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Parallelogram

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure; the congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations. By comparison, a quadrilateral with just one pair of parallel sides is a trapezoid in American English or a trapezium in British English; the three-dimensional counterpart of a parallelogram is a parallelepiped. The etymology reflects the definition. Rhomboid – A quadrilateral whose opposite sides are parallel and adjacent sides are unequal, whose angles are not right angles Rectangle – A parallelogram with four angles of equal size. Rhombus – A parallelogram with four sides of equal length. Square – A parallelogram with four sides of equal length and angles of equal size.

A simple quadrilateral is a parallelogram if and only if any one of the following statements is true: Two pairs of opposite sides are parallel. Two pairs of opposite sides are equal in length. Two pairs of opposite angles are equal in measure; the diagonals bisect each other. One pair of opposite sides equal in length. Adjacent angles are supplementary; each diagonal divides the quadrilateral into two congruent triangles. The sum of the squares of the sides equals the sum of the squares of the diagonals, it has rotational symmetry of order 2. The sum of the distances from any interior point to the sides is independent of the location of the point. There is a point X in the plane of the quadrilateral with the property that every straight line through X divides the quadrilateral into two regions of equal area, thus all parallelograms have all the properties listed above, conversely, if just one of these statements is true in a simple quadrilateral it is a parallelogram. Opposite sides of a parallelogram so will never intersect.

The area of a parallelogram is twice the area of a triangle created by one of its diagonals. The area of a parallelogram is equal to the magnitude of the vector cross product of two adjacent sides. Any line through the midpoint of a parallelogram bisects the area. Any non-degenerate affine transformation takes a parallelogram to another parallelogram. A parallelogram has rotational symmetry of order 2. If it has two lines of reflectional symmetry it must be a rhombus or an oblong. If it has four lines of reflectional symmetry, it is a square; the perimeter of a parallelogram is 2 where b are the lengths of adjacent sides. Unlike any other convex polygon, a parallelogram cannot be inscribed in any triangle with less than twice its area; the centers of four squares all constructed either internally or externally on the sides of a parallelogram are the vertices of a square. If two lines parallel to sides of a parallelogram are constructed concurrent to a diagonal the parallelograms formed on opposite sides of that diagonal are equal in area.

The diagonals of a parallelogram divide it into four triangles of equal area. All of the area formulas for general convex quadrilaterals apply to parallelograms. Further formulas are specific to parallelograms: A parallelogram with base b and height h can be divided into a trapezoid and a right triangle, rearranged into a rectangle, as shown in the figure to the left; this means that the area of a parallelogram is the same as that of a rectangle with the same base and height: K = b h. The base × height area formula can be derived using the figure to the right; the area K of the parallelogram to the right is the total area of the rectangle less the area of the two orange triangles. The area of the rectangle is K rect = × H and the area of a single orange triangle is K tri = 1 2 A × H. Therefore, the area of the parallelogram is K = K rect − 2 × K tri = − = B × H. Another area formula, for two sides B and C and angle θ, is K = B ⋅ C ⋅ sin ⁡ θ; the area of a parallelogram with sides B and C and angle γ at the intersection of the diagonals is given by K = | tan ⁡ γ | 2 ⋅ | B 2 − C 2 |.

When the parallelogram is specified from the lengths B and C of two adjacent sides together with t

Nvidia System Tools

NVIDIA System Tools is a discontinued collection of utilities for accessing and adjusting system components, including temperature and voltages with a graphical user interface within Windows, rather than through the BIOS. Additionally, System Tools has a feature that automatically adjusts settings and tests them to find what it believes to be the optimal combination of settings for a particular computer hardware configuration. Everything, including the graphics processing unit, central processing unit, Media Communications Processor, RAM, voltage and fans are adjusted, though not all motherboards support all of these adjustment options. Configurations can be saved; this allows the end user to toggle between performance gaming profiles, quiet profiles for less demanding work, or some other profile, usage-specific. NVIDIA System Tools is a front end for the BIOS. Most settings that can be changed in the BIOS are available in the utilities included. BIOS and driver updates to both nForce and GeForce hardware can be done through System Tools.

