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95-560: Lister Mills (otherwise known as Manningham Mills) was the largest silk factory in the world. It is located in the Manningham district of Bradford , West Yorkshire , England and was built by Samuel Cunliffe Lister to replace the original Manningham Mills which had been destroyed by fire in 1871. The mill is a Grade II* listed building , built in the Italianate style of Victorian architecture . On completion in 1873, Lister's

190-401: A bave . Bave diameters for tussah silk can reach 65 μm. See cited reference for cross-sectional SEM photographs. Silk has a smooth, soft texture that is not slippery, unlike many synthetic fibers . Silk is one of the strongest natural fibers, but it loses up to 20% of its strength when wet. It has a good moisture regain of 11%. Its elasticity is moderate to poor: if elongated even

285-1351: A constant η equal to 1 inverse radian (1 rad ) in a fashion similar to the introduction of the constant ε 0 . With this change the formula for the angle subtended at the center of a circle, s = rθ , is modified to become s = ηrθ , and the Taylor series for the sine of an angle θ becomes: Sin ⁡ θ = sin ⁡   x = x − x 3 3 ! + x 5 5 ! − x 7 7 ! + ⋯ = η θ − ( η θ ) 3 3 ! + ( η θ ) 5 5 ! − ( η θ ) 7 7 ! + ⋯ , {\displaystyle \operatorname {Sin} \theta =\sin \ x=x-{\frac {x^{3}}{3!}}+{\frac {x^{5}}{5!}}-{\frac {x^{7}}{7!}}+\cdots =\eta \theta -{\frac {(\eta \theta )^{3}}{3!}}+{\frac {(\eta \theta )^{5}}{5!}}-{\frac {(\eta \theta )^{7}}{7!}}+\cdots ,} where x = η θ = θ / rad {\displaystyle x=\eta \theta =\theta /{\text{rad}}}

380-451: A full turn are not equivalent. To measure an angle θ , a circular arc centered at the vertex of the angle is drawn, e.g., with a pair of compasses . The ratio of the length s of the arc by the radius r of the circle is the number of radians in the angle: θ = s r r a d . {\displaystyle \theta ={\frac {s}{r}}\,\mathrm {rad} .} Conventionally, in mathematics and

475-424: A large satin waistcoat with flaps, were got up, of which the silk was perfect, but the lining entirely gone ... from the thread giving way ... No articles of dress of woollen cloth have yet been found.' Silk is a poor conductor of electricity and thus susceptible to static cling . Silk has a high emissivity for infrared light, making it feel cool to the touch. Unwashed silk chiffon may shrink up to 8% due to

570-738: A long history of a formative textile industry in ancient China, this find of silk textiles employing "complicated techniques" of weaving and dyeing provides direct evidence for silks dating before the Mawangdui -discovery and other silks dating to the Han dynasty (202 BC – 220 AD). Silk is described in a chapter of the Fan Shengzhi shu from the Western Han (202 BC – 9 AD). There is a surviving calendar for silk production in an Eastern Han (25–220 AD) document. The two other known works on silk from

665-459: A major difficulty. In 2000, property regeneration company Urban Splash bought Lister Mills from the administrators, Ernst and Young , with plans to renovate the silk warehouse. Costs for the project were estimated to be £100 million. Renovation work began in 2003, and construction formally began in September 2004. 131 new homes and 3 ground floor commercial units were subsequently completed in

760-440: A number of small firms and cooperatives emerged. Among the most prominent of these was the cooperative utopian Northampton Association for Education and Industry, of which Sojourner Truth was a member. Following the destructive Mill River Flood of 1874 , one manufacturer, William Skinner , relocated his mill from Williamsburg to the then-new city of Holyoke . Over the next 50 years he and his sons would maintain relations between

855-539: A pair of (often parallel) lines and is associated with exterior angles , interior angles , alternate exterior angles , alternate interior angles , corresponding angles , and consecutive interior angles . The angle addition postulate states that if B is in the interior of angle AOC, then m ∠ A O C = m ∠ A O B + m ∠ B O C {\displaystyle m\angle \mathrm {AOC} =m\angle \mathrm {AOB} +m\angle \mathrm {BOC} } I.e.,

950-419: A point on a circle or describing the orientation of an object in two dimensions relative to a reference orientation, angles that differ by an exact multiple of a full turn are effectively equivalent. In other contexts, such as identifying a point on a spiral curve or describing an object's cumulative rotation in two dimensions relative to a reference orientation, angles that differ by a non-zero multiple of

1045-435: A relationship. In mathematical expressions , it is common to use Greek letters ( α , β , γ , θ , φ , . . . ) as variables denoting the size of some angle (the symbol π is typically not used for this purpose to avoid confusion with the constant denoted by that symbol ). Lower case Roman letters ( a ,  b ,  c , . . . ) are also used. In contexts where this

