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Curve

In mathematics, a curve is an object similar to a line which does not have to be straight. Intuitively, a curve may be thought as the trace left by a moving point; this is the definition that appeared, more than 2000 years ago in Euclid's Elements: "The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, is nothing else than the flow or run of the point which will leave from its imaginary moving some vestige in length, exempt of any width."This definition of a curve has been formalized in modern mathematics as: A curve is the image of a continuous function from an interval to a topological space. In some context, the function that defines the curve is called a parametrization, the curve is a parametric curve. In this article, these curves are sometimes called topological curves for distinguishing them from more constrained curves such as differentiable curves; this definition encompasses most curves. Level curves and algebraic curves are sometimes called implicit curves, since they are defined by implicit equations.

The class of topological curves is broad, contains some curves that do not look as one may expect for a curve, or cannot been drawn. This is the case of fractal curves. For insuring more regularity, the function that defines a curve is supposed to be differentiable, the curve is said a differentiable curve. A plane algebraic curve is the zero set of a polynomial in two indeterminates. More an algebraic curve is the zero set of a finite set of polynomials, which satisfies the further condition of being an algebraic variety of dimension one. If the coefficients of the polynomials belong to a field k, the curve is said to be defined over k. In the common case of a real algebraic curve, where k is the field of real numbers, an algebraic curve is a finite union of topological curves; when complex zeros are considered, one has a complex algebraic curve, from the topologically point of view, is not a curve, but a surface, is called a Riemann surface. Although not being curves in the common sense, algebraic curves defined over other fields have been studied.

In particular, algebraic curves over a finite field are used in modern cryptography. Interest in curves began long before they were the subject of mathematical study; this can be seen in numerous examples of their decorative use in art and on everyday objects dating back to prehistoric times. Curves, or at least their graphical representations, are simple to create, for example by a stick in the sand on a beach; the term line was used in place of the more modern term curve. Hence the phrases straight line and right line were used to distinguish what are today called lines from curved lines. For example, in Book I of Euclid's Elements, a line is defined as a "breadthless length", while a straight line is defined as "a line that lies evenly with the points on itself". Euclid's idea of a line is clarified by the statement "The extremities of a line are points,". Commentators further classified lines according to various schemes. For example: Composite lines Incomposite lines Determinate Indeterminate The Greek geometers had studied many other kinds of curves.

One reason was their interest in solving geometrical problems that could not be solved using standard compass and straightedge construction. These curves include: The conic sections studied by Apollonius of Perga The cissoid of Diocles, studied by Diocles and used as a method to double the cube; the conchoid of Nicomedes, studied by Nicomedes as a method to both double the cube and to trisect an angle. The Archimedean spiral, studied by Archimedes as a method to trisect an angle and square the circle; the spiric sections, sections of tori studied by Perseus as sections of cones had been studied by Apollonius. A fundamental advance in the theory of curves was the introduction of analytic geometry by René Descartes in the seventeenth century; this enabled a curve to be described using an equation rather than an elaborate geometrical construction. This not only allowed new curves to be defined and studied, but it enabled a formal distinction to be made between algebraic curves curves that can be defined using polynomial equations, transcendental curves that cannot.

Curves had been described as "geometrical" or "mechanical" according to how they were, or could be, generated. Conic sections were applied in astronomy by Kepler. Newton worked on an early example in the calculus of variations. Solutions to variational problems, such as the brachistochrone and tautochrone questions, introduced properties of curves in new ways; the catenary gets its name as the solution to the problem of a hanging chain, the sort of question that became accessible by means of differential calculus. In the eighteenth century came the beginnings of the theory of plane algebraic curves, in general. Newton had studied the cubic curves, in the general description of the real points into'ovals'; the statement of Bézout's theorem showed a number of aspects which were not directly accessible to the geometry of the time, to do with singular points and complex solutions. Since the nineteenth century, curve theory is viewed as the special case of dimension one of the theory of manifolds and algebraic varieties.

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James Pinnock

James Pinnock is an English football player from Dartford, Kent. Pinnock came through the ranks at his local Football League side Gillingham, making 16 first team appearances in total. After loan spells at Margate, Dover Athletic and Chesham United, Pinnock moved permanently from Gillingham to Conference side Kingstonian where he spent two years before joining Gravesend & Northfleet. Pinnock spent two years at'The Fleet' before joining Welling United in 2005. Pinnock spent a year at Welling and moved onto Margate for whom he had played for on loan. Pinnock had his most fruitful goalscoring spell while at Margate, averaging nearly a goal every two games in the league. In the 2008 close season Pinnock made the short trip along the M2 to join Maidstone United. Pinnock stayed at Maidstone for nearly two years, however in March 2010 he and three other players controversially left the club to join Margate, meaning Pinnock was now playing in his third spell for the Thanet side. In the summer of 2011 Pinnock rejoined relegated Maidstone United where he joined up with Jay Saunders, made player-manager of the club.

