A Saga & A Book Review

A Toroidal Knot – Imagine knitting this up with some icord!

They sucked me in.  I had no choice.  It was the title:

Making Mathematics with Needlework; Edited by Sarah-Marie Belcastro and Carolyn Yackel.

And the cover.  Two knitted donuts accompanied by two wooden needles and two balls of yarn.  The symmetry and balance were head turning.

Oh yes.  Those toruses might as well have been tornadoes, leaving me breathless at the thought of mathematics–and knitting–placed together in a single volume.

(This is the part where I could shamefacedly admit to being somewhat of a math-geek.  But I think you’ve already guessed that, so I’ll save my confessions for another time.)

Some books are predestined for certain people to read.

I placed the book on my Christmas list where it languished for two years, driving me to despair and to Amazon.

Amazon had it, plus exorbitant shipping.

Here’s a confession I will make: I don’t like paying a significant percentage of something’s cover price just to have it delivered two weeks later.  So I deepened my despair and moved on.

As a last-ditch effort, I checked our modest local library.  They didn’t have it either.  Not that I expected them to; keeping up on new DVD releases is a hit or miss process. An obscure mathematical-needlework volume would be completely beyond them.

Then came the moment of inspiration.  I just needed to work the system to get what I wanted.  Specifically, the library system.

I filled out a form with all the identifying factors of the book, title, authors, ISBN, ISBN-10, ISBN-13, date published, publisher, and what have you.  Then I submitted it to the Inter-Library Loan System.

The Inter-Library Loan System is an oblique process by which you ask a librarian to find you an impossible-to-find book from a library that neither of you have ever been to.  It takes an indefinite amount of time, has unreliable results, has no allowances for renewals of the loan period, carries triple the fine for overdue materials, and your improbable success leads to an awkward scene at the check-out counter:

I stand, waiting to catch a librarian’s attention.

ME: Hello.  I have an interlibrary loan request to pick up.

The librarian looks at me, perhaps measuring my worthiness.

LIBRARIAN:  Last name?

ME: Dale. D-A-L-E.

The spelling is insurance on my part, initial proof that I am who I say I am.  The librarian leaves to search the shelf of holds behind the counter for my Inter-Library Loan Request.  Normal requests, known by the informal term “holds”, are placed on a public shelf for easy access by a patron.  But this Inter-Library Loan Request comes from a foreign library system, and must be held in quarantine separate from other materials until I come to check it out.

The librarian returns, holding a slim volume about a foot square.

LIBRARIAN:  Is this it?  Making Mathematics with Needlework?

ME:  That’s it.

I smile and reach my hand out.  The librarian places the book just out of reach on the counter.  It’s not mine.  Yet.

LIBRARIAN:  Card please.

I hand over my card, proof of my validity as a library patron.  I’m holding my breath now.  The librarian scans my card, clicks the mouse twice, scans the book, and turns to me.

LIBRARIAN:  Have you ever had an Inter-Library Loan before?

ME:  Yes.

I have actually had quite a few Inter-Library Loans before.   Over forty in the last two months.  All of them processed by this librarian.  At this library.  The majority of Inter-Library Loans checked out from this library in the recent past.

The librarian ignores our history, and proceeds as if this is the first time for both of us.  There’s a protocol to be followed here.  

LIBRARIAN:  This is an Inter-Library Loan.  The loan period is 21-days.  There are no renewals.  The fines are twenty-five cents a day.  Do not remove this card – pointing to a 3×5 card paper-clipped onto the fly-leaf reading: DO NOT REMOVE – or this one – pointing out a second paper taped over the binding with small gray letters reading: DO NOT REMOVE.

These warnings do not escape me, nor does the fact that I have NEVER removed the DO NOT REMOVE tags from any Inter-Library Loan ever.

If they do not escape the librarian, then the librarian gives no sign.  At all.

The librarian hands over the receipt and the book simultaneously.

