text:
Lee railway station

Lee station is a suburban station on Burnt Ash Hill in Lee in south-east London, England, between Hither Green and Mottingham on the Dartford loop (also known as the Sidcup line). It is 7 mi down the line from London Charing Cross. The station name appears as Lee (London) on tickets. It was opened by the South Eastern Railway in 1866.

It is operated by Southeastern.

History
The station opened on 1 September 1866. Goods facilities were meagre at first with a single siding on the down side just east of the station building, but the goods yard was gradually enlarged over the years as freight traffic increased in importance. In the early 1870s a second siding was installed dedicated to coal, and a coal shed was erected across the track. Later a further pair of sidings was inserted alongside the existing tracks. An SER-designed signal cabin was positioned some 150 yd east of the up side station structure. In 1955 the platforms were lengthened to accommodate ten carriage trains. In British Railways days the SR green totem signs displayed the station name as Lee for Burnt Ash. In 1963, Colfe's School moved to its current location adjacent to Lee station, the station remains a method of transport for a significant portion of students. The goods yard closed in 1968. In 1988 the clapboard up side ticket office was demolished and replaced by a new ticket office. In 1992 the platforms were lengthened to accommodate twelve carriage trains.

Location
Lee Station is in Burnt Ash Road, Lee, in the London Borough of Lewisham.

Connections
London Buses routes 202, 261 and 273 serve the station.

Facilities
The station has two platforms. Platform 1, the up platform for services to London, and Platform 2, the down platform for services to Kent. A ticket hall is situated on the up side but the station has no ticket gates. There is a subway connecting both platforms. There is step free access to both platforms.

Services
All services at Lee are operated by Southeastern using, , and  EMUs.

The typical off-peak service in trains per hour is:
 * 4 tph to London Charing Cross (2 of these run direct and 2 run via Lewisham)
 * 4 tph to Dartford of which 2 continue to Gravesend

Additional services, including trains to and from London Cannon Street via either Lewisham, or via Woolwich Arsenal and Greenwich, and to London Blackfriars call at the station during the peak hours.

title: Lee railway station


text:
House of Balliol

The House of Balliol (de Bailleul) was a noble family originating from the village of Bailleul in Picardy. They held estates in England, granted during the reign of King William Rufus. Through marriage, they had claims to the Throne of Scotland. One member of the family, John Balliol, was named King of Scotland after the disputed succession following extinction of the Dunkeld line. John was deposed, leading to the First War of Scottish Independence. His son, Edward Balliol, also briefly controlled the Scottish throne during the Second War of Scottish Independence. Edward had no issue, and the direct line went extinct with him.

List of heads of the Balliol estates

 * Guy I de Balliol (died before 1130 × 1133), established lordship in northern England in 1090s
 * Bernard I de Balliol (died 1154 x 1162), nephew of Guy
 * Guy II de Balliol (died early 1160s x 1167), son of Bernard
 * Bernard II de Balliol (died c. 1190), brother of above
 * Eustace de Balliol (died c. 1209), cousin of above
 * Hugh de Balliol (died 1229), son of above
 * John I de Balliol (died 1268), son of above, the founder of Balliol College
 * John II de Balliol (died 1314), son of above, reigned as King of Scotland from 1292 to 1296, as a descendant of David I of Scotland of the House of Dunkeld.
 * Edward de Balliol (died 1364), eldest son of John; from 1332 to 1356 he was a pretender to the Scottish throne with the support of England, in opposition to David II of Scotland.

The last two on the list both had English support for their claims but both were deposed. Edward died without issue, but the Balliol descent continued through his cousin Christine de Lindsay (granddaughter of John I), who married Enguerrand V, Lord of Coucy, to the lords of Coucy and ultimately the Bourbon kings of France and Spain.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: House of Balliol


text:
Yelland

Yelland is a village of 2,000 inhabitants situated in North Devon between Instow and Fremington in the English county of Devon. Yelland is included within the parish of Fremington.

Amenities
There is a garage, and a small industrial park. Residents use the nearest major village Fremington, or the slightly smaller village of Instow for their daily needs. Supermarkets are located in the nearest towns - Barnstaple and Bideford. There is no church situated in the village.

Regular bus services are operated by Stagecoach Devon. The nearest railway station is Barnstaple railway station, and Exeter International Airport is the nearest passenger international airport by road. The nearest international ferry port is at Plymouth.

Children in the area generally attend Fremington or Instow Primary Schools at primary school age, and Bideford College, Pilton Community College or The Park Community School at secondary school age. College students attend Bideford College's sixth form, Petroc (formerly North Devon College), or may travel further afield.

Archaeology
Near Lower Yelland Farm is a Bronze Age megalithic site consisting of a double stone row. They are unusual in being sited at the river's edge rather than on higher moorland. Since its construction, thousands of years ago, the site has been smothered by silt from the widening of the River Taw. The stones are no longer visible.

Walking trails
Visitors to Yelland and the surrounding area enjoy the views and scenic paths for walking. The Tarka Trail and South West Coast Path are easily accessible from the Yelland Power Station Road. Also Lower Yelland Nature Reserve.

East Yelland Coal-fired Power Station
The East Yelland Power Station was once an operational coal-fired electricity production plant located in a partially hidden area on the estuary, next to the Tarka Trail. The power station was one of only two located to the west of Hinkley Point.

The power station was sanctioned in September 1949, and an extension approved in June 1950. The first generating set was commissioned in July 1953 and subsequent sets in November 1953, September 1954, October 1956, December 1956, and October 1957. The power station was formally opened on 21 April 1955 by Lord Fortescue. The station had a net capability to deliver 170 MW of electricity from six Parsons 31 MW turbo-alternators. There was also a 225 kW diesel engine house service set. The Thompson radiant heat steam boilers were fired by twin chain grate stokers could deliver 253 kg/s of steam at 42.7 bar and 468 °C. Cooling water to condense steam in the plant was drawn from the river estuary. The generating capacity and output was:  { "version": 2, "width": 500, "height": 200, "data": [ {			"name": "table", "values": [ {					"x": 1954, "y": 128 },				{					"x": 1955, "y": 362 },				{					"x": 1956, "y": 393 },				{					"x": 1957, "y": 512 },				{					"x": 1958, "y": 654 },				{					"x": 1961, "y": 498 },				{					"x": 1962, "y": 541 },				{					"x": 1963, "y": 659 },				{					"x": 1972, "y": 511 },				{					"x": 1979, "y": 75 },				{					"x": 1981, "y": 3 },				{					"x": 1982, "y": 15 },				{					"x": 1967, "y": 761 }			]		}	],	"scales": [ {			"name": "x", "type": "ordinal", "range": "width", "zero": false, "domain": { "data": "table", "field": "x" }		},		{			"name": "y", "type": "linear", "range": "height", "nice": true, "domain": { "data": "table", "field": "y" }		}	],	"axes": [ {			"type": "x", "scale": "x" },		{			"type": "y", "scale": "y" }	],	"marks": [ {			"type": "rect", "from": { "data": "table" },			"properties": { "enter": { "x": { "scale": "x", "field": "x" },					"y": { "scale": "y", "field": "y" },					"y2": { "scale": "y", "value": 0 },					"fill": { "value": "steelblue" },					"width": { "scale": "x", "band": "true", "offset": -1 }				}			}		}	] } In the year ending 31 March 1981 the station delivered just 0.2 per cent of its capability. In March 1984, it was announced by the Central Electricity Generating Board that the power station would close by the end of October that year.

Fuel for the power station was obtained from coal mines in South Wales, and was transported across the Bristol Channel onto a jetty specially constructed for the power station. However, due to the closure of the coal mines in the 1980s, coal would be more expensive to obtain from other areas of the country. Therefore, it was more economical to close the power station.

Today, most of the power station, which covered an area of 3.1ha, has been demolished.

title: Yelland


text: Category:Lake of the Woods County, Minnesota


text:
Talk:Euric

Euric's Iberian dominions
Euric's dominions in Iberia did not extend to the west (Luitania), which was under the control of Suevi kings. If I were more sure that this is so, I would have added it. Any Lusitanian thoughts? Wetman 14:12, 19 Jul 2004 (UTC)

This not ERWIG but EURIC (EBERARIC -> EBORIC or EBARIC -> EVORIC or EVARIC -> EURIC [EURICO in spanish]) Calabria Geoffrey (from France) 83.198.79.71 16:47, 1 May 2005 (UTC)

His principal capital is Aire-sur-Adour but there is also, Toulouse, Bordeaux, Narbonne, and Carcassone. [Calabria Geoffrey] 83.198.79.71 16:52, 1 May 2005 (UTC)

Riothamus
"Attempted invasion of Gaul by Riothamus"? What is the source for this claim? Both the eminent Roman jurist Sidonius Apollinaris and the historian Jordanes (himself a Goth) stated that Riothamus was answering the call of the Roman Emperor Anthemius, but Arvandus the Praetorian Prefect of Gaul (possibly seeking to emulate some predecessors and become Emperor himself) betrayed both by advising Euric of Riothamus's route. In central Gaul, Euric ambushed Riothamus, whose army, after hours of combat, eventually cut their way out and made their way east to the Roman post of Avallon in Burgundy, where they made their report. Arvandus was brought to trial for high treason, and Sidonius was appointed to judge the case, but being a friend of both Arvandus and Riothamus, he recused himself, became Arvandus's defence lawyer, and persuaded the replacement judge to commute the death sentence to life in exile. Zoetropo (talk) 03:48, 31 July 2014 (UTC)

External links modified
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Euric "formally declared" independence from Roman Empire - the proof
What is the document supporting that claim? By document I mean the text of the treaty and provisions it contains. Does it exist? What was the exact wording of the recognition of this independence as per that document? How do we know Euric was de jure a fully independent in the sense of breaking every subjugation to Rome, not honouring the suzerainty of Rome.

I see only a couple of links to external sources including Edward Gibbon but those either aren't related to the subject of this article such as Merovingian kings or (in the case of Gibbon) not based on actual documents. Scrutinizer798 (talk) 19:11, 22 December 2020 (UTC)

Euric's death
What sources are there that back up the claim that Euric died on the 28th of December 484? Gregory of Tours in the historia francorum book II, 20, claims that he died in the 27th year of his reign (i.e. 494). He could be wrong, but are there any other sources that verify what's written on the page? Tim mick (talk) 07:31, 26 June 2024 (UTC)

title: Talk:Euric


text:
Paleomagnetism

Paleomagnetism (occasionally palaeomagnetism) is the study of prehistoric Earth's magnetic fields recorded in rocks, sediment, or archeological materials. Geophysicists who specialize in paleomagnetism are called paleomagnetists.