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1140-462: A relaxation of the fiber macrostructure, so silk should either be washed prior to garment construction, or dry cleaned . Dry cleaning may still shrink the chiffon up to 4%. Occasionally, this shrinkage can be reversed by a gentle steaming with a press cloth. There is almost no gradual shrinkage nor shrinkage due to molecular-level deformation. Angle The magnitude of an angle is called an angular measure or simply "angle". Angle of rotation

1235-417: A small amount, it remains stretched. It can be weakened if exposed to too much sunlight. It may also be attacked by insects, especially if left dirty. One example of the durable nature of silk over other fabrics is demonstrated by the recovery in 1840 of silk garments from a wreck of 1782 : 'The most durable article found has been silk; for besides pieces of cloaks and lace, a pair of black satin breeches, and

1330-502: A triangle is supplementary to the third because the sum of the internal angles of a triangle is a straight angle. The difference between an angle and a complete angle is termed the explement of the angle or conjugate of an angle. The size of a geometric angle is usually characterized by the magnitude of the smallest rotation that maps one of the rays into the other. Angles of the same size are said to be equal congruent or equal in measure . In some contexts, such as identifying

1425-421: A two-dimensional Cartesian coordinate system , an angle is typically defined by its two sides, with its vertex at the origin. The initial side is on the positive x-axis , while the other side or terminal side is defined by the measure from the initial side in radians, degrees, or turns, with positive angles representing rotations toward the positive y-axis and negative angles representing rotations toward

1520-416: A white-colored silk thread with no mineral on the surface. The pupae are killed by either dipping them in boiling water before the adult moths emerge or by piercing them with a needle. These factors all contribute to the ability of the whole cocoon to be unravelled as one continuous thread, permitting a much stronger cloth to be woven from the silk. Wild silks also tend to be more difficult to dye than silk from

1615-427: Is ⁠ 1 / 256 ⁠ of a turn. Plane angle may be defined as θ = s / r , where θ is the magnitude in radians of the subtended angle, s is circular arc length, and r is radius. One radian corresponds to the angle for which s = r , hence 1 radian = 1 m/m = 1. However, rad is only to be used to express angles, not to express ratios of lengths in general. A similar calculation using

1710-493: Is "pedagogically unsatisfying". In 1993 the American Association of Physics Teachers Metric Committee specified that the radian should explicitly appear in quantities only when different numerical values would be obtained when other angle measures were used, such as in the quantities of angle measure (rad), angular speed (rad/s), angular acceleration (rad/s ), and torsional stiffness (N⋅m/rad), and not in

1805-519: Is a measure conventionally defined as the ratio of a circular arc length to its radius , and may be a negative number . In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation , the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation. The word angle comes from the Latin word angulus , meaning "corner". Cognate words include

1900-471: Is called the vertical angle theorem . Eudemus of Rhodes attributed the proof to Thales of Miletus . The proposition showed that since both of a pair of vertical angles are supplementary to both of the adjacent angles, the vertical angles are equal in measure. According to a historical note, when Thales visited Egypt, he observed that whenever the Egyptians drew two intersecting lines, they would measure

1995-496: Is clear that the complete form is meant. Current SI can be considered relative to this framework as a natural unit system where the equation η = 1 is assumed to hold, or similarly, 1 rad = 1 . This radian convention allows the omission of η in mathematical formulas. It is frequently helpful to impose a convention that allows positive and negative angular values to represent orientations and/or rotations in opposite directions or "sense" relative to some reference. In

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2090-509: Is composed mostly of beta-sheets , due to a 59-mer amino acid repeat sequence with some variations. The flat surfaces of the fibrils reflect light at many angles, giving silk a natural sheen. The cross-section from other silkworms can vary in shape and diameter: crescent-like for Anaphe and elongated wedge for tussah . Silkworm fibers are naturally extruded from two silkworm glands as a pair of primary filaments (brin), which are stuck together, with sericin proteins that act like glue , to form

2185-547: Is concentrated in the Coimbatore , Erode , Bhagalpuri , Tiruppur , Salem , and Dharmapuri districts. Hyderabad , Andhra Pradesh , and Gobichettipalayam , Tamil Nadu , were the first locations to have automated silk reeling units in India. In the northeastern state of Assam , three different types of indigenous variety of silk are produced, collectively called Assam silk : Muga silk , Eri silk and Pat silk . Muga,