LIBRARIAN:  Here you are.  The book is due in three weeks.  The date is on the receipt.

I gratefully take the items, thankful the book was found, thankful an unknown library agreed to share their book, thankful there were no difficulties in checking out, thankful I have three whole weeks to absorb what is between these covers.  All this thankfulness comes out in six words as I slip my card into my pocket.

ME:  Thank you.  Have a nice day.

LIBRARIAN:  You too.

I walk gleefully out to the car, feeling like I just found out Christmas comes twice a year.

A Book Review: Making Mathematics with Needlework

Ten papers, ten projects, six different types of needle work, and five knitting projects.

The book begins with an intro explaining that a)math naturally exists in needlework and b)needlework can be used to teach math.  There’s a list of research papers for people who feel the need to dig deeper, and then we move on to the papers and the projects.

The types of needlework covered are quilting, knitting, crochet, cross-stitch, sewing, and blackwork embroidery.

For each type of needle work there is one project, the exception being knitting which has five different projects.

The mathematical papers are presented at the beginning of each chapter.  The subjects covered are möbius strips, diophantine equations, Sierpinski Variations, toruses (topology), symmetry, algebra, Fortunatus’ purse (topology), braid equivalence (topology), graph theory, and hyperbolas.  They are written for both the lay person and the mathematician, so there are parts which were easy to understand and parts which went right over my head.  It wasn’t that the vocabulary used was terribly difficult, just that unless a person has some solid practice reading proofs, then the part of the paper presenting the proof can be tricky to understand.

I wouldn’t let that slow a non-math oriented knitter (or needleworker) down though.  Regardless of the topic, the summaries are easy enough to understand, and provide enough context for the project to make the projects worthwhile.

The instructions for the projects are written in plain knitters’ english, complete with the standardized abbreviations we know and love.  The knitted projects themselves are fairly straightforward – a pair of socks, a cabled pillow, a circularly knit hat, a knitted donut-shaped torus, and the most complicatedly-interesting one, a pair of hyperbolic pants (they are knit entirely in one piece).

The other crafts are the same.  Anyone familiar with embroidery charts will be able to execute the cross-stitch and blackwork projects.  Crochet-ers familiar with crochet charts will have no difficulties either.  Quilters will have no problem executing the half turn required to make a möbius strip.  Sewers will have to think slightly outside the comfort zone for their project, but a thorough read of the instructions left me confident that I could do it myself with knitted motifs stitched together in the same fashion.

And that leads me to my second most favorite thing about this book.  All of the math and all of the project ideas can be applied to knitting in a variety of ways.  Of course it is possible to knit a one piece möbius strip, but one could also knit triangles and stitch them together replicating the way quilted pieces are stitched together.  One can embroider the different patterns onto knitted fabric, or they can cable it into the fabric, and those are just two examples for the embroidery.  One can sew knitted pieces together to resemble the sewn fabric Fortunatus’ purse.  A really crazy knitter could try picking up the stitches rather than sewing afterwards.  The possibilities available are much larger than those presented in the book.

My most favorite thing about the book is its willingness to explore interdisciplinary knitting.  Beyond fashion and function in knitting lies theory, and this book dives in wholeheartedly.

Most of the knitting projects focus on some form of topology, a vast mathematical topic which I blogged about here.  The book’s editors, Sarah-Marie Belcastro and Carolyn Yackel are both knitting mathematicians who have written about topology and knitting out of their own love for both.  They make the theory tangible through the projects and are opening up new territory for the rest of us.

So.  I’m really looking forward to knitting hyperbolic one-piece pants.  And I’d love to give Fortunatus’s purse a go too.

It’s fun to push the outside of the envelope, especially if the outside is the same as the inside.

(The above is a topology joke, referring to objects whose outside really is the same as the inside – a one sided surface.  Like a möbius strip or Klein bottle.)

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Happy Knitting!



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