Certain magnetic minerals in rocks can record the direction and intensity of Earth's magnetic field at the time they formed. This record provides information on the past behavior of the geomagnetic field and the past location of tectonic plates. The record of geomagnetic reversals preserved in volcanic and sedimentary rock sequences (magnetostratigraphy) provides a time-scale that is used as a geochronologic tool.

Evidence from paleomagnetism led to the revival of the continental drift hypothesis and its transformation into the modern theory of plate tectonics. Apparent polar wander paths provided the first clear geophysical evidence for continental drift, while marine magnetic anomalies did the same for seafloor spreading. Paleomagnetic data continues to extend the history of plate tectonics back in time, constraining the ancient position and movement of continents and continental fragments (terranes).

The field of paleomagnetism also encompasses equivalent measurements of samples from other Solar System bodies, such as Moon rocks and meteorites, where it is used to investigate the ancient magnetic fields of those bodies and dynamo theory. Paleomagnetism relies on developments in rock magnetism and overlaps with biomagnetism, magnetic fabrics (used as strain indicators in rocks and soils), and environmental magnetism.

History
As early as the 18th century, it was noticed that compass needles deviated near strongly magnetized outcrops. In 1797, Alexander von Humboldt attributed this magnetization to lightning strikes (and lightning strikes do often magnetize surface rocks). 19th century studies of the direction of magnetization in rocks showed that some recent lavas were magnetized parallel to Earth's magnetic field. Early in the 20th century, work by David, Bernard Brunhes and Paul Louis Mercanton showed that many rocks were magnetized antiparallel to the field. Japanese geophysicist Motonori Matuyama showed in the late 1920s that Earth's magnetic field reversed in the mid-Quaternary, a reversal now known as the Brunhes–Matuyama reversal.

British physicist P.M.S. Blackett provided a major impetus to paleomagnetism by inventing a sensitive astatic magnetometer in 1956. His intent was to test his theory that the geomagnetic field was related to Earth's rotation, a theory that he ultimately rejected; but the astatic magnetometer became the basic tool of paleomagnetism and led to a revival of the theory of continental drift.

Alfred Wegener first proposed in 1915 that continents had once been joined together and had since moved apart. Although he produced an abundance of circumstantial evidence, his theory met with little acceptance for two reasons: (1) no mechanism for continental drift was known, and (2) there was no way to reconstruct the movements of the continents over time. Keith Runcorn and Edward A. Irving constructed apparent polar wander paths for Europe and North America. These curves diverged but could be reconciled if it was assumed that the continents had been in contact up to 200 million years ago. This provided the first clear geophysical evidence for continental drift. Then in 1963, Morley, Vine and Matthews showed that marine magnetic anomalies provided evidence for seafloor spreading.

Fields
Paleomagnetism is studied on a number of scales:
 * Geomagnetic secular variation is the small-scale changes in the direction and intensity of Earth's magnetic field. The magnetic north pole is constantly shifting relative to the axis of rotation of Earth. Magnetism is a vector and so magnetic field variation is studied by palaeodirectional measurements of magnetic declination and magnetic inclination and palaeointensity measurements.

 * Magnetostratigraphy uses the polarity reversal history of Earth's magnetic field recorded in rocks to determine the age of those rocks. Reversals have occurred at irregular intervals throughout Earth's history. The age and pattern of these reversals is known from the study of sea floor spreading zones and the dating of volcanic rocks.

Principles
The study of paleomagnetism is possible because iron-bearing minerals such as magnetite may record past polarity of Earth's magnetic field. Magnetic signatures in rocks can be recorded by several different mechanisms.

Thermoremanent magnetization
Iron-titanium oxide minerals in basalt and other igneous rocks may preserve the direction of Earth's magnetic field when the rocks cool through the Curie temperatures of those minerals. The Curie temperature of magnetite, a spinel-group iron oxide, is about 580 °C, whereas most basalt and gabbro are completely crystallized at temperatures below 900 °C. Hence, the mineral grains are not rotated physically to align with Earth's magnetic field, but rather they may record the orientation of that field. The record so preserved is called a thermoremanent magnetization (TRM).

Because complex oxidation reactions may occur as igneous rocks cool after crystallization, the orientations of Earth's magnetic field are not always accurately recorded, nor is the record necessarily maintained. Nonetheless, the record has been preserved well enough in basalts of oceanic crust to have been critical in the development of theories of sea floor spreading related to plate tectonics.

TRM can also be recorded in pottery kilns, hearths, and burned adobe buildings. The discipline based on the study of thermoremanent magnetisation in archaeological materials is called archaeomagnetic dating. Although the Māori people of New Zealand do not make pottery, their 700- to 800-year-old steam ovens, or hāngī, provide adequate archaeomagnetic material.

Detrital remanent magnetization
In a completely different process, magnetic grains in sediments may align with the magnetic field during or soon after deposition; this is known as detrital remanent magnetization. If the magnetization is acquired as the grains are deposited, the result is a depositional detrital remanent magnetization; if it is acquired soon after deposition, it is a post-depositional detrital remanent magnetization.

Chemical remanent magnetization
In a third process, magnetic grains grow during chemical reactions and record the direction of the magnetic field at the time of their formation. The field is said to be recorded by chemical remanent magnetization (CRM). A common form is held by the mineral hematite, another iron oxide. Hematite forms through chemical oxidation reactions of other minerals in the rock including magnetite. Red beds, clastic sedimentary rocks (such as sandstones) are red because of hematite that formed during sedimentary diagenesis. The CRM signatures in red beds can be quite useful, and they are common targets in magnetostratigraphy studies.

Isothermal remanent magnetization
Remanence that is acquired at a fixed temperature is called isothermal remanent magnetization (IRM). Remanence of this sort is not useful for paleomagnetism, but it can be acquired as a result of lightning strikes. Lightning-induced remanent magnetization can be distinguished by its high intensity and rapid variation in direction over scales of centimeters.

IRM is often induced in drill cores by the magnetic field of the steel core barrel. This contaminant is generally parallel to the barrel, and most of it can be removed by heating up to about 400 °C or demagnetizing in a small alternating field. In the laboratory, IRM is induced by applying fields of various strengths and is used for many purposes in rock magnetism.

Viscous remanent magnetization
Viscous remanent magnetization is remanence that is acquired by ferromagnetic materials influenced by a magnetic field for some time. In rocks, this remanence is typically aligned in the direction of the modern-day geomagnetic field. The fraction of a rock’s overall magnetization that is a viscous remanent magnetization is dependent on the magnetic mineralogy.

Sampling
The oldest rocks on the ocean floor are 200 Ma: very young when compared with the oldest continental rocks which date from 3.8 Ga. In order to collect paleomagnetic data dating beyond 200 Ma, scientists turn to magnetite-bearing samples on land to reconstruct Earth's ancient field orientation. Paleomagnetists, like many geologists, gravitate towards outcrops because layers of rock are exposed. Road cuts are a convenient man-made source of outcrops.
 * "And everywhere, in profusion along this half mile of [roadcut], there are small, neatly cored holes ... appears to be a Hilton for wrens and purple martins."

There are two main goals of sampling:
 * 1) Retrieve samples with accurate orientations, and
 * 2) Reduce statistical uncertainty.

One way to achieve the first goal is to use a rock coring drill that has an auger tipped with diamond bits. The drill cuts a cylindrical space around some rock. Into this space is inserted a pipe with a compass and inclinometer attached. These provide the orientations. Before this device is removed, a mark is scratched on the sample. After the sample is broken off, the mark can be augmented for clarity.

Applications
Paleomagnetic evidence of both reversals and polar wandering data was instrumental in verifying the theories of continental drift and plate tectonics in the 1960s and 1970s. Some applications of paleomagnetic evidence to reconstruct histories of terranes have continued to arouse controversies. Paleomagnetic evidence is also used in constraining possible ages for rocks and processes and in reconstructions of the deformational histories of parts of the crust.

Reversal magnetostratigraphy is often used to estimate the age of sites bearing fossils and hominin remains. Conversely, for a fossil of known age, the paleomagnetic data can fix the latitude at which the fossil was laid down. Such a paleolatitude provides information about the geological environment at the time of deposition. Paleomagnetic studies are combined with geochronological methods to determine absolute ages for rocks in which the magnetic record is preserved. For igneous rocks such as basalt, commonly used methods include potassium–argon and argon–argon geochronology.

title: Paleomagnetism


text:
Talk:TWINKLE

special structure for nrs sieveable by TWINKLE?
Arvindn, I can surmise, but I'm loath to do so as assumptions often land one in the soup. Does the existence of a proper TWINKLE (or TWIRL) implementation imply that 512 digit numbers are so easily factored that they should not be used in crypto applications depending on difficulty of factoring? If so, does this malediction for numbers with some properties extend to others; even if not so drastically? For example, would a 513 digit number be much easier to factor as being 'closely related' to 512 digit numbers? This is something which, I think, ought to be addressed here.

By the way, excellent enlargement of this article. It clearly took some effort to be that clear on such a topic. Thanks for it. ww 14:15, 19 Jul 2004 (UTC)

 * Hi,

 * First of all, the hardness is not dependent on any special property of the number 512. (Its bits by the way, not digits.) If 512 bits is easy then 513 is equally easy. Hardness grows superpolynomially but subexponentially with key size. RSA implementations almost always use power-of-two moduli, so that's why one considers the hardness of factoring 512 bits rather than (say) 500.

 * As for whether TWINKLE/TWIRL renders 512/1024 bit exponents useless, what I know is this:

 * There are two steps in QS/NFS. Although the sieving step is much more time consuming than the second step (matrix step), it is highly parallelizable but the matrix step is not. In the squeamish ossifrage cracking effort, for example, the second step was done on a big iron Sun Sparc with over a gig of RAM.

 * TWINKLE can trivially do the sieving step for 512 bit exponents. TWIRL can do the sieving for 1024 bit exponents, but only just. It will cost a lot more money to build than TWINKLE, and Shamir says it is infeasible for the moment to extend it to about 1100 bits without improvements in the math.

 * The matrix step (for 1024 bits) is much less clear. I read a paper that disputes Shamir et al's assertion that the sieving step is costlier for 1024 bits. Hardware devices for implementing the matrix step have also been proposed, but on the whole it has received much less research attention and it is not very clear what its cost is.

 * So the conclusion is, until such time as an analog of the EFF DES cracker is built, the answer to "can 1024 bit moduli be used" is "depends on who your enemies are". For 512 bits the threshold is much lower. Arvindn 19:56, 19 Jul 2004 (UTC)

finger gremlins

 * Arvindn, Thanks for the reply. It's finger gremlins that think it's digits, not me. I knew it was bits, all along! So then, it's not a special structure of a number, it's any number at all, with capacity limitations depending on size. I wish Shamir would quit changing everything under our feet all the time. The quicksand feeling is most disturbing! ww 15:16, 20 Jul 2004 (UTC)

title: Talk:TWINKLE


text:
Xceed (software company)

Xceed is a provider of software components and tools for the Microsoft .NET platform. It offers a broad range of software components and tools that appeal to .NET, Windows Forms, WPF, Silverlight and ASP.NET developers for building better applications. Xceed is best known for its zip compression libraries and data grid controls, used by Microsoft in Microsoft Office 2007, Team Foundation Server 2010, Windows Home Server and Flight Simulator among others.