It additionally supports hardware, certified under the Enthusiast System Architecture and connects to the motherboard via USB. The following chipsets were supported in nTune releases, but are no longer supported by NVIDIA System Tools. NForce 220, nForce 220D, nForce 415 and nForce 420D nForce2 and nForce2 400 nForce2 Ultra and nForce2 Ultra 400 nForce2 400R and nForce2 Ultra 400Gb nForce3 150 and nForce3 PRO 150 nForce3 250, nForce3 250Gb and nForce3 PRO 250 nForce4 Pro 2200, nForce4 Ultra, nForce4 SLI, nForce4 SLI x16 nForce 590 SLI, nForce 570 SLI, nForce 570 LT SLI, nForce 570 Ultra, nForce 560, nForce 550, nForce 520, nForce 520 LE nForce 680a SLI, nForce 680i SLI, nForce 680i LT SLI, nForce 650i SLI, nForce 650i Ultra, nForce 630a, nForce 630i, nForce 610i nForce 790i Ultra SLI, nForce 790i SLI, nForce 780a SLI, nForce 780i SLI, nForce 750a SLI, nForce 750i SLI, nForce 730a, nForce 720a, nForce 710a The following GPUs are supported for overclocking and temperature monitoring. GeForce 5 GeForce 6 GeForce 7 GeForce 8 GeForce 9 GeForce 200 GeForce 300 GeForce 400 GeForce 500

Gwen Nelson

Gwendoline Alexandra Nelson was an English actress, a member of the Royal Shakespeare Company and the Royal Court Theatre Company. Born in Muswell Hill, she intended to be a singer, made her West End musical debut in Tough at the Top at the Adelphi Theatre in July 1949, she went on to act in Eleanor Farjeon's The Silver Curlew at London's Arts Theatre, And So To Bed at the New Theatre, Oh, My Papa at the Garrick Theatre, Virtue in Danger, All in Love at The May Fair Theatre, Saved at the Royal Court Theatre. In 1976 she appeared in a revival of Arnold Ridley's The Ghost Train at the Old Vic Theatre in London with Wilfrid Brambell, James Villiers, Geoffrey Davies, Allan Cuthbertson and Judy Buxton. In 1981 she acted in Rose by Andrew Davies at the Richmond Theatre in Surrey with Honor Blackman and Hilda Braid, her television appearances included Z-Cars, No Hiding Place, ITV Playhouse and Hopkirk, Jude the Obscure, Clochemerle and Son, Looking For Clancy, Juliet Bravo and June, Shine on Harvey Moon, Clarence, Hill Street Blues, Ruth Rendell Mysteries.

She acted in the films Ah, Wilderness!, Laugh With Me, The Teckman Mystery, Tunes of Glory, A Kind of Loving, Stolen Hours, Doctor Zhivago, The Reckoning, Say Hello to Yesterday, Love Among the Ruins, It Shouldn't Happen to a Vet, The Last Remake of Beau Geste, National Lampoon's European Vacation and 84 Charing Cross. Nelson's last appearance was in an episode of The Bill in 1989, she died of natural causes in Suffolk, aged 89. Ah, Wilderness! - Aunt Lily Laugh With Me - Ann Bonnington The Teckman Mystery - Duty woman The Entertainer Tunes of Glory - Provost's Wife The Kitchen - 8th Waitress A Kind of Loving - Mrs. Brown Don't Talk to Strange Men - Mrs. Mason Stolen Hours - Hospital Sister The Three Lives of Thomasina - Ms. McCloud Doctor Zhivago - Female Janitor Staircase - Matron The Reckoning - Marler's Mother Say Hello to Yesterday - Char Something to Hide - 2nd Old Lady Love Among the Ruins - Hermione Davis It Shouldn't Happen to a Vet - Mrs. Kirby The Last Remake of Beau Geste - Lady in Courtroom National Lampoon's European Vacation - Hotel Manager's Mother 84 Charing Cross - Bill's Great Aunt Gwen Nelson on IMDb Gwen Nelson.

Logic in China

Formal logic in China has a special place in the history of logic due to its repression and abandonment—in contrast to the strong ancient adoption and continued development of the study of logic in Europe and the Islamic world. In China, a contemporary of Confucius, Mozi, "Master Mo", is credited with founding the Mohist school, whose canons dealt with issues relating to valid inference and the conditions of correct conclusions. However, they were not integrated into Chinese science or mathematics; the Mohist school of Chinese philosophy contained an approach to logic and argumentation that stresses rhetorical analogies over mathematical reasoning, is based on the three fa, or methods of drawing distinctions between kinds of things. One of the schools that grew out of Mohism, the Logicians, are credited by some scholars for their early investigation of formal logic. During the subsequent Qin Dynasty, the rule of Legalism repressed this Mohist line of investigation, said to have disappeared in China until the introduction of Indian philosophy and Indian logic by Buddhists.

