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Saturday, 14 October 2023

Math in Sewing [Pt 1]: How Math Makes Sewing Easier

without mathematics there is no art - luca pacioli
"Without mathematics there is no art"
Somewhere in all these blog posts, I've shared the fact that I abandoned art school after one year – due to being given the impression that there are rules on how to "make art" – and subsequently ended up with a career in IT.

In between those events, I pursued a double major at university, with one of those majors being math. It was a subject that I had excelled at in high school.

Even though post secondary level mathematics ended up being much more difficult, I never lost my appreciation for the beauty behind the art of math. It is a precise, exact and unbending science and yet can be so organically malleable at the same time. Who would have thought that, decades later, I would be thankful for being able to apply math to sewing?

Don't worry, while math is the topic of today's post, it's not going to be front and center in any "computational" form.... not until the very end!




Are you someone who wants to ask the pattern designer: how do I change this to be this high and that wide? A few simple calculations are usually all that's needed to work it out, and yet for some people, it's impossible to do.

Obviously, math is integral to sewing, especially for things that are sewn from "scratch". Pattern designers need to have a certain amount of mathematical ability in order to do what they do successfully. Those of you who use patchwork and quilt patterns can appreciate the effort that goes into figuring out what the various pieces are – and how they need to be sewn together in a certain order – to get the desired result.

Remember this? It's a fabric interpretation of iris folding. All forms of folding – including, of course, origami – are very much based in mathematics. Projects like this can be quite intricate.

Table mat by diy HandyMum Lin tv
image courtesy of diy HandyMum Lin TV...

But even at the simplest level, to sew anything of a certain size, you have to be able to take and translate measurements and understand how to add seam allowances. And then it's a matter of knowing how best to lay out and cut the fabric so that you don't waste any of it. Sometimes it's easy, like making a rectangular drawstring bag. Other times it's much harder, like when I cut up two jackets to make a duffle bag. For that, I had to come up with a plan to turn various small pieces into bigger pieces before I could even contemplate using any sort of pattern to make the bag.

So a common problem is that even if you have a pattern to follow and you intend to make whatever the same size as the pattern calls for, if your fabric allotment doesn't match, you have to make do, and making do will often involve math.

Recently, regular reader Marie corresponded with me about this post back in September. After sharing pics of her customized sewing challenge, I thought the work she did would be the perfect example to highlight for this blog post. So I did a quasi "Q&A" with her via email.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Marie's fabulous handiwork...

First of all, by way of an explanation, her project was to make some outdoor pillows (and seat cushions) based on a pattern using striped fabrics. Due to fabric constraints, however, it was not a straight forward approach, since the stripes needed to be fussy cut.

Q: Describe the inspiration for this project (as found at Sew4Home, under the title of Spun Stripes Pillow Trio).

image courtesy of Sew4Home
The three designs for the Spun Stripes Pillow Trio by Sew4Home...

A: This pillow project had three layout designs — each consisted of four fabric blocks, using three of one color and one of an alternate color. I used the pieced design for both the front and back of my pillows instead of having a plain back like the original project called for.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Both sides of Marie's pillows feature the pieced layouts...

Q. You said that you had similar fabric as the Sew4Home samples, but not in the right amounts. What exactly did you have?

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Fitting pieces made more difficult by having to match stripes...

A: I had pieces of this striped fabric (a heavy sailcloth with some kind of waterproofing that makes water bead on it) in five colors: one yellow, three red, four blue and black, and five green. The fabric wasn't one large piece but was already cut up in approximate 28" x 30" sections. They were all different sizes and with the stripe design, that changed how many blocks I could cut from each piece. That's what made this a math problem!!

Q: How would you describe the prep work that you had to do?

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Making it fit...

A: The task was to fit the pattern pieces on each fabric to see how many I could get. In each color, the largest piece gave me three blocks of each design, so I decided that the yellow would be the accent color and with nine yellow blocks, that dictated nine pillow tops. So I cut one set of three-blocks-of-each-design in each color.

