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Author Topic: The mathematics of sewing  (Read 982 times)
Hez
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« on: April 29, 2016, 12:33:47 am »

Are explained Here

My favourite bit is
Quote
I... was gratified to find that it fitted like a glove.  Of course it should have fitted like a dress.
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ForestB
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« Reply #1 on: April 29, 2016, 03:58:32 am »

That was an interesting article.... I never thought about the math and topology involved in making a dress.
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J. Wilhelm
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« Reply #2 on: April 29, 2016, 10:09:42 am »

Hmm.   So if the lining is stitched at the neck and at arm holes while "inside out" (nice side of lining inward facing dress) over the garment (which is not inside out) as he suggests, then it's topologically impossible to pull the lining in through the neck as he stated.

The curious thing is, that if he were to turn the dress inside out and, then stitch the lining with the nice side looking outward, there should be no topological obstacle, because you can simply flip both the dress and the lining together through the neck.  Same as turning a pair of swimming trunks with the lining attached, or wearing one t-shirt on top of another and then taking them both off at the same time....

The problem is you have to turn a Genus 3 surface into a Genus 1 momentarily (un-stitching the arm holes) while flipping, which is required when you want to only "flip" the lining but not the dress, or viceversa.
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Miranda.T
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« Reply #3 on: April 29, 2016, 06:24:38 pm »

Hmm.   So if the lining is stitched at the neck and at arm holes while "inside out" (nice side of lining inward facing dress) over the garment (which is not inside out) as he suggests, then it's topologically impossible to pull the lining in through the neck as he stated.

The curious thing is, that if he were to turn the dress inside out and, then stitch the lining with the nice side looking outward, there should be no topological obstacle, because you can simply flip both the dress and the lining together through the neck.  Same as turning a pair of swimming trunks with the lining attached, or wearing one t-shirt on top of another and then taking them both off at the same time....

The problem is you have to turn a Genus 3 surface into a Genus 1 momentarily (un-stitching the arm holes) while flipping, which is required when you want to only "flip" the lining but not the dress, or viceversa.

He suggests turning the dress before stitching the arm holes, which is possible, but it still leaves visible stitch lines at the hem. Much neater to leave it open at the side seam and pull through that, and then stitch that up whilst putting in the zip (stitching would be generally hidden by the arm). You still need to neaten up the arm holes though; if adding say short capped sleeves they can be sewn right side dress material on the mini-sleeves to right side of the dress body lining, giving a nice neat seam on the outside.

Yours,
Miranda.
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Hez
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« Reply #4 on: April 30, 2016, 11:35:29 pm »


The curious thing is, that if he were to turn the dress inside out and, then stitch the lining with the nice side looking outward, there should be no topological obstacle, because you can simply flip both the dress and the lining together through the neck.  Same as turning a pair of swimming trunks with the lining attached, or wearing one t-shirt on top of another and then taking them both off at the same time....


Yes but this method leaves the raw edge of the seams showing inside the dress.  The correct method hides all these.
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steiconi
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« Reply #5 on: June 16, 2016, 04:35:06 am »

I'm afraid I don't have mathematical proof of this, but can confidently assert that stitching the lining to the dress all around the hem will produce puckers and bulges.  I believe the problem is caused by unequal stretching of fabrics. 
Far better to hem each separately, then swing tack at the seams.

He suggests turning the dress before stitching the arm holes, which is possible, but it still leaves visible stitch lines at the hem. Much neater to leave it open at the side seam and pull through that, and then stitch that up whilst putting in the zip (stitching would be generally hidden by the arm).
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J. Wilhelm
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« Reply #6 on: June 16, 2016, 06:53:18 am »

I'm afraid I don't have mathematical proof of this, but can confidently assert that stitching the lining to the dress all around the hem will produce puckers and bulges.  I believe the problem is caused by unequal stretching of fabrics.  
Far better to hem each separately, then swing tack at the seams.

He suggests turning the dress before stitching the arm holes, which is possible, but it still leaves visible stitch lines at the hem. Much neater to leave it open at the side seam and pull through that, and then stitch that up whilst putting in the zip (stitching would be generally hidden by the arm).