2280-401: Is due to the triangular prism -like structure of the silk fibre, which allows silk cloth to refract incoming light at different angles , thus producing different colors. Silk is produced by several insects; but, generally, only the silk of moth caterpillars has been used for textile manufacturing. There has been some research into other types of silk, which differ at the molecular level. Silk

2375-509: Is forbidden. Modern attire has raised a number of issues, including, for instance, the permissibility of wearing silk neckties , which are masculine articles of clothing. In the Odyssey , 19.233, when Odysseus, while pretending to be someone else, is questioned by Penelope about her husband's clothing, he says that he wore a shirt "gleaming like the skin of a dried onion" (varies with translations, literal translation here) which could refer to

2470-511: Is independent of the size of the circle: if the length of the radius is changed, then the arc length changes in the same proportion, so the ratio s / r is unaltered. Throughout history, angles have been measured in various units . These are known as angular units , with the most contemporary units being the degree ( ° ), the radian (rad), and the gradian (grad), though many others have been used throughout history . Most units of angular measurement are defined such that one turn (i.e.,

2565-649: Is mainly produced by the larvae of insects undergoing complete metamorphosis , but some insects, such as webspinners and raspy crickets , produce silk throughout their lives. Silk production also occurs in hymenoptera ( bees , wasps , and ants ), silverfish , caddisflies , mayflies , thrips , leafhoppers , beetles , lacewings , fleas , flies , and midges . Other types of arthropods produce silk, most notably various arachnids , such as spiders . The word silk comes from Old English : sioloc , from Latin : sericum and Ancient Greek : σηρικός , romanized :  sērikós , "silken", ultimately from

2660-404: Is no risk of confusion, the angle may sometimes be referred to by a single vertex alone (in this case, "angle A"). In other ways, an angle denoted as, say, ∠BAC might refer to any of four angles: the clockwise angle from B to C about A, the anticlockwise angle from B to C about A, the clockwise angle from C to B about A, or the anticlockwise angle from C to B about A, where the direction in which

2755-484: Is not confusing, an angle may be denoted by the upper case Roman letter denoting its vertex. See the figures in this article for examples. The three defining points may also identify angles in geometric figures. For example, the angle with vertex A formed by the rays AB and AC (that is, the half-lines from point A through points B and C) is denoted ∠BAC or B A C ^ {\displaystyle {\widehat {\rm {BAC}}}} . Where there

2850-584: Is now part of Malaysia , a second generation of silkworm was being imported as early as 1764 for the country's silk textile industry, especially songket . However, since the 1980s, Malaysia is no longer engaged in sericulture but does plant mulberry trees. In Vietnamese legend, silk appeared in the first millennium AD and is still being woven today. The process of silk production is known as sericulture . The entire production process of silk can be divided into several steps which are typically handled by different entities. Extracting raw silk starts by cultivating

2945-531: Is potentially large when compared with other natural fibers. A life-cycle assessment of Indian silk production shows that the production process has a large carbon and water footprint, mainly due to the fact that it is an animal-derived fiber and more inputs such as fertilizer and water are needed per unit of fiber produced. Silk fibers from the Bombyx mori silkworm have a triangular cross section with rounded corners, 5–10  μm wide. The fibroin-heavy chain

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3040-415: Is soaked in extremely cold water and bleached before dyeing to remove the natural yellow coloring of Thai silk yarn. To do this, skeins of silk thread are immersed in large tubs of hydrogen peroxide . Once washed and dried, the silk is woven on a traditional hand-operated loom. The Rajshahi Division of northern Bangladesh is the hub of the country's silk industry. There are three types of silk produced in

3135-403: Is supplementary to both angles C and D , either of these angle measures may be used to determine the measure of Angle B . Using the measure of either angle C or angle D , we find the measure of angle B to be 180° − (180° − x ) = 180° − 180° + x = x . Therefore, both angle A and angle B have measures equal to x and are equal in measure. A transversal is a line that intersects

3230-462: Is the angle in radians. The capitalized function Sin is the "complete" function that takes an argument with a dimension of angle and is independent of the units expressed, while sin is the traditional function on pure numbers which assumes its argument is a dimensionless number in radians. The capitalised symbol Sin {\displaystyle \operatorname {Sin} } can be denoted sin {\displaystyle \sin } if it

3325-594: Is the presence of the silk protein fibroin in soil samples from two tombs at the neolithic site Jiahu in Henan , which date back about 8,500 years. The earliest surviving example of silk fabric dates from about 3630 BC, and was used as the wrapping for the body of a child at a Yangshao culture site in Qingtaicun near Xingyang , Henan. Legend gives credit for developing silk to a Chinese empress, Leizu (Hsi-Ling-Shih, Lei-Tzu). Silks were originally reserved for