Pinnock left the club in early 2012 after struggling to hold down a place in the first team

Short-tailed woodstar

The short-tailed woodstar is a species of hummingbird in the family Trochilidae. It is found in Peru, its natural habitat is subtropical or tropical dry shrubland where it is the only hummingbird of the woodstar variety. It feeds close to the ground and is attracted to flowers planted around houses. At 7 cm, it ties with the gorgeted woodstar as the smallest bird found in South America, though the little woodstar is scarcely longer; this bird is pale shining green with a small whitish patch on the sides of the lower back extending down to the lower flanks. The gorget is glittering violet, bordered at the sides by white malar streaks and below by a white pectoral collar extending onto the sides of the neck; the underparts are all whitish. The tail is short and black; the female and male plumages are similar but the female has no white on the lower back and is uniform pale buffy below. "The Birds of Ecuador" by Robert S. Ridgely & Paul Greenfield. Cornell University Press, ISBN 978-0-8014-8722-4

Afghanistan at the 2008 Summer Olympics

Afghanistan sent a team to compete at the 2008 Summer Olympics in Beijing, China. The team consisted of one woman. Mehboba Ahdyar prepared to run the 800 metres and 1500 metres, but left her training camp on June 4 to seek political asylum in Norway; the country was represented by two competitors in athletics, two in taekwondo. Afghanistan won its first Olympic medal at these games, with Rohullah Nikpai taking bronze in men's 58 kg taekwondo. Competitors in athletics events could qualify for the next round of competition in two ways. Qualifying by right involved ranking high enough in their heat, qualifying by result meant ranking high enough in overall standings. Ranks shown are therefore those within each heat, not in overall standings. KeyNote–Ranks given for track events are within the athlete's heat only Q = Qualified for the next round q = Qualified for the next round as a fastest loser or, in field events, by position without achieving the qualifying target NR = National record N/A = Round not applicable for the event Bye = Athlete not required to compete in round MenWomen

Ferdinando Gorges

Sir Ferdinando Gorges was a naval and military commander and governor of the important port of Plymouth in England. He was involved in Essex's Rebellion against the Queen, but escaped punishment by testifying against the main conspirators, his early involvement in English trade with and settlement of North America as well as his efforts in founding the Province of Maine in 1622 earned him the title of the "Father of English Colonization in North America," though Gorges himself never set foot in the New World. Ferdinando Gorges was born between 1565 and 1568 in Clerkenwell, in Middlesex where the family maintained their London town house, but at the family's manor of Wraxall, in Somerset, he was the second son of Edward Gorges of Wraxall, by his wife Cicely Lygon. The circumstances of his father's death aged 31 suggested to Baxter that Ferdinando was born at about the time of his father's death on 29 August 1568. Edward Gorges, evidently realizing that his illness was fatal, prepared his will on 10 August 1568, in which Edward bequeathed to Ferdinando a 23-ounce gold watch and devised to him the manor of Birdcombe, for a term of 24 years.

The terms of the testamentary gifts led an earlier memorialist to conclude that Ferdinando had been born sometime between 1565 and 1567. Ferdinando Gorges was by blood in the male line a member of the Russell family of Kingston Russell, Dorset and of Dyrham in Gloucestershire, an early member of, Sir John Russell of Kingston Russell, a household knight of King John, of the young King Henry III, to whom he acted as steward; however the last male of the ancient Anglo-Norman Gorges family, about to die childless, bequeathed his estates, including Wraxall, to Theobald Russell, a younger son of his sister Eleanor Russell, on condition that he should adopt the name and arms of Gorges. Ferdinando was a descendant of this Theobald Russell "Gorges"; the Gorges family arrived in England with the Norman invasion. The male line of the Gorges family died out in 1331 on the death of Ralph de Gorges, 2nd Baron Gorges, of Knighton, Isle of Wight, they were said to have lived in Somersetshire from the time of King Henry I and held their estates in Wraxall since the time of King Edward II.