Xceed is a registered trademark in the software domain owned by Xceed.

Products

 * Xceed DataGrid for WPF - Xceed DataGrid for WPF offers rich in-place editing, complete with versatile, themed and themable editor controls for all forms of data types.
 * Xceed Business Suite for WPF - This collection of carefully designed WPF controls fills in WPF holes and also includes the most-adopted and modified WPF datagrid in the industry. Includes Windows 10, Metro, Workplace, Windows 8 and Windows 7, and several designs produced by original designers.
 * Xceed Data Manipulation Suite - Offers data compression (.NET/ASP.NET, ActiveX, Xamarin), Zip, Streaming, FTP, FTPS, SFTP, document manipulation, file transfer, encryption and encoding.

title: Xceed (software company)


text:
Boeing YC-14

The Boeing YC-14 is a twinjet short take-off and landing (STOL) tactical military transport aircraft. It was Boeing's entrant into the United States Air Force's Advanced Medium STOL Transport (AMST) competition, which aimed to replace the Lockheed C-130 Hercules as the USAF's standard STOL tactical transport. Although both the YC-14 and the competing McDonnell Douglas YC-15 were successful, neither aircraft entered production. The AMST project was ended in 1979 and replaced by the C-X program.

Design and development
In mid-1970, the USAF began a paper study, the Tactical Aircraft Investigation (TAI), with Boeing, McDonnell Douglas, and other companies to look at possible tactical transport aircraft designs. This study was a precursor to what became the Advanced Medium STOL Transport program. As a part of this program, Boeing began to look at various high-lift aircraft configurations. Boeing had earlier proposed an underwing externally blown flap solution for their competitor for the Lockheed C-5 Galaxy, and had put this to good use when it modified its losing entry into the Boeing 747. The company had also done studies with the original Boeing 707 prototype, the Boeing 367-80, adding extensive leading and trailing edge devices using blown flaps. For the TAI studies, Boeing again looked at those mechanisms, as well as new mechanisms like boundary layer control. However, none of these studied designs were particularly appealing to Boeing.

The Boeing engineers were aware that NASA had carried out a series of "powered lift" studies some time earlier, including both externally blown flaps, as well an upper-surface blowing (USB), an unusual variation. In the USB system, the engine is arranged over the top surface of the wing, blowing over the flaps. When the flaps are lowered, the Coandă effect makes the jet exhaust "stick" to the flaps and bend down toward the ground. They searched for additional research on the concept and found that half-span upper-surface blowing research had been conducted in the NASA Langley 12-foot (3.7 m) tunnel. An examination of the preliminary results suggested that the system was as effective as any of the other concepts previously studied. Boeing immediately started to build wind-tunnel models to verify the NASA data with layouts more closely matching their own designs. By the end of 1971, several models were being actively studied.

Another NASA project the engineers were interested in was the supercritical airfoil, designed by Richard Whitcomb. The supercritical design promised to lower transonic drag greatly, as much as a swept wing in some situations. This allowed an aircraft with such a wing to have low drag in cruise while also having a wing planform more suitable for lower-speed flight—swept wings have several undesirable characteristics at low speed. Additionally, the design has a larger leading edge radius that makes it particularly suitable for low-speed high-lift applications like a transport. Boeing incorporated the concept into their design, the first non-experimental aircraft to do so.

The request for proposal (RFP) was issued in January 1972, asking for operations into a 2,000-foot (610 m) semi-prepared field at 500 nmi with a 27,000 lb (12,000 kg) payload in both directions with no refueling. For comparison, the C-130 of that era required about 4,000 ft (1,200 m) for this load. Five companies submitted designs at this stage of the competition, Boeing with their Model 953 in March 1972. On 10 November 1972 the downselect was carried out, and Boeing and McDonnell Douglas won development contracts for two prototypes each.

Wind tunnel tests continued through this period. In November, John K. Wimpress again visited Langley looking for an update on NASA's own USB program. Joe Johnson and Dudley Hammond both reported on testing and showed Wimpress data that verified the high-lift performance that Boeing had quoted in its proposal. By December 1975, Boeing and NASA Langley had arranged a contract for a full-scale USB testbed, which Boeing built at their Tulalip test facility consisting of a 1/4-scale wing with one JT-15D engine and a partial fuselage. Langley was particularly interested in the effectiveness of the D-shaped nozzle that directed the jet flow over the upper surface of the wing, as well as the resulting sound levels, at that time a major focus of NASA's civilian aerodynamics research.

Two major problems were found and corrected during testing. The first was a problem with air circulating around the wing when operating at low speeds close to the ground, which had a serious effect on the spreading of the jet flow through the nozzle. This led to flow separation near the flap, and a decrease in the effectiveness of the USB system. In response, Boeing added a series of vortex generators on the upper surface of the wing, which retracted when the flap was raised above 30°. Additionally, the tail surfaces were initially placed well aft in order to maximize control effectiveness. This positioning turned out to interfere with the airflow over the wings during USB operations, and a new tail with a more vertical profile was introduced to move the elevator forward.

Operational history
The first Boeing YC-14 (serial number 72-1873) flew on 9 August 1976. Two aircraft were built, the second being s/n 72-1874. The competing YC-15 had started flights almost a year earlier. Head-to-head flight testing at Edwards Air Force Base started in early November 1976. During flight testing, the YC-14 was flown at speeds as low as 59 kn and as high as Mach0.78 at 38000 ft. However, it was found that the YC-14's drag was 11% higher than originally predicted. Modifications developed in wind tunnel testing, comprising the addition of vortex generators to the upper aft portion of the nacelles, deletion of the nozzle door actuator fairing, alterations to the aft end of the landing gear pods and the addition of aft fuselage strakes, reduced this drag increment to 7%. The YC-14 also demonstrated the capability to carry the 109200 lb M60 Patton main battle tank, which was not demonstrated with the YC-15.

At the completion of testing in the late summer of 1977, the YC-14 prototypes were returned to Boeing. The prototypes were not scrapped; one is stored at the 309th Aerospace Maintenance and Regeneration Group (AMARG), located at Davis-Monthan Air Force Base and the other is on display at the nearby Pima Air & Space Museum.

By this point, the seeds of the AMST program's demise had already been sown. In March 1976, the Air Force Chief of Staff, Gen. David C. Jones, asked the Air Force Systems Command to see if it would be possible to use a single model of the AMST for both strategic and tactical airlift roles, or alternatively, if it would be possible to develop conventional derivatives of the AMST for the strategic airlift role. This led to a series of studies that basically stated that such a modification was not easy, and would require major changes to either design to produce a much larger aircraft.

Both the YC-14 and YC-15 met or exceeded the AMST specifications under most conditions. However, the increasing importance of the strategic vs. tactical mission eventually led to the end of the AMST program in December 1979. Then, in November 1979, the C-X Task Force formed to develop the required strategic aircraft with tactical capability. The C-X program selected a proposal for an enlarged and upgraded YC-15 that was later developed into C-17 Globemaster III.

Upper surface blowing remains a fairly rare concept in use, and has been seen only on a few other aircraft, such as the Antonov An-72.

Aircraft on display

 * Aircraft serial number 72-1873, the first aircraft, is on display at the Pima Air & Space Museum in Tucson, Arizona.
 * Aircraft serial number 72-1874, the second aircraft, is in storage at the 309th AMARG boneyard at Davis Monthan Air Force Base (32.17184°N, -110.84743°W).

title: Boeing YC-14


text:
McDonnell Douglas YC-15

The McDonnell Douglas YC-15 is a replaced prototype four-engine short take-off and landing (STOL) tactical transport. It was McDonnell Douglas' entrant into the United States Air Force's Advanced Medium STOL Transport (AMST) competition to replace the Lockheed C-130 Hercules as the USAF's standard STOL tactical transport. In the end, neither the YC-15 nor the Boeing YC-14 was ordered into production, although the YC-15's basic design would be used to form the successful McDonnell Douglas (later Boeing) C-17 Globemaster III.

Design and development

In 1968, the USAF started work on a series of prototype proposals, which would lead to both the AMST project and the Light Weight Fighter. The official Request for proposal (RFP) was issued in January 1972, asking for operations into a 2000 ft semi-prepared field with a 27000 lb payload and a 400 nmi mission radius. For comparison, the C-130 of that era required about 4000 ft for this load. Proposals were submitted by Bell, Boeing, Fairchild, McDonnell Douglas and the Lockheed/North American Rockwell team at this stage of the competition. On 10 November 1972, the two top bids (from Boeing and McDonnell Douglas) were selected. The companies were awarded development contracts for two prototypes each. McDonnell Douglas' prototype was designated YC-15.

McDonnell Douglas's design incorporated a supercritical wing, the result of NASA research carried out by the already famous Richard Whitcomb. This wing design dramatically lowers transonic wave drag by as much as 30% compared to more conventional profiles, while at the same time offering excellent low-speed lift. Most contemporary aircraft used swept wings to lower wave drag, but this led to poor low-speed handling, which made them unsuitable for STOL operations.

The design team also chose to use externally blown flaps to increase lift. This system uses double-slotted flaps to direct part of the jet exhaust downwards, while the rest of the exhaust passed through the flap and then followed the downward curve due to the Coandă effect. Although the effects had been studied for some time at NASA, along with similar concepts, until the introduction of the turbofan the hot and concentrated exhaust of existing engines made the system difficult to use. By the time of the AMST project, engines had changed dramatically and now provided larger volumes of less-concentrated and much cooler air. The YC-15 prototype was the first jet powered aircraft to use externally blown flaps.

For later prototypes, there were several modifications including a computer on the YC-15 was devised that would calculate the best flap angle for various flight conditions given the current gross weight. Together these modifications offered a reduction in approach speed of 10 kn.

For the YC-15, four engines were used, versions of the Pratt & Whitney JT8D-17 widely used on the Boeing 727 and Douglas DC-9. The YC-15 borrowed components from other McDonnell Douglas aircraft, with its nose gear coming from the Douglas DC-8 and the nose section and cockpit being derived from the Douglas DC-10. Parts borrowed from other aircraft included the Universal Aerial Refueling Receptacle Slipway Installation (UARRSI), taken from a Fairchild A-10, anti-tipover stabilizer struts from the Lockheed C-141 Starlifter, pumps taken from the McDonnell Douglas F-15 Eagle, Lockheed C-5 Galaxy, DC-9 and C-141 and actuators taken from the C-5 Galaxy and DC-10. In addition, the environmental cooling system was composed of components taken from the DC-9, C-141 and Boeing KC-135.