3420-479: Is the second largest producer of silk in the world after China. About 97% of the raw mulberry silk comes from six Indian states, namely, Andhra Pradesh , Karnataka , Jammu and Kashmir , Tamil Nadu , Bihar , and West Bengal . North Bangalore, the upcoming site of a $ 20 million "Silk City" Ramanagara and Mysore , contribute to a majority of silk production in Karnataka. In Tamil Nadu , mulberry cultivation

3515-404: Is typically determined by a normal vector passing through the angle's vertex and perpendicular to the plane in which the rays of the angle lie. In navigation , bearings or azimuth are measured relative to north. By convention, viewed from above, bearing angles are positive clockwise, so a bearing of 45° corresponds to a north-east orientation. Negative bearings are not used in navigation, so

3610-634: The Great Palace complex in Constantinople, and the cloth produced was used in imperial robes or in diplomacy, as gifts to foreign dignitaries. The remainder was sold at very high prices. Italy was the most important producer of silk during the Medieval age. The first center to introduce silk production to Italy was the city of Catanzaro during the 11th century in the region of Calabria . The silk of Catanzaro supplied almost all of Europe and

3705-610: The Greek ἀγκύλος ([ankylοs] Error: {{Lang}}: Non-latn text/Latn script subtag mismatch ( help ) ) meaning "crooked, curved" and the English word " ankle ". Both are connected with the Proto-Indo-European root *ank- , meaning "to bend" or "bow". Euclid defines a plane angle as the inclination to each other, in a plane, of two lines that meet each other and do not lie straight with respect to each other. According to

3800-632: The President Ford White House . During the Second World War Lister's produced 1,330 miles (2,140 km) of real parachute silk, 284 miles (457 km) of flame-proof wool, 50 miles (80 km) of khaki battledress and 4,430 miles (7,130 km) of parachute cord. A strike in 1890–91 at the mill was important in the establishment of the Independent Labour Party which later helped found

3895-681: The SI , the radian is treated as being equal to the dimensionless unit 1, thus being normally omitted. The angle expressed by another angular unit may then be obtained by multiplying the angle by a suitable conversion constant of the form ⁠ k / 2 π ⁠ , where k is the measure of a complete turn expressed in the chosen unit (for example, k = 360° for degrees or 400 grad for gradians ): θ = k 2 π ⋅ s r . {\displaystyle \theta ={\frac {k}{2\pi }}\cdot {\frac {s}{r}}.} The value of θ thus defined

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3990-730: The Torah , a scarlet cloth item called in Hebrew "sheni tola'at" שני תולעת – literally "crimson of the worm" – is described as being used in purification ceremonies, such as those following a leprosy outbreak (Leviticus 14), alongside cedar wood and hyssop ( za'atar ). Eminent scholar and leading medieval translator of Jewish sources and books of the Bible into Arabic , Rabbi Saadia Gaon , translates this phrase explicitly as "crimson silk" – חריר קרמז حرير قرمز. In Islamic teachings, Muslim men are forbidden to wear silk. Many religious jurists believe

4085-521: The Yayoi period . The silk industry was dominant from the 1930s to 1950s, but is less common now. Silk from East Asia had declined in importance after silkworms were smuggled from China to the Byzantine Empire. However, in 1845, an epidemic of flacherie among European silkworms devastated the silk industry there. This led to a demand for silk from China and Japan , where as late as

4180-484: The area of a circle , π r . The other option is to introduce a dimensional constant. According to Quincey this approach is "logically rigorous" compared to SI, but requires "the modification of many familiar mathematical and physical equations". A dimensional constant for angle is "rather strange" and the difficulty of modifying equations to add the dimensional constant is likely to preclude widespread use. In particular, Quincey identifies Torrens' proposal to introduce

4275-655: The complement of the angle. If angles A and B are complementary, the following relationships hold: sin 2 ⁡ A + sin 2 ⁡ B = 1 cos 2 ⁡ A + cos 2 ⁡ B = 1 tan ⁡ A = cot ⁡ B sec ⁡ A = csc ⁡ B {\displaystyle {\begin{aligned}&\sin ^{2}A+\sin ^{2}B=1&&\cos ^{2}A+\cos ^{2}B=1\\[3pt]&\tan A=\cot B&&\sec A=\csc B\end{aligned}}} (The tangent of an angle equals

4370-446: The cotangent of its complement, and its secant equals the cosecant of its complement.) The prefix " co- " in the names of some trigonometric ratios refers to the word "complementary". If the two supplementary angles are adjacent (i.e., have a common vertex and share just one side), their non-shared sides form a straight line . Such angles are called a linear pair of angles . However, supplementary angles do not have to be on

