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The Duckport Canal was an unsuccessful military venture by Union forces during the Vicksburg campaign of the American Civil War. Ordered built in late March 1863 by Major General Ulysses S. Grant, the canal stretched from the Mississippi River near Duckport, Louisiana, to New Carthage, Louisiana, and utilized a series of swampy bayous for much of its path. It was intended to provide a water-based supply route for a southward movement against the Confederate-held city of Vicksburg, Mississippi, as high water levels made overland travel difficult. Manual digging was provided by 3,500 soldiers from Grant's army and was finished on April 12. The next day, the levee separating the canal cut and the Mississippi River was breached, and water flowed into the canal. Trees that had grown up in the bayous and falling water levels that reached as shallow as 6 inches (15 cm) at one point hampered the use of the canal, and the project was abandoned on May 4. Grant moved men and supplies through the overland route, which had been made more accessible by the same falling water levels that doomed the canal. After some inland maneuvering and a lengthy siege, Vicksburg surrendered on July 4, marking a significant turning point in the war.
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The 1876 FA Cup final was an association football match between Wanderers F.C. and Old Etonians F.C. on 11 March 1876 at Kennington Oval in London. It was the fifth final of the world's oldest football competition, the Football Association Challenge Cup (known in the modern era as the FA Cup). The Wanderers had won the Cup on two previous occasions. The Etonians were playing in their second consecutive final, having lost in the 1875 match after a replay. Both teams had conceded only one goal in the four rounds of the competition prior to the final. In the semi-finals, the Wanderers defeated the Swifts and the Etonians beat the 1874 Cup winners Oxford University.
The match ended in a 1–1 draw, the second consecutive FA Cup final to finish level and require a replay. John Hawley Edwards scored for the Wanderers, but the Etonians equalised with a goal credited in modern publications to Alexander Bonsor, although contemporary newspaper reports do not definitively identify him as the scorer. A week later, the teams met again at the same venue. The Etonians were forced to make several changes to their line-up due to players being unavailable, and the revised team lost 3–0. Charles Wollaston and Thomas Hughes scored a goal apiece in a five-minute spell before half-time, and Hughes added the third early in the second half.
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The Young Head coinage consists of the issues of British coins with an obverse bust of Queen Victoria first used in 1838 while Victoria was still a teenager. Designed by William Wyon, the bust remained on some denominations of British coins until 1887, by which time she was almost 70 years of age and had ceased to resemble her depiction. Wyon's bust of Victoria also appeared on coinage for British dependencies.
The young queen sat for Wyon multiple times in August and September 1837. Wyon then created his coinage portrait of her, which was approved in February 1838. Production with the portrait began later that year; some of the new issues had reverses by Wyon, others by Jean Baptiste Merlen. The new issue produced generally favourable reactions, especially the Una and the Lion reverse used for the five-pound piece.
The Wyon portrait of Victoria proved to be a favourite of hers, and because of that continued on the coinage even after she no longer resembled it. It was replaced on the penny and its fractions when the copper coinage was replaced with bronze in the 1860s, but continued on some of the gold and silver coinage. It was finally superseded by the Jubilee coinage in 1887. Wyon's portrait was imitated or reproduced from the time of its issue, and both the portrait and the Una reverse appeared on British commemorative coins in 2019.
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Swift Justice is an American detective drama television series created by Dick Wolf and Richard Albarino. It aired for one season on United Paramount Network (UPN) from March 13 to July 17, 1996. It follows former Navy SEAL Mac Swift (James McCaffrey), a private investigator who was fired from the New York City Police Department. He receives support from his former partner Detective Randall Patterson (Gary Dourdan) and his father Al Swift (Len Cariou). Completed on a limited budget, episodes were filmed on location in New York.
Critics noted Swift Justice's emphasis on violence, specifically in the pilot episode's opening sequence, comparing it to the crime drama The Equalizer (1985–1989) and the 1988 film Die Hard. UPN canceled the program after receiving complaints from viewers, advertisers, and critics of its violent scenes. Wolf considered the cancellation a mistake due to the show's good ratings. The series was praised for its visuals and McCaffrey's performance, but criticized as being either too violent or formulaic.
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The number π (/paɪ/ ⓘ; spelled out as pi) is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter. It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The number π is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as
22
7
{\displaystyle {\tfrac {22}{7}}} are commonly used to approximate it. Consequently, its decimal representation never ends, nor enters a permanently repeating pattern. It is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The decimal digits of π appear to be evenly distributed, but no proof of this conjecture has been found.
For thousands of years, mathematicians have attempted to extend their understanding of π, sometimes by computing its value to a high degree of accuracy. Ancient civilizations, including the Egyptians and Babylonians, required fairly accurate approximations of π for practical computations. Around 250 BC, the Greek mathematician Archimedes created an algorithm to approximate π with arbitrary accuracy. In the 5th century AD, Chinese mathematicians approximated π to seven digits, while Indian mathematicians made a five-digit approximation, both using geometrical techniques. The first computational formula for π, based on infinite series, was discovered a millennium later.
The earliest known use of the Greek letter π to represent the ratio of a circle's circumference to its diameter was by the Welsh mathematician William Jones in 1706. The invention of calculus soon led to the calculation of hundreds of digits of π, enough for all practical scientific computations. Nevertheless, in the 20th and 21st centuries, mathematicians and computer scientists have pursued new approaches that, when combined with increasing computational power, extended the decimal representation of π to many trillions of digits. These computations are motivated by the development of efficient algorithms to calculate numeric series, as well as the human quest to break records. The extensive computations involved have also been used to test the correctness of new computer processors.
Because it relates to a circle, π is found in many formulae in trigonometry and geometry, especially those concerning circles, ellipses and spheres. It is also found in formulae from other topics in science, such as cosmology, fractals, thermodynamics, mechanics, and electromagnetism. It also appears in areas having little to do with geometry, such as number theory and statistics, and in modern mathematical analysis can be defined without any reference to geometry. The ubiquity of π makes it one of the most widely known mathematical constants inside and outside of science. Several books devoted to π have been published, and record-setting calculations of the digits of π often result in news headlines.
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