The YC-15 interior cargo hold was large, with dimensions 47 x 11.8 x 11.4 feet.

The YC-15 was the first aircraft to offer pilots a heads up display. It was especially designed to help with short field landings, showing the pilot the horizon, flight path scale, airspeed indexer and touchdown point.

Operational history

Two YC-15s were built, one with a wingspan of 110 ft (#72-1876) and one of 132 ft (#72-1875). Both were 124 ft long and powered by four Pratt & Whitney JT8D-17 engines, each with 15500 lbf of thrust.

The first flight was on 26 August 1975. The second prototype followed in December. They were tested for some time at McDonnell Douglas as the Boeing entry was not ready until almost a year later. In November 1976, both designs were transferred to Edwards Air Force Base for head-to-head testing, including lifting heavy loads like tanks and artillery from dirt airfields at Graham Ranch, off the end of Runway 22.

In Phase II of the flight test program, a "refanned" Pratt & Whitney JT8D-209 was tested in No. 1 nacelle of 72–1876, and a CFM International CFM56 was tested in the No. 1 nacelle of 72–1875. In addition, a new wing with increased chord and span was flown on 72–1875.

The YC-15 met specifications under most, but not all, conditions. It was a very good STOL plane for its size. At a gross weight of 149,300lbs, the YC-15 flew short landing approaches at only 87 kn at a 6 degree glide slope yielding a sink rate of 15.4 feet per second, compared with normal approaches that were made at about 127 kn with a typical 8-12 feet per second sink rate. For short landings, the touch down aim-point was only about 300 feet from the runway end. Pilots of the YC-15 tested both no-flare and with-flare landing techniques in STOL mode. Because of slow actuation of the thrust reversers, testing at Edwards AFB showed the plane was unable to consistently stop in “hot-and-high” conditions in the required 2000 feet.

However, the seeds of the AMST program's demise had already been sown. In March 1976, the Air Force Chief of Staff, Gen. David C. Jones, asked the Air Force Systems Command to see if it was possible to use a single model of the AMST for both strategic and tactical airlift roles, or alternatively, if it was possible to develop non-STOL derivatives of the AMST for the strategic airlift role. This led to a series of studies that basically stated that such a modification was not easy, and would require major changes to either design to produce a much larger aircraft.

The increasing importance of the strategic vs. tactical mission eventually led to the end of the AMST program in December 1979. Then, in November 1979, the C-X Task Force formed to develop the required strategic aircraft with tactical capability. The C-X program selected a proposal for an enlarged and upgraded YC-15 that was later developed into the C-17 Globemaster III. The Lockheed C-130 Hercules would be further improved into the C-130J and remains in service.

After the flight test program, the two aircraft were stored at the AMARC, located at Davis-Monthan Air Force Base. One aircraft (72-1875) was subsequently moved to the nearby Pima Air & Space Museum in 1981, but was returned to flying status by McDonnell Douglas in 1996; it was first reflown on 11 April 1997. On 16 April 1997, the aircraft was ferried to Long Beach, California to support the C-17 program. On 11 July 1998, the aircraft suffered a massive failure of the No. 1 engine during flight and made an emergency landing at Palmdale, California. On inspection, the aircraft was deemed too expensive to repair and was stored at Palmdale. In 2008, the aircraft was moved by road to Edwards AFB, where it is now on display at the Air Force Flight Test Center Museum's "Century Circle" display area, just outside the base's west gate. The other airframe (72–1876), which had remained on Celebrity Row at the AMARC for many years, was destroyed in place in April 2012.

title: McDonnell Douglas YC-15


text:
Talk:Dave Gorman

Modern Life is Goodish
There should probably be more about this show. I'll get around to it eventually if nobody else does, but consider this a request in the meantime. --Walnuts go kapow (talk) 09:43, 23 September 2015 (UTC)

citogenesis of pacific rim hitchhike
in January 2014 someone added a claim that he did a hitchike around the pacific rim. This was later repeated in a newspaper, but has no basis other than the unsourced wikipedia claim and is denied by Dave https://twitter.com/DaveGorman/status/730351115368271873 — Preceding unsigned comment added by Alanbelllibertus (talk • contribs) 11:24, 11 May 2016 (UTC)
 * Thanks. I have added this to List of citogenesis incidents.--Shantavira|feed me 10:04, 23 November 2016 (UTC)
 * Does anyone have the newspaper? Does anyone have evidence the newspaper got it from wikipedia? Otherwise it's not citogenesis. What it is is an unsourced claim in a BLP. I've removed it, mostly for the crocodile thing that seems entirely unsourced. SPACKlick (talk) 12:53, 23 November 2016 (UTC)

 * The hitch-hiking claim was introduced on 1 January 2014 by '. The citation of the 9 September 2014 edition of The Northern Echo that reported the claim was added by '. It is of course possible that the Northern Echo's source was unconnected to Wikipedia. Verbcatcher (talk) 00:16, 25 November 2016 (UTC)

Semi-protected edit request on 4 December 2016
Dave originally grew his beard to raise money for Red Pandas but liked it so much he decided to keep it. 95.147.5.199 (talk) 22:14, 4 December 2016 (UTC)

You need to provide a reference from a reliable source for this edit to go ahead Neiltonks (talk) 22:34, 4 December 2016 (UTC)

 * No source provided. - X201 (talk) 10:31, 6 December 2016 (UTC)

Distant relations
I've deleted "On an episode of Taskmaster, Gorman revealed that he is distantly related to Hollywood actor Cary Grant." How is this encyclopedic? It was just a throwaway comment. Everyone is distantly related to millions of people.--Shantavira|feed me 17:19, 10 August 2020 (UTC)

Date of marriage confirmed
He married 8th of Oct. 2010. See his show "Modern Life Is Goodish" S2E5 at about 6:35 min.

youtu .be/m5vtoADa3jU?t=395 — Preceding unsigned comment added by 2a02:810c:c240:c4:a581:e81a:e0d0:b4b0 (talk) 19:27, 29 April 2021 (UTC)
 * Thanks; I've added that to the article. Graham 87 05:14, 17 May 2022 (UTC)

title: Talk:Dave Gorman


text:
Diego Forlán

Diego Martín Forlán Corazo (born 19 May 1979) is a Uruguayan professional football manager and former player who played as a striker. Regarded as one of the best forwards of his generation, Forlán is a two-time winner of both the Pichichi Trophy and the European Golden Shoe at club level. With the Uruguay national team, he had notable individual success at the 2010 FIFA World Cup, finishing as joint top scorer with five goals, winning the goal of the tournament, and winning the Golden Ball as the tournament's best player.

Forlán began his career in his native Uruguay as a youth player with Peñarol and Danubio, before joining Argentine club Independiente. After rising through their youth team and after a successful four-year spell, he sealed a move to England with Manchester United in 2002. His form for United was not as successful as at Independiente, although he won the Premier League in 2002–03 and the FA Cup in 2003–04.

In the summer of 2004, Forlán moved to Spanish side Villarreal. In his first season in Spanish football, he won the Pichichi Trophy. After two more successful seasons with Villarreal, Forlán joined Atlético Madrid, where he once again became the league's top scorer, and became the first player to win the Pichichi Trophy twice since Ronaldo in 1996–97 and 2003–04. Forlán scored in Atlético's 2010 Europa League final victory against Fulham. In 2011, he joined Inter Milan of Italy before moving to Internacional in 2012. After spells in Japan with Cerezo Osaka, back in Uruguay with his boyhood club Peñarol, in India with Mumbai City and in Hong Kong with Kitchee, Forlán retired from professional football in August 2019.

Forlán also had a successful international career, scoring 36 times for his country between his debut in 2002 and his retirement in 2015, including six goals at FIFA World Cups. On 12 July 2011, at the 2011 Copa América in Argentina, which Uruguay won, Forlán earned his 79th international cap in a match against Mexico, breaking the record held since 1986 by goalkeeper Rodolfo Rodríguez. On 20 June 2013, in a match against Nigeria at the 2013 Confederations Cup, Forlán became the first Uruguayan to win 100 caps. Forlán was Uruguay's all-time leading top scorer from 2011 until Luis Suárez overtook him two years later.

Early life and education
Forlán was born and brought up in the Montevideo barrio of Carrasco. His family — which included three brothers, a sister, four cousins, his maternal grandmother and her sister — resided in an apartment building on Potosi street, a short distance from the casino and the rambla. He is the son of former player and Uruguayan international Pablo Forlán.

Forlán attended multiple schools in the private and state sector. He started at Liceo Francés Jules Supervielle in Buceo, but later switched to Erwy School because it was closer to his home. This was followed by Scuola Italiana di Montevideo and then Liceo 15 in Carrasco. He learned English at school from a young age. As a child, Forlán played tennis at Carrasco Lawn Tennis Club in addition to football, which often took place on the streets.

On 14 September 1991, Forlán's sister Alejandra was seriously injured and eventually left handicapped by a car accident that also killed her boyfriend. The cost of the medical bills plunged his family into financial crisis, though this was later averted due to the fundraising efforts of Diego Maradona. Until this point Forlán was also dedicated to tennis, but having been inspired by Maradona's generosity, began to focus more on football in the hope that he might contribute to paying for his sister's treatment himself.

Early career
Forlán was a boyhood fan of Peñarol and played youth football for both Peñarol and Danubio In 1995, a 16 year old Forlán moved to France, where he spent four months on trial at Nancy, but was ultimately not offered a contract by manager László Bölöni.

Independiente
Forlán received an offer to join Argentine side Independiente through the help of one of his father's contacts, José Omar Pastoriza. He soon accepted, rejecting a simultaneous offer from Boca Juniors. Arriving in Argentina on 28 January 1998, Forlán made his way up the Independiente reserve teams and thanks to strong performances, started training with the first team. Injuries to several forward players who were ahead of him in the pecking order created an opportunity for the young Uruguayan, who made his professional debut on 26 October 1998 in a match against Argentinos Juniors.

Forlán scored 37 goals in 80 league games. His goalscoring attracted the attention of European sides, and in January 2002, Independiente agreed a £6.9 million deal with Middlesbrough of the Premier League; the transfer fee would be paid over 18 installments. Forlán travelled to England expecting to negotiate with Middlesbrough, but at the last minute Manchester United gazumped the Teesside club, offering Independiente the same fee in a single payment, as well as a more lucrative salary for Forlán. On arriving in England, he negotiated with United officials for four hours, then informed the press of his decision. "Manchester United is a big club, so I've decided to go there," he explained. "The thing is, they offered more money than Middlesbrough." He signed for United soon after.