4465-476: The 12th century. Other Italian cities involved in silk production were Genoa , Venice , and Florence . The Piedmont area of Northern Italy became a major silk producing area when water-powered silk throwing machines were developed. The Silk Exchange in Valencia from the 15th century—where previously in 1348 also perxal ( percale ) was traded as some kind of silk—illustrates the power and wealth of one of

4560-595: The 17th century. James I attempted to establish silk production in England, purchasing and planting 100,000 mulberry trees, some on land adjacent to Hampton Court Palace , but they were of a species unsuited to the silk worms, and the attempt failed. In 1732 John Guardivaglio set up a silk throwing enterprise at Logwood mill in Stockport ; in 1744, Burton Mill was erected in Macclesfield ; and in 1753 Old Mill

4655-646: The American silk industry and its counterparts in Japan, and expanded their business to the point that by 1911, the Skinner Mill complex contained the largest silk mill under one roof in the world, and the brand Skinner Fabrics had become the largest manufacturer of silk satins internationally. Other efforts later in the 19th century would also bring the new silk industry to Paterson, New Jersey , with several firms hiring European-born textile workers and granting it

4750-591: The Chinese monopoly . Nonetheless, sericulture reached Korea with technological aid from China around 200 BC, the ancient Kingdom of Khotan by AD 50, and India by AD 140. In the ancient era, silk from China was the most lucrative and sought-after luxury item traded across the Eurasian continent, and many civilizations, such as the ancient Persians, benefited economically from trade. Archaeological evidence indicates that sericulture has been practiced since

4845-567: The Chinese word "sī" and other Asian sources—compare Mandarin sī "silk", Manchurian sirghe , Mongolian sirkek . The production of silk originated in China in the Neolithic period, although it would eventually reach other places of the world ( Yangshao culture, 4th millennium BC). Silk production remained confined to China until the Silk Road opened at some point during

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4940-649: The Han period are lost. The first evidence of the long distance silk trade is the finding of silk in the hair of an Egyptian mummy of the 21st dynasty, c.1070 BC. The silk trade reached as far as the Indian subcontinent , the Middle East , Europe , and North Africa . This trade was so extensive that the major set of trade routes between Europe and Asia came to be known as the Silk Road . The emperors of China strove to keep knowledge of sericulture secret to maintain

5035-634: The Japanese silk industry and its position as the lead silk exporter of the world. Today, China exports the largest volume of raw silk in the world. Silk has a long history in India. It is known as Resham in eastern and north India, and Pattu in southern parts of India . Recent archaeological discoveries in Harappa and Chanhu-daro suggest that sericulture , employing wild silk threads from native silkworm species, existed in South Asia during

5130-530: The Middle East by Peter Gaddum . Wild silk taken from the nests of native caterpillars was used by the Aztecs to make containers and as paper. Silkworms were introduced to Oaxaca from Spain in the 1530s and the region profited from silk production until the early 17th century, when the king of Spain banned export to protect Spain's silk industry. Silk production for local consumption has continued until

5225-460: The Neoplatonic metaphysician Proclus , an angle must be either a quality, a quantity, or a relationship. The first concept, angle as quality, was used by Eudemus of Rhodes , who regarded an angle as a deviation from a straight line ; the second, angle as quantity, by Carpus of Antioch , who regarded it as the interval or space between the intersecting lines; Euclid adopted the third: angle as

5320-433: The angle is measured determines its sign (see § Signed angles ). However, in many geometrical situations, it is evident from the context that the positive angle less than or equal to 180 degrees is meant, and in these cases, no ambiguity arises. Otherwise, to avoid ambiguity, specific conventions may be adopted so that, for instance, ∠BAC always refers to the anticlockwise (positive) angle from B to C about A and ∠CAB

5415-567: The angle subtended by the circumference of a circle at its centre) is equal to n units, for some whole number n . Two exceptions are the radian (and its decimal submultiples) and the diameter part. In the International System of Quantities , an angle is defined as a dimensionless quantity, and in particular, the radian unit is dimensionless. This convention impacts how angles are treated in dimensional analysis . The following table lists some units used to represent angles. It

5510-447: The anticlockwise (positive) angle from C to B about A. There is some common terminology for angles, whose measure is always non-negative (see § Signed angles ): The names, intervals, and measuring units are shown in the table below: When two straight lines intersect at a point, four angles are formed. Pairwise, these angles are named according to their location relative to each other. The equality of vertically opposite angles

5605-497: The area of a circular sector θ = 2 A / r gives 1 radian as 1 m /m = 1. The key fact is that the radian is a dimensionless unit equal to 1 . In SI 2019, the SI radian is defined accordingly as 1 rad = 1 . It is a long-established practice in mathematics and across all areas of science to make use of rad = 1 . Giacomo Prando writes "the current state of affairs leads inevitably to ghostly appearances and disappearances of

