Monday, September 26, 2011
Thursday, September 22, 2011
History Of Pentagon
Stimson told President Franklin D. Roosevelt in May 1941 that the War Department needed additional space. On July 17, 1941, a congressional hearing took place, organized by Virginia congressman Clifton Woodrum, regarding proposals for new War Department buildings. Woodrum pressed Brigadier General Eugene Reybold, who was representing the War Department at the hearing, for an "overall solution" to the department's "space problem" rather than building yet more temporary buildings. Reybold agreed to report back to the congressman within five days. The War Department called upon its construction chief, General Brehon Somervell, to come up with a plan.[9]
Main Navy Building (foreground) and the Munitions Building were temporary structures built during World War I on the National Mall. The Munitions Building served as the Department of War headquarters for several years before moving into the Pentagon.
Government officials agreed that the War Department building should be constructed across the Potomac River, in Arlington, Virginia. Requirements for the new building were that it be no more than four stories tall, and that it use a minimal amount of steel. The requirements meant that, instead of rising vertically, the building would be sprawling over a large area. Possible sites for the building included Arlington Farm, adjacent to Arlington National Cemetery, and the obsolete Washington Hoover Airport site.[10]
The site originally chosen was Arlington Farms which had a roughly pentagonal shape, so the building was planned accordingly as an irregular pentagon.[11] Concerned that the new building could obstruct the view of Washington, D.C. from Arlington Cemetery, President Roosevelt ended up selecting the Hoover Airport site instead.[12] The building retained its pentagonal layout because a major redesign at that stage would have been costly, and Roosevelt liked the design. Freed of the constraints of the asymmetric Arlington Farms site, it was modified into a regular pentagon.[13][14]
Southwest view of the Pentagon with the Potomac River and Washington Monument in background (1998).
On July 28 Congress authorized funding for a new Department of War building in Arlington, which would house the entire department under one roof,[15] and President Roosevelt officially approved of the Hoover Airport site on September 2.[16] While the project went through the approval process in late July 1941, Somervell selected the contractors, including John McShain, Inc. of Philadelphia, which had built Washington National Airport in Arlington, the Jefferson Memorial in Washington, and the National Naval Medical Center in Bethesda, Maryland, along with Wise Contracting Company, Inc. and Doyle and Russell, both from Virginia.[17] In addition to the Hoover Airport site and other government-owned land, construction of the Pentagon required an additional 287 acres (1.16 km2), which were acquired at a cost of $2.2 million.[18] The Hell's Bottom neighborhood, a slum with numerous pawnshops, factories, approximately 150 homes, and other buildings around Columbia Pike, was also cleared to make way for the Pentagon.[19] Later 300 acres (1.2 km2) of land were transferred to Arlington National Cemetery and to Fort Myer, leaving 280 acres (1.1 km2) for the Pentagon.[18]
Northwest exposure of the Pentagon's construction underway, July 1, 1942
Contracts totaling $31,100,000 were finalized with McShain and the other contractors on September 11, and ground was broken for the Pentagon the same day.[20] Among the design requirements, Somervell required the structural design to accommodate floor loads of up to 150 pounds per square inch, which was done in case the building became a records storage facility at some time after the end of the current war.[16] A minimal amount of steel was used as it was in short supply during World War II. Instead, the Pentagon was built as a reinforced concrete structure, using 680,000 tons of sand dredged from the Potomac River, and a lagoon was created beneath the Pentagon's river entrance.[21] To minimize steel, concrete ramps were built rather than installing elevators.[22][23] Indiana limestone was used for the building's facade.[24]
Architectural and structural design work for the Pentagon proceeded simultaneously with construction, with initial drawings provided in early October 1941, and most of the design work completed by June 1, 1942. At times the construction work got ahead of the design, with different materials used than specified in the plans. Pressure to speed up design and construction intensified after the attack on Pearl Harbor on December 7, 1941, with Somervell demanding that 1,000,000 sq ft (9.3 ha) of space at the Pentagon be available for occupation by April 1, 1942.[25] David J. Witmer replaced Bergstrom as chief architect on April 11 after Bergstorm resigned due to charges, unrelated to the Pentagon project, of improper conduct while he was president of the American Institute of Architects.[26]
Construction of the Pentagon was done during segregation in the United States. This had structural consequences to the design of the building. Under the supervision of colonel Leslie R. Groves, the decision to have separate eating and lavatory accommodations for whites and blacks was made and carried out. The dining areas for blacks were put in the basement and on each floor there were double toilet facilities separated by gender and race. These measures of segregation were said to have been done in compliance with the state of Virginia’s racial laws. The Pentagon as a result has double the standard amount of toilet facilities that would be needed for a building of its size.[27][28]
President Roosevelt had made an order ending such racial discrimination in the U.S. military in June 1941. When the President visited the Pentagon before its dedication he questioned Groves regarding the number of washrooms and ordered him to remove the “Whites Only” signs. The Pentagon for a long time was the only building in Virginia where segregation was not allowed.[28]
The soil conditions of the Pentagon site, located on the Potomac River floodplain, presented challenges to engineers, as did the varying elevations across the site, which ranged from 10–40 ft (3.0–12 m) above sea level. Two retaining walls were built to compensate for the elevation variations, and cast-in-place (Franki) piles were used to deal with the soil conditions.[29] Construction of the Pentagon was completed in approximately 16 months at a total cost of $83 million. The building is 77 feet (23 m) tall, and each of the five sides of the building is 921 feet (281 m) long.[30]
[edit] Protests
Military police keep back Vietnam War protesters during their sit-in on October 21, 1969, at the mall entrance to the Pentagon
The Pentagon became a spot for protests against the Vietnam War during the late 1960s. A group of 2,500 women, organized by Women Strike for Peace, demonstrated outside of Secretary of Defense Robert S. McNamara's office at the Pentagon on February 15, 1967.[31] In May 1967, a group of 20 demonstrators held a sit-in outside the Joint Chiefs of Staff's office, which lasted four days before they were arrested.[32] In one of the better known incidents, on October 21, 1967, some 35,000 anti-war protesters organized by the National Mobilization Committee to End the War in Vietnam, gathered for a demonstration at the Defense Department (the "March on the Pentagon"), where they were confronted by some 2,500 armed soldiers. During the protest, a famous picture was taken, where George Harris placed carnations into the soldiers' gun barrels.[33] On May 19, 1972, the American radicals known as the Weather Underground Organization successfully planted and detonated a bomb in a fourth-floor women's restroom in the Pentagon. They announced it was in retaliation for the Nixon administration's bombing attacks on Hanoi during the final stages of the Vietnam War.[34]
On March 17, 2007, 4,000 to 15,000 people (estimates vary significantly) protested against the Iraq War.[35] The protesters marched from the Lincoln Memorial, down Washington Boulevard to the Pentagon’s north parking lot.