Manchester United
Forlán was signed for Manchester United by Sir Alex Ferguson for £6.9 million on 22 January 2002. He made his debut on 29 January as a 76th-minute substitute for Ole Gunnar Solskjær in a 4–0 away win at Bolton Wanderers. He made his first start in 4–0 home victory over Tottenham Hotspur on 6 March. Forlán made 13 Premier League and five UEFA Champions League appearances in the 2001–02 season but did not score.

On 18 September 2002, Forlán came on as a 56th-minute substitute for Ryan Giggs in a Champions League match versus Maccabi Haifa. He scored his first United goal as an 89th-minute penalty kick in the 5–2 win. His first Premier League goal was a 77th-minute equaliser in a home 1–1 draw against Aston Villa on 26 October. In Forlán's next Premier League game, at home to Southampton on 2 November, he came on as a 79th-minute substitute for United's goalscorer Phil Neville with the score at 1–1, and scored the winner with a dipping shot over Southampton goalkeeper Antti Niemi in the 85th minute. The goal also became notable due to his goal celebration where he ripped off his jersey, but then struggled to put it back on as the game recommenced, with Forlan making a blocked tackle while shirtless.

On 1 December, Forlan scored his first brace for Manchester United with goals in the 64th and 67th minute of an away 2–1 Premier League win at rivals Liverpool. On 17 December 2002, Forlán scored the winning goal as United defeated Chelsea in the quarter-finals of the Football League Cup. On 18 January 2003, Forlán scored a 90th-minute winning goal to again defeat Chelsea, this time in a Premier League match. Manchester United went on to win the Premier League title in 2002–03, and Forlán scored six goals to make him the club's third best-scoring striker that season after Ruud van Nistelrooy and Ole Gunnar Solskjær.

At the start of the 2003–04 season, Forlán played seven Premier League games without scoring. This run was broken on 25 October, when he equalised the score to 1–1 in the 45th minute of a home match versus Fulham, a game which United lost 3–1. Forlán then scored a goal in his three subsequent matches in three different competitions, starting with an extra-time goal in an away League Cup game at Leeds United which Manchester United won 3–2. This was followed by the opener in a 3–0 home Premier League victory over Portsmouth and a sixth-minute goal in a win by the same score over Rangers in the Champions League. In his next Champions League game, he scored the 85th-minute winner for United over Panathinaikos in a 1–0 away victory. On 6 December 2003, Forlán scored two injury-time goals as Manchester United beat Aston Villa 4–0 at home in the Premier League. These were Forlán's last Premier League goals despite him playing 10 more league games over the season. His only other Manchester United goal was in a 3–0 victory over Northampton Town of Division Three on 24 January 2004 in the FA Cup. Diego Forlán did not feature at all in United's 3–0 victory over Millwall in the 2004 FA Cup Final on 22 May 2004.

He started the 2004–05 season with Manchester United and played in a Champions League qualifier against Dinamo București and a 3–1 defeat to Arsenal on 8 August in the 2004 FA Community Shield. His last match for United was their first Premier League game that season, a 1–0 defeat away to Chelsea on 15 August.

United supporters would continue to sing Forlán's name in tribute to the two goals he scored against Liverpool for several years after Forlán's departure from the club, with the chant "He came from Uruguay, he made the scousers cry". Forlán spoke of this fondly in 2010.

Villarreal
Forlán was strongly linked with a move to Spanish clubs Levante and Athletic Bilbao, but on 21 August 2004, he signed with Villarreal.

Forlán's debut for Villarreal was on 30 August 2004, starting away to rivals Valencia and scoring his club's goal in the 77th minute of a 2–1 defeat. His next goal came in a home 2–0 win over Real Zaragoza on 3 October, and was followed with an equaliser in a 1–1 draw at Mallorca and the final goal of a 4–0 win at home to Numancia. Between 12 December 2004 and 16 January 2005, Forlán scored seven goals in five Primera División matches, including a brace in a 3–0 home victory over Barcelona on 9 January. On 22 May 2005, he scored his first hat-trick for a European club with all of Villarreal's goals in a 3–3 away draw against eventual league champions Barcelona. A week later, he scored two in a 4–1 victory over local rivals Levante as Villarreal ended the season in third, qualifying for the Champions League for the first time in the club's history. Forlán won the 2004–05 Pichichi Trophy for most goals in La Liga, with 25. He also shared the 2005 European Golden Boot with Arsenal striker Thierry Henry.

His goal rate declined in the 2005–06 season as Villarreal underwent several changes, yet the club reached the semi-finals of the Champions League where they were knocked out by Arsenal.

In 2006–07, he ended the season with 19 goals in 36 league appearances.

2007–08 season
Forlán was linked with a transfer jointly with Juan Román Riquelme to Atlético Madrid in exchange for Luis Perea plus cash in June 2007. On 30 June 2007, following the departure of their captain Fernando Torres to Liverpool, Atlético Madrid confirmed that they had agreed to a fee of around €21 million. He returned to England in February 2008 to take part in Atlético's UEFA Cup clash against Bolton Wanderers (the club against whom he made his Manchester United debut), but the side lost out 1–0 on aggregate. In May 2008, Forlán helped Atlético qualify for the Champions League for the first time in over a decade, scoring the winning goal against Deportivo de La Coruña. He ended his first season in Madrid with 23 goals and formed a potent partnership with Argentinian striker Sergio Agüero.

2008–09 season
On 9 May 2009, Forlán scored twice against Espanyol to help Atlético clinch Champions League qualification for a second successive year. Los Rojiblancos were trailing 2–0 at half-time and had seen Luis Perea sent off, but came back to win 3–2 thanks to a goal of the season contender from Forlán, as well as a last minute winner. He also scored crucial goals in wins over Barcelona, Villarreal and Valencia. On 23 May 2009, Forlán scored a hat-trick against Athletic Bilbao, which helped him win the La Liga Pichichi Trophy, as well as the European Golden Boot for a second time. He ended the 2008–09 season with a very impressive 32 goals in 33 matches.

2009–10 season
Forlán started the 2009–10 season slowly, and struggled for form as Atlético made their worst start to a league season since their relegation in 2000. On 24 October 2009, Forlán scored a penalty and missed another as Atlético were held to a 1–1 draw at home against Mallorca, who had played the majority of the second half with just nine players on the field. The disappointing result and performance led to protests from Atlético supporters, as well as criticism for Forlán, who was subsequently left out of the squad for the next game. Atlético started to improve after the arrival new manager Quique Sánchez Flores, and once again, Forlán flourished in the second half of the season, as Atlético reached the finals of both the Europa League and Copa del Rey. On 14 February 2010, Forlán scored the first goal as Atlético beat Barcelona 2–1 at the Vicente Calderón, inflicting the eventual Champions only league defeat of the season. On 22 April 2010, Forlán scored the only goal of the game in Atlético's Europa League semi-final first leg at home to Liverpool. A week later, Liverpool took the tie to extra time before taking a 2–1 aggregate lead. Forlán then scored again to make it 2–2 on aggregate, giving Atlético the away goal they needed to reach the final, in which they played against Fulham at Volksparkstadion, Hamburg, on 12 May. Forlán scored twice against Fulham in the final, in a 2–1 win and was awarded man of the match. He ended the season with a total of 28 goals, including six in Atlético's successful Europa League campaign.

2010–11 season
The 2010–11 season began with another trophy for Forlán and Atlético, winning the UEFA Super Cup, beating Inter Milan 2–0 in Monaco on 27 August 2010. Again Forlán started the season slowly, and despite finding the net three times in the opening two league games, he then went 12 matches in all competitions without a goal before finally scoring a double in a 3–0 win against Osasuna on 13 November.

Inter Milan
On 29 August 2011, it was confirmed that Forlán had joined Inter Milan as a replacement for the departing Samuel Eto'o. No financial details were announced but it is believed the 32-year-old signed an initial two-year deal. He made his debut on 11 September 2011, scoring with a high left foot shot in a 4–3 defeat at Sicilian club Palermo. On 4 March 2012, Forlán scored his second goal for Inter against Catania in a 2–2 draw. In April, Forlán declared his loyalty to Inter and his intention to stay when he told Sky Sports: "I want to stay at Inter. You haven't seen the real Forlán yet... I wouldn't want to leave Inter like this. I like challenges and I wouldn't want to leave when the team are not in a good position." In June, his father confirmed the belief that the striker would see out his contract with the Nerazzurri. On 5 July, however, after only scoring twice in 22 appearances, the Italian club confirmed that he had been released, terminating the final year of his contract. Forlán has stated that his poor performance with the Nerazzuri was due to being played out of position. In addition, former Inter and Uruguay player Álvaro Recoba believed that his compatriot struggled at Inter due to the success of his predecessor Samuel Eto'o, which led Forlán to fail to live up to expectations.

Internacional
On 6 July 2012, after terminating his contract with Inter, Forlán signed a three-year deal with Brazilian club Internacional. He was also linked to Mexican teams Tigres UANL and Club América. In January 2013, Forlán was linked with another Mexican team, the recently promoted Club León. At León, Forlán had the chance to play the 2013 Copa Libertadores; Internacional, however, retained Forlán's services for the 2013 season.

On 28 July 2012, he made his debut for the Brazilian club against Vasco da Gama. Forlán scored his first two goals for Internacional in a 4–1 win against Flamengo. Forlán also helped the club win 2013 Campeonato Gaúcho, scoring nine goals, the highest total at the tournament.

Cerezo Osaka
On 22 January 2014, Forlán signed an 18-month deal with Japanese J1 League side Cerezo Osaka. He made his AFC Champions League debut in a 1–1 draw with Pohang Steelers, and his J. League debut in a 1–0 loss against defending champions Sanfrecce Hiroshima. He scored his first goal for Cerezo in a 4–0 win over Buriram United in an AFC Champions League match. On 12 April, Forlán scored two goals in the Osaka derby against local club rivals Gamba Osaka. He scored a crucial goal against Shandong Luneng on 23 April to put his team through to the knockout stage of the AFC Champions League. Cerezo Osaka were knocked out in the first round by Guangzhou Evergrande, losing 5–1 at home in the first leg. In spite of the disappointing home defeat, they managed to secure a 1–0 away win after an own goal by Liao Lisheng. However, this was not enough to overcome the 5–2 aggregate lead.

Having been relegated in his first season to J2 League, he started off the new campaign with a goal against Tokyo Verdy drawing 1–1. Forlán scored his first hat-trick against Kyoto Sanga on 29 April 2015, his side winning 3–0.

Peñarol
On 10 July 2015, Forlán signed an 18-month contract with his boyhood club Peñarol. In his only season at the club, he scored eight goals in 31 appearances as Peñarol won the championship title. On 14 June 2016 at a press conference, Forlán said he would be leaving the club.

Mumbai City
In August 2016, Forlán signed a three-month deal with Indian Super League club Mumbai City. He scored a hat-trick against Kerala Blasters in their 5–0 win on 19 November.