5700-642: The arrival of electric power in 1934, the mill was driven by steam engines. Every week the boilers consumed 1,000 tons of coal brought in on company rail wagons from the company collieries near Pontefract . Water was also vital in the process and the company had its own supply network including a large covered reservoir on-site (now in 2006 that area is a piazza and underground car park). At its height, Lister's employed 11,000 men, women and children – manufacturing high-quality textiles such as velvet and silk. It supplied 1,000 yards (910 m) of velvet for King George V 's coronation and in 1976 new velvet curtains for

5795-486: The cultivated silkworm. A technique known as demineralizing allows the mineral layer around the cocoon of wild silk moths to be removed, leaving only variability in color as a barrier to creating a commercial silk industry based on wild silks in the parts of the world where wild silk moths thrive, such as in Africa and South America. Silk use in fabric was first developed in ancient China. The earliest evidence for silk

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5890-488: The design of David Morley Architects. The new homes went on sale in early 2007. Silk Silk is a natural protein fiber , some forms of which can be woven into textiles . The protein fiber of silk is composed mainly of fibroin and is produced by certain insect larvae to form cocoons . The best-known silk is obtained from the cocoons of the larvae of the mulberry silkworm Bombyx mori reared in captivity ( sericulture ). The shimmering appearance of silk

5985-511: The domesticated varieties in colour and texture and are therefore less uniform; second, cocoons gathered in the wild have usually had the pupa emerge from them before being discovered so the silk thread that makes up the cocoon has been torn into shorter lengths; and third, many wild cocoons are covered in a mineral layer that prevents attempts to reel from them long strands of silk. Thus, the only way to obtain silk suitable for spinning into textiles in areas where commercial silks are not cultivated

6080-740: The early center of the silk industry in America, when the Cheney Brothers became the first in the United States to properly raise silkworms on an industrial scale; today the Cheney Brothers Historic District showcases their former mills. With the mulberry tree craze of that decade, other smaller producers began raising silkworms. This economy particularly gained traction in the vicinity of Northampton, Massachusetts and its neighboring Williamsburg , where

6175-411: The emperors of China for their own use and gifts to others, but spread gradually through Chinese culture and trade both geographically and socially, and then to many regions of Asia . Because of its texture and lustre, silk rapidly became a popular luxury fabric in the many areas accessible to Chinese merchants. Silk was in great demand, and became a staple of pre- industrial international trade . Silk

6270-450: The final position is the same, a physical rotation (movement) of −45° is not the same as a rotation of 315° (for example, the rotation of a person holding a broom resting on a dusty floor would leave visually different traces of swept regions on the floor). In three-dimensional geometry, "clockwise" and "anticlockwise" have no absolute meaning, so the direction of positive and negative angles must be defined in terms of an orientation , which

6365-500: The golden silk, and Eri are produced by silkworms that are native only to Assam. They have been reared since ancient times similar to other East and South-East Asian countries. Silk is produced year-round in Thailand by two types of silkworms, the cultured Bombycidae and wild Saturniidae. Most production is after the rice harvest in the southern and northeastern parts of the country. Women traditionally weave silk on hand looms and pass

6460-571: The great Mediterranean mercantile cities. Silk was produced in and exported from the province of Granada , Spain, especially the Alpujarras region, until the Moriscos , whose industry it was, were expelled from Granada in 1571. Since the 15th century, silk production in France has been centered around the city of Lyon where many mechanic tools for mass production were first introduced in

6555-428: The large buildings. Construction was finished in 2006, but evidently left a majority of the site unmaintained. The second phase was the regeneration of the largest building on the site, the velvet mill, by replacing the existing roof of the building with a glass and steel structure, housing two storey apartments and creating additional ground floor commercial spaces, whilst preserving original architectural features under

6650-557: The largest silk exporter in the world. This increase in exports was mostly due to the economic reforms during the Meiji period and the decline of the Qing dynasty in China, which led to rapid industrialization of Japan whilst the Chinese industries stagnated. During World War II , embargoes against Japan had led to adoption of synthetic materials such as nylon , which led to the decline of

6745-460: The latter part of the 1st millennium BC, though China maintained its virtual monopoly over silk production for another thousand years. Several kinds of wild silk, produced by caterpillars other than the mulberry silkworm, have been known and spun in China , South Asia , and Europe since ancient times. However, the scale of production was always far smaller than for cultivated silks. There are several reasons for this: first, they differ from