Drawing out the color layout designs, and taking a pic of what could fit on each different color fabric piece helped me plan before cutting, because I needed four different blocks to make one pillow top.


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Q: Did you end up with a fixed plan, or was it a fluid, changing process?

Laying them out and sewing drew my attention to the beauty of the blue and green together, so I switched the pattern design and made layout A (the predominantly red one in the original Sew4Home sample pic) with two each blue and green instead of the one and three design! I made them both the same, but could have switched one to have the green pointing in — saw that long after it was sewed and stuffed… otherwise I would have taken it apart and rearranged it.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
The surprising appeal of blue and green...

Q: I noticed in your photos that this project encompassed more than just pillows. Tell us about the seat cushions.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Matching seat cushions...

A: Before making more pillow tops, I had to plan for the chair seats. I didn't want to waste even an inch of fabric, and after days of pondering how to squeeze five seat cushions out of the least number of fabric squares, I sewed three fabric pieces together with the stripes of the middle section going the opposite way: =|||=  Then I could squeeze two seat cushion covers out of each of the three fabric sections. The sizes of the fabric pieces were all different, so I measured and laid this out a zillion times until it worked. I labeled each piece with its measurement and used the smallest fabric pieces so that I could save the larger pieces to cut more pillow top designs. Each cushion had a a single pattern on one side and two on the reverse. The fabric folded over the front of each cushion. The back seam was hand sewn with invisible stitches.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Seat cushions pieced side...

Q: Did you run into any hiccups during this "make it fit" project?

A: I learned that the bias cut layout C (the predominantly gray one in the Sew4Home sample pic) was hardest to fit on smaller fabric pieces.

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
The bias cut challenge...

But I found this task to fit my perfectionist attitude and it was actually quite fun. Many others might not have enjoyed this incredible puzzle. I was not in a hurry and it took over five weeks start to finish for making five seat cushions and eight pillows (that's sixteen pillow top panels — all different except for the two blue/green).

Q: We originally connected about this via a post on sustainability. You've told me that this fabric was in your possession for decades and that it came to you at no cost. Were there any other recycling opportunities involved with this project?

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Seat cushions plain side...

A: The seat cushion foam came from my neighbor's garbage: an old 2" thick camping sleeping mat, covered in ripped up nylon. I saved this in my shed and ripped off the nylon when I had a use for it. I cut four seat sections using the long stretch and the fifth seat was pieces of foam from the extra side cut off. Foam in pieces can be glued together, but I just basted it and wrapped each seat with batting which I hand basted on. The batting also helped hold the foam sections together. It took me numerous drawings and measurement alterations to squeeze the five seat cushions out. I have a 3" x 16" foam piece left over to make a neck brace for sleeping on a plane.

I stuffed the pillows with old and new (Walmart $3.57) pillows cut in half. It's much cheaper than buying stuffing and it's the same exact material. I did use invisible zippers in the pillow tops to make it easier to change the stuffing. (Wawak is my inexpensive online sewing supply for thread/zippers, etc.)

Marie R's Sew4Home Inspired Spun Stripes Pillows & Cushions
Some left over...

But I have three pillow tops and other fabric left over to make an ottoman! The stuffing will be those large peanut shaped shipping foam material that I have been saving up for years. It will be a nice surprise for my son!

ME: How many of you agree that Marie's pillow and cushion project is just stupendous? When I first saw this project on Sew4Home, I thought it was awesome. But I knew I would never attempt it, because I had no need for the pillows, nor – perhaps most importantly – the fabric to make it work. It's wonderful to see someone execute it to such perfection!


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Of course, you've noticed by now that the title of this post implies a "part two" is still to come. I have a special tutorial to share with you in that one, which arose out of this equation:

the golden ratio
One of the "fun" ways to calculate phi (courtesy of Erol Karazincir)...

And just in case you don't find anything fun in the above, let me reassure you that the project itself is not at all as esoteric!

Thanks again to Marie for contributing to today's post; hope you enjoyed.

'Til next...

2 comments:

  1. I understand trying to piece fabric together to make it work. This was impressive and the outcome looks excellent

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