Mumbai finished first in the league table and progressed to the semi-final of the playoffs where they would face ATK. After conceding an early goal, Mumbai equalised and soon took the lead from the headers of Leo Costa and Gerson Vieira. In both cases the free kicks were taken by Forlán. Forlán received a red card in the second half as ATK won the match 3–2.

Kitchee
On 4 January 2018, Forlán joined Hong Kong Premier League club Kitchee. He made his debut for Kitchee on 14 January 2018, coming off the bench in the 88th minute in a 2–2 draw against Southern. On 28 January, Forlán scored his first and second goals for Kitchee in a 7–0 victory over Biu Chun Rangers. He scored a hat-trick in a 5–1 win against Lee Man in the following match. Forlán played in Kitchee's 1–0 victory over Kashiwa Reysol in the 2018 AFC Champions League, helping Kitchee to become the first-ever team from Hong Kong to win a match in AFC Champions League history. On 13 May 2018, Forlán played his final match with the club, featuring in the first 56 minutes of a 2–0 victory, and went on to win the Hong Kong Premier League that season.

Retirement
A year after leaving Kitchee, Forlán announced his retirement from professional football on 7 August 2019.

International career
Forlán's 100th cap came in the 2013 FIFA Confederations Cup match against Nigeria. On 11 October 2011, he scored his 32nd goal, which made him Uruguay's top scorer of all time in official matches, beating Héctor Scarone who had held the record alone with 31 goals since 1930. (Scarone scored 42 goals in total, but 11 of them were in unofficial matches).

2002 FIFA World Cup, 2004 Copa América, and 2007 Copa América
Forlán made his debut for Uruguay on 27 March 2002, scoring his first goal in a 3–2 friendly defeat against Saudi Arabia. During the 2002 World Cup, he scored a volley on 11 June 2002 in the group stage 3–3 draw against Senegal. Despite coming from three goals down to draw the game, Uruguay were eliminated from the tournament along with France in Group A. Forlán and Youri Djorkaeff were, respectively, members of the Uruguay and France squads that met in the 2002 World Cup, in Group A. Their respective fathers, Pablo and Jean, featured in the match between Uruguay and France at the 1966 World Cup, which was also in Group A.

Forlán wore the number 21 for Uruguay at the 2004 Copa América in Peru, shortly before his transfer from Manchester United to Villarreal. He played all six games as they, under the management of Jorge Fossati, came third. Forlán's only goal was in the 2–1 victory over Ecuador, Uruguay's only group win. They advanced in third place out of four in the group.

Forlán scored against Brazil in the 35th minute of the 2007 Copa América semi-final. However, he missed his shot during the subsequent penalty shoot-out, which Brazil ultimately won 5–4.

2010 FIFA World Cup
On 17 June 2008, Forlán scored a hat-trick in a World Cup qualifying game against Peru.

On 16 June 2010, during Uruguay's second group game in the 2010 World Cup against South Africa, Forlán opened the scoring with a right footed long range effort. Later in the game, Forlán scored from the penalty spot, shooting high into the net for his second and also had a hand in Uruguay's third, in a 3–0 win over the host nation. On 2 July 2010, Forlán scored a free kick against Ghana to equalise in the quarter-final. The game ended 1–1 and Uruguay advanced to the semi-finals after defeating Ghana 4–2 in the penalty shootout. On 6 July 2010, Forlán scored another long range goal, this time with his left foot to equalise against the Netherlands in the semi-final. Despite a half-time score of 1–1, Uruguay eventually lost 3–2 as the Dutch advanced to the final. Forlán became the first player since Lothar Matthäus in 1990 to score three goals from outside the penalty area in one tournament. On 10 July 2010, Forlán scored for the final time in the tournament as he netted a well-executed volley from the edge of the area to give Uruguay the lead. This goal, from a pass by Egidio Arévalo Ríos, was selected by FIFA as the Goal of the Tournament. Forlán then hit the crossbar with the final kick of the game from a free kick as they lost to Germany 3–2 in the third place play-off. Forlán was awarded the Golden Ball as the tournament's best player. He was also picked for the team of the tournament, and was the joint top scorer at the World Cup with five goals.

2011 Copa América

On 24 July 2011, Forlán scored twice after Luis Suárez's opening goal helping Uruguay win their 15th Copa América title and became Uruguay's joint top scorer at international level, his 31 goals matching those of Héctor Scarone after beating Paraguay 3–0 in the final. Forlán's father and grandfather were also South American champions with Uruguay over a period spanning the 95 years of the world's oldest active tournament.

2013 FIFA Confederations Cup
On 16 June 2013, Forlán appeared as a 69th-minute substitute in Uruguay's opening 2013 Confederations Cup match against Spain. In Uruguay's second group game, a match where he won his 100th cap for his country, Forlán scored the winning goal to defeat Nigeria 2–1. He was subsequently rested for the next match against Tahiti. He was again in the starting line-up as Uruguay lost 1–2 to Brazil in the semi-final, where he had a penalty kick saved by Brazilian goalkeeper Júlio César.

2014 FIFA World Cup
Forlán was a part of the Uruguay squad for the 2014 World Cup in Brazil. At the age of 35, he started the opening match against group underdogs Costa Rica in place of the absent Luis Suárez. He had a deflected shot saved by Costa Rican goalkeeper Keylor Navas as Uruguay lost the game 3–1. Forlán did not appear again until the Round of 16, where Uruguay were beaten 2–0 by Colombia.

Retirement
On 11 March 2015, Forlán announced his retirement from the national team. He represented Uruguay with 112 caps, scoring 36 times.

Style of play
A talented, technically gifted, hardworking and creative player, with an eye for goal, Forlán was a quick, clever, complete and versatile forward, with a good positional sense, who was capable of playing anywhere along the front line. He was deployed as a main striker (his favoured position), as a supporting forward, as an attacking midfielder, and even as a winger, often drifting onto the flank to begin attacking plays. He was capable of scoring with either foot, both from inside and outside the area; in fact, Forlán was most known for his powerful and accurate long range shots, which made him a large threat if given space outside the box. Alongside this, Forlán was also an accurate set-piece and penalty kick taker. In addition to his accurate finishing, movement, and goalscoring ability, Forlán was a skilful player, gifted with good technical ability and ball control, as well as good vision, passing ability, intelligence, and awareness on the ball; these attributes also enabled him to be deployed in a more creative role, in which he could play-off of other players and drop into deeper positions to link-up the midfield with the attack, making him a capable assist provider. In addition to his footballing skills, Forlán was also praised for his leadership, longevity and determination throughout his career.

Coaching career
On 20 December 2019, Forlán was appointed as manager of his former club Peñarol. He was sacked on 1 September 2020, after winning just four of his eleven games in charge. On 17 March 2021, he was appointed as manager of Atenas of the Uruguayan Segunda División. On 16 September 2021, after a 2–1 loss to Rampla Juniors, he was released.

Tennis career
Since July 2023, Forlán has been competing on the ITF Masters professional tennis tour, and is a ranked player in the 35+, 40+, and 45+ age categories. In June 2024, Forlán attracted media coverage after reaching the quarterfinals of the ITF MT1000 Lima 45+ tournament in Peru, winning three matches in straight sets.

Personal life
Forlán was born into a family of footballers – his father Pablo having played for Peñarol (1963–1970), São Paulo (1970–1975) and Uruguay in the 1966 and 1974 World Cups, and his maternal grandfather, Juan Carlos Corazzo, for Independiente in Argentina. Forlán is of Italian, Basque, and Irish descent, and because of his Basque ancestry from his grandmother who was originally from San Sebastián, he was linked to Athletic Bilbao after his departure from Manchester United, even though the club only permits Basque players. His nickname is Cachavacha, a witch who is one of the antagonists from the Argentine cartoon series The Adventures of Hijitus. In addition to his native Spanish, Forlán also speaks English.

He is a founding member of Fundación Alejandra Forlán, an organization headed by his sister that promotes safer driving.

In 2009, Forlán appeared in a music video for Coti starring alongside Argentine footballer Maxi Rodríguez. In 2021, Forlán began playing amateur football for the Old Boys Club, the alumni team of The British Schools of Montevideo.

Relationships
Forlán announced on 9 March 2011 on his official Twitter page that he and Argentinian model/actress Zaira Nara were engaged to be married. In June 2011, however, Forlán and Nara announced they were breaking their engagement. No reason was released for the breakup. During 2011 and 2012 he dated model Victoria Saravia.

Forlán is married to Paz Cardoso and together the pair have two sons and a daughter.

Club

 * Source:

International

 * Source:

 * Scores and results list Uruguay's goal tally first.

Honours
Manchester United
 * Premier League: 2002–03
 * FA Cup: 2003–04
 * FA Community Shield: 2003

Villarreal
 * UEFA Intertoto Cup: 2004

Atlético Madrid
 * UEFA Europa League: 2009–10
 * UEFA Super Cup: 2010

Internacional
 * Campeonato Gaúcho: 2013

Peñarol
 * Primera División: 2015–16

Kitchee
 * Hong Kong Premier League: 2017–18

Uruguay
 * Copa América: 2011

Individual
 * La Liga Ibero-American Player of the Year: 2004–05
 * Pichichi Trophy: 2004–05, 2008–09
 * European Golden Shoe: 2004–05, 2008–09
 * FIFA World Cup Golden Ball: 2010
 * FIFA World Cup Goal of the Tournament: 2010
 * FIFA World Cup Top Scorer: 2010
 * FIFA World Cup Dream Team: 2010
 * UEFA Europa League Final Man of The Match: 2010
 * Campeonato Gaúcho Top Scorer: 2013
 * IFFHS Uruguayan Men's Dream Team (Team B)

title: Diego Forlán


text:
Josef František

Josef František (7 October 1914 – 8 October 1940) was a Czechoslovak fighter pilot and Second World War fighter ace who flew for the air forces of Czechoslovakia, Poland, France, and the United Kingdom. He was the highest-scoring non-British Allied ace in the Battle of Britain, with 17 confirmed victories and one probable, all gained in a period of four weeks in September 1940.

František was a brilliant pilot and combatant but frequently breached air force discipline first in Czechoslovakia, in France and Britain. The RAF found it best to let him patrol alone, a role in which he was highly successful. He was killed in a crash in October 1940 in the final week of the Battle of Britain.

Life in Czechoslovakia
Josef František was born in 1914 in Otaslavice in Moravia, Austria-Hungary (now the Czech Republic), the son of a carpenter. After leaving school, he was apprenticed to a locksmith, but in 1934 he joined the Czechoslovak Air Force. He was trained at the Air Training School at Prostějov. In 1935, he was a corporal in the 1st Air Regiment. In 1936, he completed training and was posted to the 2nd Air Regiment at Olomouc in Moravia, where he flew Aero A.11 and Letov Š-328 reconnaissance biplanes. By 1937, he was a sergeant.