6840-467: The lustrous quality of silk fabric. Aristotle wrote of Coa vestis , a wild silk textile from Kos . Sea silk from certain large sea shells was also valued. The Roman Empire knew of and traded in silk, and Chinese silk was the most highly priced luxury good imported by them. During the reign of emperor Tiberius , sumptuary laws were passed that forbade men from wearing silk garments, but these proved ineffectual. The Historia Augusta mentions that

6935-458: The measure of the angle AOC is the sum of the measure of angle AOB and the measure of angle BOC. Three special angle pairs involve the summation of angles: The adjective complementary is from the Latin complementum , associated with the verb complere , "to fill up". An acute angle is "filled up" by its complement to form a right angle. The difference between an angle and a right angle is termed

7030-410: The modern-day Labour Party . The Listers' business decreased considerably during the 1980s. Stiff foreign competition and changing textile trends such as increased use of artificial fibres were the reasons. In 1999, the mills were closed. Being a prominent structure, the mills attracted a great deal of attention and several regeneration proposals came and went. The sheer size of the buildings being

7125-467: The negative y -axis. When Cartesian coordinates are represented by standard position , defined by the x -axis rightward and the y -axis upward, positive rotations are anticlockwise , and negative cycles are clockwise . In many contexts, an angle of − θ is effectively equivalent to an angle of "one full turn minus θ ". For example, an orientation represented as −45° is effectively equal to an orientation defined as 360° − 45° or 315°. Although

7220-488: The nickname "Silk City" as another major center of production in the United States. World War II interrupted the silk trade from Asia, and silk prices increased dramatically. U.S. industry began to look for substitutes, which led to the use of synthetics such as nylon . Synthetic silks have also been made from lyocell , a type of cellulose fiber, and are often difficult to distinguish from real silk (see spider silk for more on synthetic silks). In Terengganu , which

7315-422: The nineteenth and early twentieth centuries, Japanese exports competed directly with Chinese in the international market in such low value-added, labor-intensive products as raw silk. Between 1850 and 1930, raw silk ranked as the leading export for both countries, accounting for 20%–40% of Japan's total exports and 20%–30% of China's. Between the 1890s and the 1930s, Japanese silk exports quadrupled, making Japan

7410-586: The present day, sometimes spinning wild silk. King James I introduced silk-growing to the British colonies in America around 1619, ostensibly to discourage tobacco planting. The Shakers in Kentucky adopted the practice. The history of industrial silk in the United States is largely tied to several smaller urban centers in the Northeast region. Beginning in the 1830s, Manchester, Connecticut emerged as

7505-437: The quantities of torque (N⋅m) and angular momentum (kg⋅m /s). At least a dozen scientists between 1936 and 2022 have made proposals to treat the radian as a base unit of measurement for a base quantity (and dimension) of "plane angle". Quincey's review of proposals outlines two classes of proposal. The first option changes the unit of a radius to meters per radian, but this is incompatible with dimensional analysis for

7600-404: The radian in the dimensional analysis of physical equations". For example, an object hanging by a string from a pulley will rise or drop by y = rθ centimetres, where r is the magnitude of the radius of the pulley in centimetres and θ is the magnitude of the angle through which the pulley turns in radians. When multiplying r by θ , the unit radian does not appear in the product, nor does

7695-399: The reasoning behind the prohibition lies in avoiding clothing for men that can be considered feminine or extravagant. There are disputes regarding the amount of silk a fabric can consist of (e.g., whether a small decorative silk piece on a cotton caftan is permissible or not) for it to be lawful for men to wear, but the dominant opinion of most Muslim scholars is that the wearing of silk by men

7790-466: The region: mulberry, endi, and tassar. Bengali silk was a major item of international trade for centuries. It was known as Ganges silk in medieval Europe. Bengal was the leading exporter of silk between the 16th and 19th centuries. The 7th century CE murals of Afrasiyab in Samarkand , Sogdiana , show a Chinese Embassy carrying silk and a string of silkworm cocoons to the local Sogdian ruler. In

7885-582: The same line and can be separated in space. For example, adjacent angles of a parallelogram are supplementary, and opposite angles of a cyclic quadrilateral (one whose vertices all fall on a single circle) are supplementary. If a point P is exterior to a circle with center O, and if the tangent lines from P touch the circle at points T and Q, then ∠TPQ and ∠TOQ are supplementary. The sines of supplementary angles are equal. Their cosines and tangents (unless undefined) are equal in magnitude but have opposite signs. In Euclidean geometry, any sum of two angles in

7980-748: The silkworms on mulberry leaves. Once the worms start pupating in their cocoons, these are dissolved in boiling water in order for individual long fibres to be extracted and fed into the spinning reel. To produce 1 kg of silk, 104 kg of mulberry leaves must be eaten by 3000 silkworms. It takes about 5000 silkworms to make a pure silk kimono . The major silk producers are China (54%) and India (14%). Other statistics: Production in Int $ 1000 have been calculated based on 1999–2001 international prices Source: Food And Agricultural Organization of United Nations: Economic And Social Department: The Statistical Division The environmental impact of silk production