Indeed, dear ladies, as you point out the problem is more complicated.  You talk about stretching. That's the difference between mathematics and physics and engineering. How much of a complication you are willing to take into account and your approach to solving the problem is different for each branch of science.

Indeed, Ms. Steiconi, in fact he did consider stretching, but he considered stretching of one type material, when you really have two materials.

The discussion on topology he gave was strictly a "geometric" discussion. No real physics involved at all. He did cover stretching of fabric, but did it in just an "introductory" manner, justifying why he cut patterns the way he did, and thereafter no discussion on actual stretching and limits of stretching.

The actual mathematical problem should not just deal with topological possibilities and the mathematics of quadric surfaces (made from magic unstretchable strings), but take into account the mechanical material properties that he vaguely touched on. Rayon vs Nylon. Linen vs Cotton. Spandex vs. Polyester. And that means discussing the difference between liner and exterior, and how they interact with one another.

The issue is not that you can't obtain a mathematical proof, but rather, you need a mathematical description, and it's usually a very complicated description, perhaps only expressible as an approximation or computer model as opposed to analytical mathematical equations.

https://en.wikipedia.org/wiki/Cloth_modeling

PS. Right now I'm getting some self-education on the subject of corset/waist cincher physics with a dash of cloth economics. Lesson 1: creases bad. Lesson 2: you get what you pay for  Grin
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steiconi
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« Reply #7 on: June 16, 2016, 10:21:18 am »

Lesson 3:  make it up in cheap fabric first.
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Cora Courcelle
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« Reply #8 on: June 17, 2016, 04:12:21 pm »



PS. Right now I'm getting some self-education on the subject of corset/waist cincher physics with a dash of cloth economics. Lesson 1: creases bad. Lesson 2: you get what you pay for  Grin

Try using a steam iron, but don't actually press the garment just hold the iron a little above it.
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silkfabric
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« Reply #9 on: August 12, 2016, 10:37:19 am »

 :DThis is such a creative idea The fantastic:mathematics of sewing.
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morozow
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« Reply #10 on: August 13, 2016, 12:00:55 pm »

Sorry. My English. And I don't remember the math.

But in 1878 the XIX century the Russian mathematician Chebyshev wrote an article (in Paris a report) cutting the garment" is devoted to differential geometry of surfaces in it the scientist has introduced a new class of grids, called "network Chebyshev.

Funny story of the birth of this study. Chebyshev noticed a hunched back carrying his cab. The fabric of the clothes without a single wrinkle filling a spherical volume. With this observation began a mathematical study on the theory of Chebyshev nets. And after a while he gave in Paris a report.
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Sorry for the errors, rudeness and stupidity. It's not me, this online translator. Really convenient?
J. Wilhelm
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« Reply #11 on: August 13, 2016, 05:07:37 pm »

Sorry. My English. And I don't remember the math.

But in 1878 the XIX century the Russian mathematician Chebyshev wrote an article (in Paris a report) cutting the garment" is devoted to differential geometry of surfaces in it the scientist has introduced a new class of grids, called "network Chebyshev.

Funny story of the birth of this study. Chebyshev noticed a hunched back carrying his cab. The fabric of the clothes without a single wrinkle filling a spherical volume. With this observation began a mathematical study on the theory of Chebyshev nets. And after a while he gave in Paris a report.

In advanced computational fluid mechanics courses, we used Chevishev polynomials for interpolation and grid generation in a type of approximations called "Spectral Methods"

The idea is to use Fourier Transforms to approximate (figuratively speaking) the equations for the laws of physics and transform back and forth between frequency space (hence the "spectral"),  and real space to solve difficult differential equations. Those of you familiar with mp3 compression should recognize the use of Fourier Transforms.

We generated special grids along whose points you can solve the laws of physics.  The Chevishev grids are unusual in that the lines (like the thread in a weave)  are not uniformly spaced,  but rather have sinusoidal distributions.  I guess this could be similar to the threads in the garment worn by that hunchback!

https://people.maths.ox.ac.uk/trefethen/8all.pdf
« Last Edit: August 13, 2016, 09:49:04 pm by J. Wilhelm » Logged
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