A prominent scholar suggests that the version assembled for the Imperial Library of the Han Dynasty would have been as disorganised as the current extant text, thus would have only been'intermittently intelligible', as it is for current readers who do not consult a critical edition. Disagreeing with Hajime Nakamura, Graham argues the school of Neo-Taoism maintained some interest in the Canons, although they may have some of the terminology difficult to understand. Before the end of the Sui Dynasty, a shortened version of Mozi appeared, which appears to have replaced the Han edition. Although the original Mozi had been preserved in the Taoist, became known once more in the 1552 Lu edition and 1553 Tang edition, the damage was done: the dialectical chapters were considered incomprehensible. With the rise of Chinese critical textual scholarship, the book benefited from explanatory and critical commentaries: first, by Bi Yuan, his assistant, Sun Xingyan. However, the summit of this late Imperial scholarship, according to Graham, was the'magnificent' commentary of Sun Yirang, which'threw open the sanctum of the Canons to all comers.

Graham summarises the arduous textual history of the Canons by arguing that the Canons were neglected throughout most of China's history. The study of logic in China was revived following the transmission of Buddhism in China, which introduced the Buddhist logical tradition that began in Indian logic. Buddhist logic has been misunderstood by scholars of Chinese Buddhism because they lack the necessary background in Indian logic. Chmielewski, Notes on Early Chinese Logic, Rocznik Orientalistyczny 26.1: 7-22. Chmielewski, Janusz, 2009. Language and Logic in Ancient China, Collected Papers on the Chinese Language and Logic, edited by Marek Mejor, Warswa: PAN. Graham, Angus Charles, 2003. Mohist Logic and Science, Hong Kong: Chinese University Press. Greniewski and Wojtasiewicz, Olgierd, 1956. From the History of Chinese Logic, Studia Logica Vol. 4, 1, pp. 241–243. Harbsmeier, Christopher, 1998. Language and Logic. Volume 7, Part 1 of Science and Civilisation in China, edited by Joseph Needham, Cambridge: Cambridge University Press.

Hansen, Chad, 1983. Language and Logic in Ancient China. Michigan Studies on China. Ann Arbor. Kurtz, Joachim 2011; the Development of Chinese Logic, Leiden: Brill. Lucas, Thierry, 1993. Hui Shih and Kung Sun Lung: an Approach from Contemporary Logic, Journal of Chinese Philosophy 20.2: 211-55. Lucas, Thierry, 2005. Mohist Logic, Lei and Sorts, Journal of Chinese Philosophy 32: 349-366. Rošker, Jana S. 2014. Specific features of Chinese logic. Synthesis philosophica, ISSN 1848-2317. Vol. 29, no. 1, pp. 23-40. Rošker, Jana S. 2015. Classical Chinese logic. Philosophy compass, ISSN 1747-9991, vol. 10, issue 5, pp. 301-309. Willman, Marshall. "Logic and Language in Early Chinese Philosophy". In Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Fraser, Chris. "Mohist Canons". In Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Fraser, Chris. "The School of Names". In Zalta, Edward N.. Stanford Encyclopedia of Philosophy. Mohist Dialecticians Language and Logic in Ancient China Synthesis philosophica, Vol.29 No.1, 2014 Jana Rosker, Classical Chinese Logic

Pedra Badejo

Pedra Badejo is a city in the eastern part of the island of Santiago, Cape Verde. It is situated on the east coast, 25 km north of the island capital Praia, 8 km southeast of Calheta de São Miguel and 15 km east of Assomada, it is the seat of Santa Cruz municipality. At the 2010 census, the town had 9,859 inhabitants. In 1971, Pedra Badejo became part of the new municipality of Santa Cruz and Pedra Badejo became its seat. In 2010, the town Pedra Badejo was awarded city status. There are a lot of shops in the Market Place. Many daytrippers from Praia visit the beach, close to the center of the city. A former health center close to the beach was transformed into a hotel. Pedra Badejo has a small fishing port and at least five churches: the modern Catholic Church is in the new, upper part of the city, the smaller New Apostolic Church is in Main Street. A Presbyterian Church, a Nazarene Church, a Baptist church serve the community. Southeast of the city are an important wetland area; the city is surrounded by irrigated land.

An artificial lake was laid out between the villages Poilão and Levada with a fill dam, completed in 2006. The reservoir has a capacity of 1.7 million cubic meters making the drip irrigation of 64 ha of land corresponding to about 100 farms possible. The construction of the first concrete dam of Cape Verde was planned by China. There is an information pavilion in the South of the artificial lake where some rare birds can be observed; the national road from Praia to Tarrafal via Calheta de São Miguel passes through Pedra Badejo. Minibus services connect the cities of Praia and Tarrafal, it is about 30 km from 33 km from the ferry port of Praia. Lito, former footballer manager of Sporting Praia Djaniny, footballer Elida Almeida, singer Presenting "Urban Profile" of the City of Pedra Badejo", RTC video, 2 November 2011