8075-400: The skill on to their daughters, as weaving is considered to be a sign of maturity and eligibility for marriage. Thai silk textiles often use complicated patterns in various colours and styles. Most regions of Thailand have their own typical silks. A single thread filament is too thin to use on its own so women combine many threads to produce a thicker, usable fiber. They do this by hand-reeling

8170-569: The third-century emperor Elagabalus was the first Roman to wear garments of pure silk, whereas it had been customary to wear fabrics of silk/cotton or silk/linen blends. Despite the popularity of silk, the secret of silk-making only reached Europe around AD 550, via the Byzantine Empire . Contemporary accounts state that monks working for the emperor Justinian I smuggled silkworm eggs to Constantinople from China inside hollow canes. All top-quality looms and weavers were located inside

8265-435: The threads onto a wooden spindle to produce a uniform strand of raw silk. The process takes around 40 hours to produce a half kilogram of silk. Many local operations use a reeling machine for this task, but some silk threads are still hand-reeled. The difference is that hand-reeled threads produce three grades of silk: two fine grades that are ideal for lightweight fabrics, and a thick grade for heavier material. The silk fabric

8360-727: The time of the Indus Valley civilisation (now in Pakistan and India) dating between 2450 BC and 2000 BC. Shelagh Vainker, a silk expert at the Ashmolean Museum in Oxford, who sees evidence for silk production in China "significantly earlier" than 2500–2000 BC, suggests, "people of the Indus civilization either harvested silkworm cocoons or traded with people who did, and that they knew a considerable amount about silk." India

8455-489: The unit centimetre—because both factors are magnitudes (numbers). Similarly in the formula for the angular velocity of a rolling wheel, ω = v / r , radians appear in the units of ω but not on the right hand side. Anthony French calls this phenomenon "a perennial problem in the teaching of mechanics". Oberhofer says that the typical advice of ignoring radians during dimensional analysis and adding or removing radians in units according to convention and contextual knowledge

8550-518: The vertical angles to make sure that they were equal. Thales concluded that one could prove that all vertical angles are equal if one accepted some general notions such as: When two adjacent angles form a straight line, they are supplementary. Therefore, if we assume that the measure of angle A equals x , the measure of angle C would be 180° − x . Similarly, the measure of angle D would be 180° − x . Both angle C and angle D have measures equal to 180° − x and are congruent. Since angle B

8645-685: Was also used as a surface for writing, especially during the Warring States period (475–221 BCE). The fabric was light, it survived the damp climate of the Yangtze region, absorbed ink well, and provided a white background for the text. In July 2007, archaeologists discovered intricately woven and dyed silk textiles in a tomb in Jiangxi province, dated to the Eastern Zhou dynasty roughly 2,500 years ago. Although historians have suspected

8740-830: Was built in Congleton . These three towns remained the centre of the English silk throwing industry until silk throwing was replaced by silk waste spinning . British enterprise also established silk filature in Cyprus in 1928. In England in the mid-20th century, raw silk was produced at Lullingstone Castle in Kent. Silkworms were raised and reeled under the direction of Zoe Lady Hart Dyke , later moving to Ayot St Lawrence in Hertfordshire in 1956. During World War II , supplies of silk for UK parachute manufacture were secured from

8835-470: Was by tedious and labor-intensive carding . Some natural silk structures have been used without being unwound or spun. Spider webs were used as a wound dressing in ancient Greece and Rome, and as a base for painting from the 16th century. Caterpillar nests were pasted together to make a fabric in the Aztec Empire . Commercial silks originate from reared silkworm pupae, which are bred to produce

8930-619: Was sold in a large market fair in the port of Reggio Calabria , to Spanish, Venetian, Genovese, and Dutch merchants. Catanzaro became the lace capital of the world with a large silkworm breeding facility that produced all the laces and linens used in the Vatican. The city was world-famous for its fine fabrication of silks, velvets, damasks, and brocades. Another notable center was the Italian city-state of Lucca which largely financed itself through silk-production and silk-trading, beginning in

9025-499: Was the largest textile mill in the north of England. Floor space in the mill amounts to 27 acres (11 ha), and its imposing shape remains a dominant feature of the Bradford skyline. The chimney of the mill is 249 feet (76 m) high, and can be seen from most areas of Bradford. It cost about £10,000 to build, and its total weight has been estimated at 8,000 long tons (8,100 t). Samuel Lister called it "Lister's Pride". Until

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