František got into trouble for fighting, returning late to his unit, and other breaches of discipline. He could have been dishonourably discharged, but he showed exceptional promise as a pilot, so he was sent to the 4th Air Regiment to train as a fighter pilot. In June 1938, he became a fighter pilot with the 40th Fighter Flight at Prague-Kbely flying Avia B-534 and Bk-534 biplane fighters. Here he developed his flying and combat skills.

On 30 September 1938, France and the United Kingdom allowed Germany to annex the Sudetenland, and on 15 March 1939 Germany occupied the remainder of Bohemia and Moravia. It imposed a Protectorate of Bohemia and Moravia with a puppet government that it ordered to dissolve its armed forces.

Polish Air Force
Many Czechoslovak airmen covertly escaped over the border to Poland. František was one of a group of four that was smuggled across the border by train at Šumbark on 13 June. The group reported to the Czechoslovak Consulate in Kraków and was accommodated in a Czechoslovak transit camp at Bronowice Małe that had been converted from a disused Austro-Hungarian Army camp.

Initially, Poles showed no interest in Czechoslovak pilots. In July 1939, a party of Czechoslovak airmen including František and another future RAF ace, Karel Kuttelwascher, went to the Port of Gdynia to sail to France. On 29 July, they were about to embark on a Swedish cargo steamship, the Kastelholm. Meanwhile, the Poles were already sure that the German invasion was inevitable. While Czechoslovak pilots were preparing for departure, they received an offer to join the Polish Air Force, to which many agreed. František was in a group of friends that tossed a coin to decide. It landed "tails", so they stayed in Poland. In total, eight Slovaks and thirteen Czechs joined the Polish Air Force.

František and his group retrained on Polish aircraft at Dęblin airbase in Małopolska. František was made an instructor, flying obsolescent Potez 25, Breguet 19, PWS-26, RWD 8, RWD-14 Czapla and Lublin R-XIII aircraft.

On 1 September 1939 Germany invaded Poland, and on the morning of 2 September a Luftwaffe air raid destroyed Dęblin airbase. František's unit evacuated its surviving aircraft to Góra Puławska, further to the southeast. On one patrol from Góra Puławska a fellow Czechoslovak pilot, Zdeněk Škavarda, was flying a Breguet 19 when he ran out of fuel, made a forced landing near German lines and was at risk of capture. František landed nearby and rescued him.

František's unit retreated again, to Sosnowice Wielke airfield near Parczew. From 7 September he flew reconnaissance missions in unarmed 2-person RWD 8 and PWS-25 training aircraft, carrying an observer. On 19–20 September he attacked enemy columns near Kamionka Strumiłowa, throwing hand grenades at German troops below. On 20 September his aircraft was damaged by enemy fire from the ground so he made a forced landing near Złoczów. Two other pilots, one of whom was another Czechoslovak, landed and rescued František and his Polish observer.

For his Polish service František was awarded the Virtuti Militari 5th class and received the Cross of Valour four times.

On 22 September, František's unit was ordered to withdraw with its remaining aircraft to Romania. The unit flew first to Ispas in Bukovina, and then via various airfields eventually to Pipera near Bucharest, where it was interned by the Romanian authorities. But many interned members of the Polish Air Force escaped. They included a group of four Czechoslovak airmen nicknamed the "Czech Cloverleaf": František, Josef Balejka, Vilém Košař (one of the pilots who had landed to rescue František after his forced landing in Poland) and Matěj Pavlovič. The four went to Constanța, whence a Romanian cargo steamship, the Dacia, took them to Beirut in French-ruled Lebanon.

French Air Force
In Beirut, staff of the Czechoslovak Embassy came to meet them and explained their only options were to either join the French Foreign Legion or be deported to the Protectorate of Bohemia and Moravia. The four airmen joined the Legion at the local barracks. A week later, the four embarked on a Messageries Maritimes cargo ship, the Theophile Gautier, which landed them at Marseille on 20 October 1939. They continued training at the Foreign Legion base in Marseille. A Polish sergeant recognised their Polish war decorations and helped to get them released to join the new Free Polish Air Force at le Bourget.

Once in France, escaped Czechoslovak airmen were being retrained to fly l'Armée d'Air equipment. Košař was a naturalised Polish citizen but with Balejka, František and Pavlovič went to see the Czechoslovak Air Attaché to ask to be transferred to join fellow Czechoslovaks in l'Armée d'Air. The attaché accused them of deserting the Foreign Legion, so František accused the Czechoslovak Air Force of failing to evacuate its aircraft to Poland when Germany invaded in March 1939, whereupon the attaché called the French police. The police found the trio's Polish military identity documents to be in order and refused to arrest them. Balejka, František and Pavlovič remained with their Free Polish units.

František was posted to a Polish airbase at Clermont-Ferrand where he served as a mechanic. He tried to learn to fly as many types of French aircraft as he could. He also got into trouble several times for going absent without leave. There are no official French records to confirm he flew combat missions during the Battle of France, though some older sources credit him with 11 victories: nine in the air and two on the ground. In his home town of Otaslavice there is a museum in his memory and its collection of his medals includes a Croix de Guerre. His French Air Force records are known to have been destroyed, so there is no official confirmation of whether or why the cross was awarded to him.

Royal Air Force

After France surrendered, František fled to Britain and after training on 2 August was assigned to Polish No. 303 Squadron based at RAF Northolt, flying Hawker Hurricane fighters. František was used to obsolescent aircraft with fixed landing gear, and on 8 August at the end of a training flight, he forgot to lower his Hurricane's retractable undercarriage and accidentally made a belly landing. He was unhurt, and the aircraft was repairable. The squadron entered action in the last phase of the Battle of Britain. František's first confirmed victory was shooting down a Messerschmitt Bf 109E fighter on 2 September 1940. His fifth victory nearly cost him his life. On 6 September he shot down a Bf 109E of III/JG 52 near Sevenoaks in Kent, but František's Hurricane was damaged so badly that he had to make a forced landing near Falmer.

An unruly pilot, he was seen by his commanding officers as a danger to his colleagues when flying in formation. His British CO, Squadron Leader Ronald Kellett, offered to get František transferred to a Czech squadron. František, perhaps due to his clash with the Czechoslovak air attaché in Paris, chose to stay with his Polish colleagues. As all pilots were valuable, a compromise was reached whereby František was allotted a "spare" aircraft so he could fly as a "guest" of the squadron as and when he wanted. Thus František fought his own private war – accompanying the squadron into the air and peeling off to fly a lone patrol over Kent, patrolling in the area through which he knew the German aircraft being intercepted would fly on their way back to base, possibly damaged and low on fuel and ammunition.

Between 2 and 30 September he shot down 17 German aircraft and 1 probable, including nine Bf 109 fighters, six Heinkel He 111 bombers and one Junkers Ju 88 bomber. This made him one of the top scoring Allied fighter pilots of the Battle of Britain and on 20 September, King George VI decorated him with the Distinguished Flying Medal. A bar was later added to his DFM. His final confirmed victory was a Bf 109 near Brooklands in Surrey on 30 September 1940.

On 8 October 1940, František's Hurricane crashed in Ewell, Surrey, on return from a patrol. The cause is not known. It has been suggested that he may have been making aerobatic figures to impress his girlfriend, who lived nearby, or it might have been a result of battle fatigue and physical exhaustion. František is buried in the military section of Northwood cemetery in Middlesex, with a Polish headstone and alongside Polish and British RAF colleagues.

Legacy

František was the first non-British pilot to have a bar added to his Distinguished Flying Medal when he posthumously received one on 28 October 1940. In 1942, Air Vice-Marshal Karel Janoušek called František an "almost legendary figure". Janoušek also quoted the anonymous author of the 1941 book Together we Fly, A Salute to Airmen, who called František "the greatest of all Czechoslovak pilots, perhaps one of the greatest fighters of all time". In Otaslavice there is a museum in František's memory, a monument outside the František family home, and a plaque outside the local primary school. A street in the Černý Most suburb of Prague is named "Františkova" after him. The centenary of his birth was commemorated in Otaslavice on 4 October 2014. On 6 October 2015 the Polish Institute in Prague commemorated the 75th anniversary of František's death. Wreaths and floral tributes continue to be laid on his birthday each year at the monument outside the family home in Otaslavice. On 4 September 2022 a memorial was unveiled on Priest Hill in Ewell, England, not far from the place he died.

Honours and awards

 * POL Virtuti Militari Srebrny BAR.svg Virtuti Militari Silver Cross (Poland)
 * POL Krzyż Walecznych 4r BAR.svg Cross of Valour 4 times (Poland)
 * Croix de guerre 1939-1945 with palm (France) - ribbon bar.png Croix de guerre with palm leaf (France)
 * DFM w Bar ribbon.svg Distinguished Flying Medal and bar (United Kingdom) (1 Oct. 1940, 28 Oct. 1940)
 * 1939-45 Star & Battle of Britain clasp.png 1939–1945 Star with Battle of Britain clasp
 * Czechoslovak War Cross 1939-1945 Bar.png Czechoslovak War Cross 1939–1945
 * TCH CS Medaile Za chrabrost pred nepritelem BAR.svg Československá medaile Za chrabrost před nepřítelem ("Bravery in Face of the Enemy")
 * TCH CS Voj Med Za Zasluhy ribbon.svg Československá medaile za zásluhy, 2. stupně ("Medal of Merit, Second Class")

Posthumously the president of Czech Republic, Miloš Zeman awarded him the Order of the White Lion 1st Class Military Division on 28 Oct. 2015. In 2017, the Czech Mint issued silver and gold commemorative coins (under the authority of Niue) paying tribute to Josef František.

In popular culture
Josef František was portrayed by Kryštof Hádek in the 2018 film Hurricane: 303 Squadron. He was also referenced by Polish rock band Elektryczne Gitary in the song "Pilot Josef František", as a part of their 2016 album "Czasowniki".

title: Josef František


text:
Talk:Tubal-Cain

It is made a blunder here. This is discussed under "Tubalcain." The two articles should be merged.

 * Done. IZAK 06:51, 16 Aug 2004 (UTC)

Brazil?
I'm not deleting this line yet, but what substantiation is there for the statement in the article that the posited form Barzillah "can possibly be linked to the country of Brazil"? The "references" listed by the editor who added this line (User:68.187.223.195, who has edited nothing else on WP) have the odor of crank about them. -EDM 20:08, 17 Jun 2005 (UTC)

I've deleted the last paragraph of the article, for being so incorret and foolish.