Grumman F8F Bearcat

The Grumman F8F Bearcat is an American single-engine carrier-based fighter aircraft introduced in late World War II. It served during the mid-20th century in the United States Navy, the United States Marine Corps, the air forces of other nations, it was Grumman Aircraft's last piston engined fighter aircraft. Modified versions have broken speed records for piston-engined aircraft, are popular among warbird owners and air racers; the Bearcat concept began during a meeting between Battle of Midway veteran F4F Wildcat pilots and Grumman Vice President Jake Swirbul at Pearl Harbor on 23 June 1942. At the meeting, Lieutenant Commander Jimmie Thach emphasized one of the most important requirements in a good fighter plane was "climb rate". Climb performance is related to the power-to-weight ratio, is maximized by wrapping the smallest and lightest possible airframe around the most powerful available engine. Another goal was that the G-58 should be able to operate from escort carriers, which were limited to the obsolescent F4F Wildcat as the Grumman F6F Hellcat was too large and heavy.

A small, lightweight aircraft would make this possible. After intensively analyzing carrier warfare in the Pacific Theater of Operations for a year and a half, Grumman began development of the G-58 Bearcat in late 1943. There is considerable debate among sources as to whether or not the Focke-Wulf Fw 190 influenced the design of the G-58, it is known that test pilots from Grumman examined and flew a captured Fw 190 in England in early 1943, the G-58 has a number of design notes in common with the Fw 190 that the Hellcat did not in the cowling and landing gear arrangements. However, no definitive evidence has been presented that these tests had a direct input to the G-58 design. In 1943, Grumman was in the process of introducing the F6F Hellcat, powered by the Pratt & Whitney R-2800 engine which provided 2,000 horsepower; the R-2800 was the most powerful American engine available at that time, so it would be retained for the G-58. This meant. To meet this goal, the Bearcat's fuselage was about 5 feet shorter than the Hellcat, was cut down vertically behind the cockpit area.

This allowed the use of the first to be fitted to a US Navy fighter. The vertical stabilizer was the same height as the Hellcat's, but increased aspect ratio, giving it a thinner look; the wingspan was 7 feet less than the Hellcat's. Structurally the fuselage used flush riveting as well as spot welding, with a heavy gauge 302W aluminum alloy skin suitable for carrier landings. Armor protection was provided for the pilot and oil cooler; the Hellcat used. A slight reduction in size was made by moving to a 12 ft 7 in Aeroproducts four-bladed propeller. Keeping the prop clear of the deck required long landing gear, combined with the shortened fuselage, gave the Bearcat a significant "nose-up" profile on land; the hydraulically operated undercarriage used an articulated trunnion which extended the length of the oleo legs when lowered. An additional benefit of the inward retracting units was a wide track, which helped counter propeller torque on takeoff and gave the F8F good ground and carrier deck handling.

The design team had set the goal that the G-58 should weigh 8,750 lb/3,969 kg loaded. As development continued it became clear this was impossible to achieve as the structure of the new fighter had to be made strong enough for aircraft carrier landings. Much of the weight-saving measures included restricting the internal fuel capacity to 160 gal and limiting the fixed armament to four.50 cal Browning M2/AN machine guns, two in each wing. The limited range due to the reduced fuel load would mean it would be useful in the interception role, but meant that the Hellcat would still be needed for longer range patrols. A role was defending the fleet against airborne kamikaze attacks. Compared to the Hellcat, the Bearcat was 20% lighter, had a 30% better rate of climb and was 50 mph faster. Another weight-saving concept the designers came up with was detachable wingtips; the wings were designed to fold at a point about ​2⁄3 out along the span, reducing the space taken up on the carrier. The hinge system would have to be built strong in order to transmit loads from the outer portions of the wing to the main spar in the inner section, which adds considerable weight.

Instead of building the entire wing to be able to withstand high-g loads, only the inner portion of the wing was able to do this. The outer portions were more constructed, designed to snap off at the hinge line if the g-force exceeded 7.5 g. In this case the aircraft would still be flyable and could be repaired after returning to the carrier; this saved 230 pounds of weight. The design was completed in November 1943 and an order for two prototypes was placed on 27 November 1943 under the BuAir designation XF8F-1; the first prototype flew on 21 August 1944. The initial flight test demonstrated a 4,800 feet per minute climb rate and a top speed of 424 miles per hour. Compared to the Vought F4U Corsair, the Bearcat was marginally slower but more maneuverable and climbed more quickly. Testing demonstrated a number of problems, notably a lack of horizontal stability, an underpowered trim system, landing gear that could be extended only at slow speeds, an unreliable airspeed indicator, a cramped cockpit.

The test pilots requested that six guns be inst