What a physicist sees when she looks at a fancy gown
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As someone who has built high-grade muscle and body simulations for the film industry, trying to respond well to the full range of motions and deformations of the human body is definitely a non-trivial engineering challenge. In men's fashion, for example, Italian cut pants look great when you wear them but the front pockets are guaranteed to lose any coins you're wearing when you sit down because the engineering tradeoff swung too far one way and didn't address enough issues the other way (the issue has to do with the way the inner pocket structure is anchored to the seam of the pants, so it never gets out of place but also is forced to tilt the wrong direction dumping its contents if you sit on an overstuffed couch). The spacesuit designers had to get every part of the body right (though as anyone who has watched The Right Stuff[1] knows the original suits weren't actually designed to manage a couple key body functions, which became an issue when launches got delayed).
As a physics dropout (hey, '90s tech boom) who works with theatrical costumers on a regular basis as the "engineering" guy (who sews, rhinestones, and hot-glues with the rest of them) there's absolutely a cross-over of material science, geometry, structure, and other engineering practices with fashion/costuming. However, this is almost never formalized around a grounding in physics. Instead, it is ingrained and intuitive in the practitioner. Ask most fashion designers about manifolds, gradients, and curvatures, and you'll get blank stares.
Furthermore, if you're going to write up something to pitch fashion to the sciency/nerdy, how about not asserting that euclidean geometry is purely planar... Gaussian curvature and it's applications to fabric? Sure. Perspective transforms per pattern projection and apparent parallelism/colinearity? Okay. (Neither of these in the article...)
Euclidean geometry is gone when you bend fabric? Oh man. That's where I face-palmed.
If you're going to pitch to nerds, be rock solid on the nerdy stuff, because the larger point, that fabric and fashion are engineering and design practices as much as laptops, cars, and bridges, is arguably true.
I had high hopes for this one, but it comes off as a poorly-crafted attempt to pitch a personal interest as scientifically dismissed because it's feminine (rather than artistically practiced), from a woman who, sadly, doesn't seem well-versed in the technical aspects of the discipline, unselling her point.
Notes:
1) Men design fashion, and have for a long time.
2) It's okay to like something aesthetic and over-the-top without trying to jam it through a science-nerd hole.
Do you just mean that everything is still Euclidean in the complete 3D space of real life? This is true but does not make the 2D-curved-spaced analysis any less fundamental. All curved manifolds (including curved spacetimes) of dimension d can be embedded in a Euclidean space of dimension 2d such that the metric on the former is just the one you get by projecting down from the latter. Insofar as all the quantities you are working with are confined to the curved d-dimensional manifold, it's as fundamental a notion of curved space as ever exists.
1) Euclidean geometry is a plane (though, on re-reading, she said that a plane is pure Euclidean geometry). So, to be fair to the author, that may well be me over-reading her statement (could be "within", rather than "equal to").
2) That Burberry's dress on Ruby Rose for the 2017 Met Gala somehow meaningfully steps outside of Euclidean geometry for it's execution. It's a layered skirt composed of rectangular-ish cuts. Any apparent colinearity stems from the center-start of each panel and vertical alignment (aided, visually, by the aspect ratio of the panels).
Maybe the ruching around the body? I don't see it, and to hang an argument for involvement of a field on the particulars of that dress is pretty baffling.
The best I could suggest is that any dress could be called non-euclidean when cut from planar fabric due to the (general) requirement that a dress be at least a genus one manifold (or a public indecency ticket). I don't see anything in Ruby Rose's dress that implies any meaningful departure from or special knowledge of euclidean to non-euclidean considerations.
Except maybe the price tag... That probably bends more than just space...
http://www.neatorama.com/2013/12/31/A-Stress-Analysis-of-a-S...
Note: I teach basic maths in vocational colleges in UK.
It adds something, sure, but it's way over-hyped.
UI design is just wrapping paper for programs.
Presentation is just wrapping paper for food.
Interior design is just wrapping paper for homes and offices.
Typesetting is just wrapping paper for words.
It's thinking like this that gets us poor experiences in all these fields. Aesthetics matter, but treating these things jut as aesthetics misses both their beauty and their engineering.
And hey, art is cool. Even when it is just art. Paint is just paint, but it can make beautiful things when handled well. It may not be your thing, but no need to hate on it.
And that includes wrapping paper!
Again, you may not value these things, but the vast majority of the world does. One of the things that I struggle with from fresh graduates out of technical schools is that they don't value it and it hurts them professionally because their peers and management do. That might not be right, but until one becomes the boss, it's important to understand and effectively utilize this language. I'd feel pretty stupid if I didn't reach my professional goals because I didn't value how I dress sufficiently enough. And, yes, there's a limit to how much it matters just as there are limits to all language. Though, that doesn't minimize its impact.
With respect to the article, the physics and modeling of fabric is incredibly difficult. Part of the reason that clothing manufacturing hasn't been as automated as other fields is a testament to how difficult it is. Personally, I find such models fascinating.
As a thought-experiment, replace fashion by typography. Imagine you wake up, and you have to think about typography, then you get to work, people talk about typography, you come home and turn on the TV, people talk about typography, then at some point, it becomes too much. Personally, I'll probably still appreciate the craft, but I consider it a "solved" problem for myself, something that others deal with, and I direct my attention elsewhere.
As for the communication aspect of clothing, that's actually something I have resentment against. You change clothes only once or perhaps twice a day, so the communication is extremely low-bandwidth to start with. And an even bigger problem: it reduces the person to one thing. A person wearing a pilot suit becomes a pilot (only), a person wearing a labcoat becomes a doctor (only). But obviously people are more than their profession.
And clothing can also be a way to intimidate or to mask intentions (think of the used car salesman wearing a suit, not because he likes it, but because he wants to sell that car).
(On the other hand, we do see an awful lot of criticism of UI design and that includes complaints about typography :-)