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# The Geometry and Physics of Fashion Design

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## Edgar Rodriguez

on 22 May 2014

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#### Transcript of The Geometry and Physics of Fashion Design

SHAPES
NAIL POLISH
TESSELATIONS
FASHION
SYMMETRY
The Geometry and Physics of
Fashion Design

What Necessarily is...
Fashion Design
?
Fashion Design in this sense includes not only the creation of clothing however that of shoes, jewelry, nail polish, make-up (including special effect make-up), accessories, etc. as well.
Mirror Symmetry (String Theory)
The Mirror Symmetry Theory (or String Theory) states that mirror symmetry is a relationship between geometric objects called
Calabi–Yau manifolds
. It is very possible that two Calabi–Yau manifolds look different geometrically but are nevertheless equivalent if they are asserted as extra dimensions of string theory. In this case, they are called mirror manifolds.
Magnetic Nail Polish
Scale Factor
A scale factor is a certain number that scales (multiplies) some quantity, i.e., the equation y=Cx,
C
is the scale factor and coefficient for
x
. and may be called the constant of proportionality of
y
to
x
. In the measurements world, the scale factor of a certain item is sometimes referred as sensitivity. The ratio of any two corresponding lengths in two similar geometric figures is called as Scale Factor.
Specific Geometric Designs Used Frequently In Fashion Design
Plaid and Pinstripes
Specific Geometric Designs Used Frequently In Fashion Design
Tessellations
In fashion design, a somewhat simplified example of mirror symmetry is used with different patterns and prints designers use for a certain piece of clothing or accessory.
A common nail polish trend is magnetic nail polish- not literal nail polish that attains authentic magnetism however "shiny" polish that creates unique designs. A typical way to visualize a magnetic field, which explains how a magnet affects close-by magnetic materials , is to sprinkle elongated, thin pieces of iron in the magnet's aura. when one sprinkles the iron filings around a magnet, each of the filings becomes a small magnet, attracting and repelling the original magnet and the rest of the pieces of iron. The filings are pushed and pulled by the forces until they form into a pattern where they meet a balanced attractive and repulsive force . If one performs an alike process with magnets of various shapes, or use a lot of magnets, different patterns get created.

The designs in magnetic nail polish emerge in the same process. Nail polish makers mix iron powder in with the polish. The color of polish looks in unison when it is painted on, because at that point the iron is evenly dispersed within the polish. However, when a magnet is placed near the polish, the bits of iron are attracted and repelled by the magnet and each other, and create a pattern as the iron filings do in a lab. The pattern that emerges on the nail depends on the assortment of magnets and where you place them on the nail.
Fashion designers use scale factor when rationing materials to use when making certain items of dress. As well as to determine and scale a certain design to a sizing chart.
For example, a designer might want a pattern 'x' times smaller than the actual garmet's size.
The parallel lines in plaid and pinstripe designs have the same undefined slope which if it wasn't undefined they would not be parallel. For the other inversely position lines to be perpendicular the lines would need to have slopes that have negative reciprocals and have a product of -1. These lines meet, obviously making a quadrilateral square.
A tessellation is the tiling of a plane with the use of one or various geometric shapes or tiles, without any overlaps or gaps. In the study of geometry, tessellations can be generalized to higher dimensions.
Tessellations are used by fashion designers to create designs that repeat itself through-out the entire piece
Crystals + Cosmetics
An X-ray diffraction study of archaeological powders has given insight on the processes that ancient Egyptians used to make their well-known black eye make-up. According to Tamas Ungár of the University of Budapest in Hungary, the crystal structure of conserved lead-based cosmetics shows that crushing, sieving and even annealing were used to produce make-up four thousand years ago
The foremost ingredients of early cosmetics were lead sulphide and lead carbonate. Lead sulphide – or ‘galena’ – is gray and rather soft with a cubic crystal structure. Lead carbonate – or ‘cerussite’ – is white, harder than galena, and has an orthorhombic crystal structure.

Ungár and colleagues analyzed (39) ancient lead-based cosmetic powders from the Louvre museum in Paris. Lead compounds powerfully absorb X-rays, so the researchers used the dominant X-ray source at the European Synchrotron Radiation Facility in Grenoble, France, for their diffraction studies.

When X-rays go into a crystal, they are diffracted by the crystal lattice. The position of the peaks in the diffraction pattern reveals the spacing of the atoms in the crystal. Since the crystals in a powder are aimlessly oriented, X-ray diffraction leads to a wide range of diffraction angles. Ungár’s team were able to analyse these ‘peak profiles’ to reveal strain in the crystal lattices, which depends on the level of defects, such as dislocations.

By fitting their data to established models of crystallography, Ungár and co-workers also calculated the size of the crystallites, their size distribution and the density of dislocations in the samples.
Ungár and colleagues discovered that the ancient cosmetics were either dull or shiny, and that these were mixed in different proportions to vary the color of the make-up.

The dull powders had small crystals – between 130 and 240 nanometers across – with a high density of dislocations. Comparison with the artificial specimens suggested that these powders were ground for up to an hour. These fine powders were black with a matt texture.

The shiny powders contained crystals between 400 and 550 nanometers across, with a much lower dislocation density. This suggests that they were gently crushed then sieved to retain the larger crystallites, which contained a high reflectivity.

Ungár’s team also found some evidence that ancient Egyptians heated lead compounds to create different colored cosmetics. Lead sulphide oxidises upon heating, turning first yellow and then blue, but the samples were too small to confirm that this method was used.

Works Cited
"Crystals give clues to ancient cosmetics." <i></i>. physicsworld.com, 1 Jan. 2002. Web. 1 Jan. 2014. &lt;http://physicsworld.com/cws/article/news/2002/feb/21/crystals-give-clues-to-ancient-cosmetics&gt;.
"Magnets: Where Physics Meets High Fashion." <i></i>. Physics Central, 1 Jan. 2010. Web. 1 Jan. 2014. &lt;http://www.physicscentral.com/explore/action/nailpolish.cfm&gt;.
Taimina, Daina. "hyperbolic crochet: Geometry is in fashion!." hyperbolic crochet: Geometry is in fashion!. N.p., 1 Jan. 2011. Web. 22 May 2014. <http://hyperbolic-crochet.blogspot.com/2010/03/geometry-is-in-fashion.html>.
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