes with a look at the final knit product that was created: a sweater vest symmetry sampler representing the seven frieze patterns. The chapter follows along the process of designing the motifs used and transforming these motifs to represent the various frieze patterns.

Emma will be online to field comments on April 16:

noon-2pm EDT (PST: 9-11am, Africa/Europe: late afternoon)

Emma- You have done so well this year and I am so proud of you! I could see how the mathematics influenced your knitting, and I believe that the act of knitting your frieze patterns actually solidified your knowledge of the group theory. It was a wonderful combination of math and the fiber arts. So well done–congratulations!

Thank you Dr. Pierce! I have appreciated all your support this year in finishing my project and looking towards the future!

Thank you for sharing your work Emma! This is a terrific project, the end result is so well done. Congratulations! This is a great presentation, you have a lot to be proud of.

Thank you Dean Bowen! I appreciated all your thoughtful questions at orals and your support in getting through a project about group theory without taking a class on it!

bestie, this is fantastic! congrats on a job well done!

Thank you Lindsey for all your support!

Nice project (and title), Emma! I’ve seen the mathematical fiber arts displays at math meetings but I didn’t know anything about how the actual knitting related to the mathematics. This was a really nice explanation!

Thanks Dr. Long! I have appreciated all your support this year!

Emma – this is brilliant! Congratulations! As a fellow math nerd this was fun and fascinating to hear about.

Thank you Paige for all your support since the days of watching Milo and Otis in kindergarten!

Emma thank you for inspiring me to be crafty this year! I am so proud of how amazing this project is and how easy it is to understand for even someone who isn’t strong at math. It is amazing that you were able to join two of your big interests into one project.

Thank you Marian! I’m glad that I could support you in your crochet journey and cannot wait to see all the fun things you make!

Very original project! Some of us got the math, and others the knitting – you combined them both in a very original manner.

Thank you! I loved being able to combine two of my interests so that writing about them all year felt a bit more enjoyable!

Wonderful presentation. A great title. As both a math person and a person who likes knitting this presentation gave me so much to think about. I had really never given a lot of thought to the construction of patterns and how they are related to math. Thanks for a good lesson this morning. So very proud of you!

Thank you Gigi! I will have to show you the more in depth presentation with more of the specifics on math and knitting some time when I’m back home! Thank you for all the support and for being my knitting role model! Love you!

Interesting project, Emma. Best wishes for your next endeavors!

Thank you Dr. Uber!

Congrats, Emma! This is a great project in the midst of sports analytics and I’m so proud of your originality!

Thank you Carina for all your support this year! We truly love being a woman in STEM!

From the title to your finished knitted vest, this study was incredibly thoughtful and creative! I am probably the worst math student on the planet, but your presentation had me hooked from the beginning. Congratulations on a job well done! It’s been a pleasure to know you and your family these past four years through your friendship with Abby. Best of luck in the years ahead!

Thank you Mr. Cunningham! I’m glad that I was able to communicate the math concepts in an understandable and interesting way for everyone!

Hi Emma! This is a super neat project. I love that you were able to combine your major with one of your passions. Do you plan to knit more Frieze patterns in the future?

Thank you Wave! I don’t have a set plan for my next mathematical knitting project but I am interested in attempting to represent other types of symmetry like the wallpaper groups potentially in a project as well!

Emma, thanks for sharing this fun application of group theory. You’re right – I didn’t realize how mathematical knitting is. Congratulations and awesome sweater!

Thank you Dr. Guarnera! I was actually able to use some of the concepts from Combinatorics in a proof that there are exactly seven frieze patterns and did some comparisons between the definitions of isometries and other concepts in graph theory and group theory so I appreciate the support that your teaching this year had on my knowledge of that!

Emma congrats!! This is such an awesome, innovative, and creative project.

Thank you Rachel!

Congratulations Emma! This project is super interesting, I would have never thought to look at the mathematical relationships in knitting!

Thank you Kayla!!

Fantastic IS, Emma! I’m so happy to see you were able to dive into Group Theory and apply it to a hobby. I like your example of a knitted torus. In your research, did you find any other examples of mathematical shapes or objects that people have been able to knit? Is there a favorite example that you found (other than the torus/donut of course). Thanks!