POV
The author here seems to be making every effort to prove that the biblical story corresponds somehow with reality. This is POV and doesn't belong in an encyclopedia.

title: Talk:Tubal-Cain


text:
Evolute

In the differential geometry of curves, the evolute of a curve is the locus of all its centers of curvature. That is to say that when the center of curvature of each point on a curve is drawn, the resultant shape will be the evolute of that curve. The evolute of a circle is therefore a single point at its center. Equivalently, an evolute is the envelope of the normals to a curve.

The evolute of a curve, a surface, or more generally a submanifold, is the caustic of the normal map. Let $M$ be a smooth, regular submanifold in $R^{n}$. For each point $p$ in $M$ and each vector $v$, based at $p$ and normal to $M$, we associate the point $p + v$. This defines a Lagrangian map, called the normal map. The caustic of the normal map is the evolute of $M$.

Evolutes are closely connected to involutes: A curve is the evolute of any of its involutes.

History
Apollonius (c. 200 BC) discussed evolutes in Book V of his Conics. However, Huygens is sometimes credited with being the first to study them (1673). Huygens formulated his theory of evolutes sometime around 1659 to help solve the problem of finding the tautochrone curve, which in turn helped him construct an isochronous pendulum. This was because the tautochrone curve is a cycloid, and the cycloid has the unique property that its evolute is also a cycloid. The theory of evolutes, in fact, allowed Huygens to achieve many results that would later be found using calculus.

Evolute of a parametric curve
If $$\vec x= \vec c(t),\; t\in [t_1, t_2]$$ is the parametric representation of a regular curve in the plane with its curvature nowhere 0 and $$\rho(t)$$ its curvature radius and $$\vec n(t)$$ the unit normal pointing to the curvature center, then $$\vec E(t) = \vec c(t) + \rho (t) \vec n(t)$$ describes the evolute of the given curve.

For $$\vec c(t)=(x(t),y(t))^\mathsf{T}$$ and $$\vec E=(X,Y)^\mathsf{T}$$ one gets $$ X(t) = x(t) - \frac{y'(t) \Big(x'(t)^2+y'(t)^2\Big)}{x'(t) y(t) - x(t) y'(t)}$$ and $$ Y(t) = y(t) + \frac{x'(t) \Big(x'(t)^2+y'(t)^2\Big)}{x'(t) y(t) - x(t) y'(t)}.$$

Properties of the evolute
In order to derive properties of a regular curve it is advantageous to use the arc length $$s$$ of the given curve as its parameter, because of $\left|\vec c'\right| = 1$  and $\vec n' = -\vec c'/\rho$  (see Frenet–Serret formulas). Hence the tangent vector of the evolute $\vec E=\vec c +\rho \vec n $ is: $$\vec E' = \vec c' +\rho'\vec n + \rho\vec n' = \rho'\vec n\ .$$ From this equation one gets the following properties of the evolute:
 * At points with $$\rho' = 0$$ the evolute is not regular. That means: at points with maximal or minimal curvature (vertices of the given curve) the evolute has cusps. (See the diagrams of the evolutes of the parabola, the ellipse, the cycloid and the nephroid.)
 * For any arc of the evolute that does not include a cusp, the length of the arc equals the difference between the radii of curvature at its endpoints. This fact leads to an easy proof of the Tait–Kneser theorem on nesting of osculating circles.
 * The normals of the given curve at points of nonzero curvature are tangents to the evolute, and the normals of the curve at points of zero curvature are asymptotes to the evolute. Hence: the evolute is the envelope of the normals of the given curve.
 * At sections of the curve with $$\rho' > 0$$ or $$\rho' < 0$$ the curve is an involute of its evolute. (In the diagram: The blue parabola is an involute of the red semicubic parabola, which is actually the evolute of the blue parabola.)

Proof of the last property:

Let be $$\rho' > 0$$ at the section of consideration. An involute of the evolute can be described as follows: $$\vec C_0=\vec E -\frac{\vec E'}{\left|\vec E'\right|} \left(\int_0^s\left|\vec E'(w)\right| \mathrm dw + l_0 \right) ,$$ where $$l_0$$ is a fixed string extension (see Involute of a parameterized curve ).

With $$\vec E=\vec c +\rho\vec n\; ,\; \vec E'=\rho'\vec n$$ and $$\rho'>0$$ one gets $$\vec C_0 = \vec c +\rho\vec n-\vec n \left(\int_0^s \rho'(w) \; \mathrm dw \;+l_0\right)= \vec c + (\rho(0) - l_0)\; \vec n\, .$$ That means: For the string extension $$l_0=\rho(0)$$ the given curve is reproduced.

 * Parallel curves have the same evolute.

Proof: A parallel curve with distance $$d$$ off the given curve has the parametric representation $$\vec c_d = \vec c + d\vec n$$ and the radius of curvature $$\rho_d=\rho -d$$ (see parallel curve). Hence the evolute of the parallel curve is $$\vec E_d = \vec c_d +\rho_d \vec n =\vec c +d\vec n +(\rho -d)\vec n=\vec c +\rho \vec n = \vec E\; .$$

Evolute of a parabola
For the parabola with the parametric representation $$(t,t^2)$$ one gets from the formulae above the equations: $$X=\cdots=-4t^3$$ $$Y=\cdots=\frac{1}{2} + 3t^2 \, ,$$ which describes a semicubic parabola

Evolute of an ellipse
For the ellipse with the parametric representation $$(a\cos t, b\sin t)$$ one gets: $$X= \cdots = \frac{a^2-b^2}{a}\cos ^3t$$ $$Y= \cdots = \frac{b^2-a^2}{b}\sin ^3t \; .$$ These are the equations of a non symmetric astroid. Eliminating parameter $$t$$ leads to the implicit representation $$(aX)^{\tfrac{2}{3}} +(bY)^{\tfrac{2}{3}} = (a^2-b^2)^{\tfrac{2}{3}}\ .$$

Evolute of a cycloid
For the cycloid with the parametric representation $$(r(t - \sin t), r(1 - \cos t))$$ the evolute will be: $$X=\cdots=r(t + \sin t)$$ $$Y=\cdots=r(\cos t - 1)$$ which describes a transposed replica of itself.

Evolute of log-aesthetic curves
The evolute of a log-aesthetic curve is another log-aesthetic curve. One instance of this relation is that the evolute of an Euler spiral is a spiral with Cesàro equation $$\kappa(s) = -s^{-3}$$.

Evolutes of some curves
The evolute
 * of a parabola is a semicubic parabola (see above),
 * of an ellipse is a non symmetric astroid (see above),
 * of a line is an ideal point,
 * of a nephroid is a nephroid (half as large, see diagram),
 * of an astroid is an astroid (twice as large),
 * of a cardioid is a cardioid (one third as large),
 * of a circle is its center,
 * of a deltoid is a deltoid (three times as large),
 * of a cycloid is a congruent cycloid,
 * of a logarithmic spiral is the same logarithmic spiral,
 * of a tractrix is a catenary.

Radial curve
A curve with a similar definition is the radial of a given curve. For each point on the curve take the vector from the point to the center of curvature and translate it so that it begins at the origin. Then the locus of points at the end of such vectors is called the radial of the curve. The equation for the radial is obtained by removing the $x$ and $y$ terms from the equation of the evolute. This produces $$(X, Y)= \left(-y'\frac{{x'}^2+{y'}^2}{x'y-xy'}\; ,\; x'\frac{{x'}^2+{y'}^2}{x'y-xy'}\right) .$$

title: Evolute


text:
Emtricitabine

Emtricitabine (commonly called FTC, systematic name 2',3'-dideoxy-5-fluoro-3'-thiacytidine ), with trade name Emtriva (formerly Coviracil), is a nucleoside reverse-transcriptase inhibitor (NRTI) for the prevention and treatment of HIV infection in adults and children. In 2019, it was the 494th most commonly prescribed medication in the United States, with more than 3thousand prescriptions.

Emtricitabine makes up one fourth of the Quad pill (brand names: Stribild and Genvoya). It is also marketed in a fixed-dose combination with tenofovir disoproxil (Viread) under the brand name Truvada, and with tenofovir alafenamide (Vemlidy) under the brand name Descovy. In fixed-dose combinations with tenofovir or with efavirenz and tenofovir it is on the World Health Organization's List of Essential Medicines. A fixed-dose triple combination of emtricitabine, tenofovir and efavirenz (Sustiva, marketed by Bristol-Myers Squibb) was approved by the U.S. Food and Drug Administration (FDA) on July 12, 2006, under the brand name Atripla.

HIV infection
Emtricitabine is indicated in combination with other antiretroviral agents for the prevention and treatment of HIV-1 infection.

HBV infection
Emtricitabine exhibits clinical activity against the hepatitis B virus (HBV), but is not approved by the U.S. Food and Drug Administration (FDA) for the treatment of HBV infection. Among individuals with chronic HBV infection, emtricitabine treatment results in significant histologic, virologic, and biochemical improvement. The safety profile of emtricitabine during treatment is similar to that of a placebo. Emtricitabine, like all other FDA approved drugs, cures neither HIV nor HBV infection. In a study involving individuals with HBV infection, symptoms of infection returned in 23% of emtricitabine-treated individuals who were taken off therapy. In studies involving individuals with chronic HIV infection, viral replication also resumes when study subjects are taken off therapy. As with drugs used to treat HIV infection, drugs used to treat HBV infection may have to be used in combination to prevent the evolution of drug resistant strains. The effectiveness of emtricitabine in combination with other anti-HBV drugs has not been established.

Side effects
In clinical practice, toxicity with emtricitabine is unusual. The most common treatment-related adverse events are diarrhea, headache, nausea, and rash. These symptoms are generally mild to moderate in severity, but they caused 1% of clinical trial patients to give up treatment. Skin discoloration, which is typically reported as hyperpigmentation and usually affects either the palms of the hands or the soles of the feet, is reported in less than 2% of individuals and is almost exclusive to patients of African origin.

Among the more severe side effects patients may experience are a hepatotoxicity or a lactic acidosis.

Mechanism of action
Emtricitabine is an analogue of cytidine. The drug works by inhibiting reverse transcriptase, the enzyme that copies HIV RNA into new viral DNA. By interfering with this process, which is central to the replication of HIV, emtricitabine can help to lower the amount of HIV, or "viral load", in a patient's body and can indirectly increase the number of immune system cells (namely T cells/CD4+ T-cells). Both of these changes are associated with healthier immune systems and decreased likelihood of serious illness.

History
Emtricitabine was discovered by Dennis C. Liotta, Raymond F. Schinazi, and Woo-Baeg Choi of Emory University and licensed to Triangle Pharmaceuticals by Emory in 1996. Triangle Pharmaceuticals was acquired in 2003 by Gilead Sciences, which completed development and now markets the product with the brand name Emtriva.

It was approved by the FDA July 2, 2003. It is very similar to lamivudine (3TC) and cross-resistance between the two is near-universal.

title: Emtricitabine