The Gorges were recipients of many royal privileges since Edward's time. Ferdinando's great-great-grandfather married the eldest daughter of John Howard, 1st Duke of Norfolk, from which connection they claim royal descent. Ferdinando's father Edward Gorges, as first born, became the heir of the family estate in Wraxal when his father died in 1558 when he was 21. Notwithstanding the family tradition in royal offices, neither Edward nor his father Edmund took part in public affairs. Ferdinando's mother was Cecily Lygon, a daughter of William Lygon of Madresfield, Worcestershire, by his wife Eleanor Denys, a daughter of Sir William Denys of Dyrham, High Sheriff of Gloucestershire, whose family was the heir of the Russells of Dyrham, a descendant of which family in a direct male line was Ferdinando Gorges. Among their descendants were the Earls Beauchamp. Ferdinando Gorges was named after Ferdinando Lygon. After the death of Edward Gorges, Cecily married John Vivian of Brydges. Ferdinando's only sibling was his older brother Edward, baptized at Wraxall on 5 September 1564.

Edward entered Hart's College, Oxford, in 1582. Little documentation exists regarding his early life and education, he was brought up at Nailsea Court at Kenn near Wraxall. Although as far as is known Ferdinando had no direct connection with the Court in his youth, he could not have been impervious to two great cultural currents of the time: the growing resistance to the absolute power of the monarchy in ecclesiastical matter, sometimes subsumed under the concept of "Puritanism", the beginnings of English exploration and exploitation of the Western Hemisphere, the latter owing to his distant family connections with Humphrey Gilbert and his half-brother Walter Raleigh. No documentary evidence records Gorges's activities before 1587, but because in that year he is referred to as a captain, it is probable that he took up the profession of arms several years before perhaps in his mid-teens, it is that he was engaged in active duty shortly after the outbreak of the Anglo-Spanish War in 1585. In 1587 he was one of the "several eminent chieftains" commanding the 800 soldiers sent from Flushing by Sir William Russell to aid the Earl of Leicester's attempt to relieve the Siege of Sluis laid by the Spanish Governor General of the Netherlands, whose revolt against the Spanish Habsburg rule England had pledged to aid.

Gorges fought under the command of Lord Willoughby, whose family he developed a close connection with. It is unknown whether he was captured during that engagement or but by September 1588 he was listed as among the prisoners at Lisle, for his name is among those English prisoners who friends in England petitioned to have Spanish prisoner exchanged for. In 1589 Gorges was wounded at the siege of Paris, he was knighted at the siege of Rouen in 1591. He was rewarded for his services by the post of Governor of the Fort at Plymouth, which he held for many years. During the Spanish Armada of 1597 Gorges was able to raise the alarm that enabled the defence of the country, but autumn storms made sure that the Spanish fleet was dispersed. In 1601, he became involved in the Essex Conspirac

Heterorachis

Heterorachis is a genus of moths in the family Geometridae described by Warren in 1898. Heterorachis abdita Herbulot, 1955 Heterorachis acuta Herbulot, 1955 Heterorachis amplior Herbulot, 1955 Heterorachis asyllaria Heterorachis carpenteri Heterorachis conradti Prout, 1938 Heterorachis defossa Herbulot, 1955 Heterorachis despoliata Prout, 1916 Heterorachis devocata Heterorachis diaphana Heterorachis dichorda Prout, 1915 Heterorachis diphrontis Prout, 1922 Heterorachis disconotata Prout, 1916 Heterorachis extrema Herbulot, 1996 Heterorachis fulcrata Herbulot, 1996 Heterorachis furcata Herbulot, 1965 Heterorachis fuscoterminata Prout, 1915 Heterorachis gloriola Thierry-Mieg, 1915 Heterorachis haploa Heterorachis harpifera Herbulot, 1955 Heterorachis idmon Fawcett, 1916 Heterorachis insolens Heterorachis insueta Prout, 1922 Heterorachis lunatimargo Heterorachis malachitica Heterorachis melanophragma Prout, 1918 Heterorachis perviridis Heterorachis platti Janse, 1935 Heterorachis prouti Heterorachis reducta Herbulot, 1955 Heterorachis simplicissima Heterorachis soaindrana Herbulot, 1972 Heterorachis suarezi Herbulot, 1965 Heterorachis tanala Herbulot, 1965 Heterorachis tornata Prout, 1922 Heterorachis trita Prout, 1922 Heterorachis tsara Viette, 1971 Heterorachis turlini Herbulot, 1977 Heterorachis ultramarina Herbulot, 1968 Heterorachis viettei Herbulot, 1955 Warren, W..

"New species and genera of the families Drepanulidae, Uraniidae and Geometridae from the Old-World regions". Novitates Zoologicae. 5: 221–258. De Prins, J. & De Prins, W.. "Heterorachis Warren, 1898". Afromoths. Retrieved April 19, 2019. Pitkin, Brian & Jenkins, Paul. "Search results Family: Geometridae". Butterflies and Moths of the World. Natural History Museum, London