Thank you Dr. Kelvey! Your teaching and encouragement in proof writing this year definitely helped with the proofs that I wrote in my project! While researching, I found a plethora of mathematical objects that have been either knitted or crocheted. One of my favorite categories of those were knitted mathematical objects that were also functional. For example, this cowl represents a mobius band (https://www.ravelry.com/patterns/library/y-x-i-twist-cowl) and I think the ability to be able to wear a mathematical object represents a very cool application of the mathematical fiber arts.

Emma! This is such a cool and very original project. You should be very proud of yourself. Congrats!!

Thank you Mari!!

Congratulations Emma! Great title, great sweater and an understandable presentation of a somewhat difficult concept. I like that knitting a sweater can bring an abstract concept to fruition in a pleasing visual design and in turn the sweater may help one think about the concept more deeply and maybe have new insights about math. Appreciate your hard work, creativity and sense of humor.

Thank you mom for all the support this year! I’m glad that the symbiotic relationship between math and knitting came across in my presentation as each field benefits the understanding of the other!

Congratulations Emma, this is so cool! We wish you all the best in your plans beyond Wooster!

Thank you Dr. Pasteur!

Emma, I lack the cognitive ability to understand a lot of mathematical concepts. However, you successfully made a presentation that I can understand. I enjoyed hearing about the different groups and how you melded two of your passions together. This project is very original, and the final product is something you should be proud of. Congratulations on being finISed!!!

Thank you Reaghan! I have appreciated all your support these past four years so much even if we have not been able to see each other as much as one would hope!

I am constantly amazed by your creativity, and this project perfectly shows your ability to add a bit of fun to everything in life. You found a way to show off your talent and interests in an academic setting, and that is the coolest thing to me. Congrats Emma!

Thank you Rachel, this is such a nice compliment! Thank you for all the support this year in everything that I do, I appreciate it lots.

Emma this is such a cool project! Congratulations on all your hard work!

Thank you Devon!

Emma, I love this. In math, we often tend to forget the applicability of theoretical math (vs. applied math) in real-world situations. Thank you for bringing that back!

Thank you Alayt! I have loved being able to have both running and math class with you and always enjoy hearing your jazz focus music in the background of class. I agree! I think looking at the various ways that fiber artists have incorporated theoretical math into their projects provides an opening into theoretical math for those that need more concrete applications or examples to learn off of.

Congrats Emma on a well done IS! Did you come across other papers regarding math and knitting? I think when you get home I’ll have to get some tutoring on some of what you did and the concepts. 🙂

Very creative!

Hi Dad! Thank you for all the support! I found a whole community of artists and mathematicians who have formed the field of the mathematical fiber arts and through the connections of my advisor, got to speak with one of the main forces in the field, Dr. Goldstine, about my project! Once we’re back home, I can give you and mom the more in-depth presentation of the mathematics that I looked at.

This is so cool, Emma! I love how you combined your love for fiber arts and math into such an interesting project.

Thank you Olivia! I have appreciated all your support this year so much!

Such a creative study Emma! I am a knitter too but not strong in math and you made the relationship between the two very understandable. I can see this being used as a teaching tool with our young students to help them see real world examples of math in action.

It’s been a joy to get to know you. Best of luck with your future endeavours!

Thank you! I actually have a whole section in one of my chapters about how knitting can be used as a teaching tool to help understand math! There are a few professors at various colleges that have entire classes on it and there are two fiber artists that create knit wall hangings representing mathematical concepts for elementary and high school classrooms.

Congratulations Emma!! This project is absolutely amazing!!

Thank you Megan!

Great job Emma! Love the sweater. It looks so good on you

Thank you Noah!!

Emma, this is an amazing project. I am impressed how you integrate math and art together. Unique. Thank you for your detailed presentation too. Your scholarly and artistic sensibility –and pedagogy–is absolutely impressive. Congratulations!

Gracias Dr. Medina! Thank you for all your support this year- I have learned a lot from your classes.

Congratulations Emma! Your IS is so interesting and I’m so glad you got to combine your love of math and knitting!

Thank you Abby!!

Amazing I.S. research project Emma! So proud of you!!

Congratulations, Emma!

Awesome project! I’m not great at knitting but I love to crochet. Maybe I’ll look into mathematical crocheting!