[edit] Renovation
Main article: Pentagon Renovation Program
From 1998 to 2011, the Pentagon underwent a major renovation, known as the Pentagon Renovation Program. This program, completed in June, 2011, involved the complete gutting and reconstruction of the entire building in phases to bring the building up to modern standards, removing asbestos, improving security, providing greater efficiency for Pentagon tenants, and sealing of all office windows.[36]
As originally built, most Pentagon office space consisted of open bays which spanned an entire ring. These offices used cross-ventilation from operable windows instead of air conditioning for cooling. Gradually, bays were subdivided into private offices with many using window air conditioning units. With renovations now complete, the new space includes a return to open office bays, a new Universal Space Plan of standardized office furniture and partitions developed by Studios Architecture.[37]
[edit] September 11 attacks
Main articles: American Airlines Flight 77 and Pentagon Memorial
Pentagon Security Camera 1.ogv
Security camera footage of Flight 77 hitting the Pentagon.[38]
9/11 anniversary illumination
On September 11, 2001, The Pentagon's 60th birthday, a team of five al-Qaeda affiliated hijackers took control of American Airlines Flight 77, en route from Washington Dulles International Airport to Los Angeles International Airport, and deliberately crashed into the Western side of the Pentagon at 9:37 am EDT as part of the September 11 attacks. All 64 people on the airliner were killed as were 125 people who were in the building. The impact of the plane severely damaged the structure of the building and caused its partial collapse.[39] At the time of the attacks, the Pentagon was under renovation and several offices were unoccupied, resulting in fewer casualties. Only 800 of 4,500 people who would have been in the area were there because of the work. Furthermore the area hit, on the side of the Heliport Entrance facade, was the section best prepared for such an attack. The renovation there, improvements which resulted from the Oklahoma City bombing, had nearly been completed.[40][41][42]
It was the only area of the Pentagon with a sprinkler system, and it had been reconstructed with a web of steel columns and bars to withstand bomb blasts. The steel reinforcement, bolted together to form a continuous structure through all of the Pentagon's five floors, kept that section of the building from collapsing for 30 minutes—enough time for hundreds of people to crawl out to safety. The area struck by the plane also had blast-resistant windows—2 inches thick and 2,500 pounds each—that stayed intact during the crash and fire. It had fire doors that opened automatically and newly built exits that allowed people to get out.[40]
Contractors already involved with the renovation were given the added task of rebuilding the sections damaged in the attacks. This additional project was named the "Phoenix Project", and was charged with having the outermost offices of the damaged section occupied by September 11, 2002.[43][44][45]
When the damaged section of the Pentagon was rebuilt, a small indoor memorial and chapel were included, located at the point of impact. For the fifth anniversary of the September 11, 2001 attacks, a memorial of 184 beams of light shone up from the center courtyard of the Pentagon, one light for each victim of the attack. In addition, an American flag is hung each year on the side of the Pentagon damaged in the attacks, and the side of the building is illuminated at night with blue lights. After the attacks, plans were developed for an outdoor memorial, with construction underway in 2006. The Pentagon Memorial, which consists of a 2 acres (8,100 m2) park with 184 benches, according to the victims' ages, from 3 to 71, was opened to the public on September 11, 2008
Tuesday, August 30, 2011
Tuesday, August 16, 2011
Pierre de Fermat
Buste in the Salle des Illustres in Capitole de Toulouse
He attended the University of Toulouse before moving to Bordeaux in the second half of the 1620s. In Bordeaux he began his first serious mathematical researches and in 1629 he gave a copy of his restoration of Apollonius's De Locis Planis to one of the mathematicians there. Certainly in Bordeaux he was in contact with Beaugrand and during this time he produced important work on maxima and minima which he gave to Étienne d'Espagnet who clearly shared mathematical interests with Fermat. There he became much influenced by the work of François Viète.
From Bordeaux, Fermat went to Orléans where he studied law at the University. He received a degree in civil law before, in 1631, receiving the title of councillor at the High Court of Judicature in Toulouse, which he held for the rest of his life. Due to the office he now held he became entitled to change his name from Pierre Fermat to Pierre de Fermat. Fluent in Latin, Basque[citation needed], classical Greek, Italian, and Spanish, Fermat was praised for his written verse in several languages, and his advice was eagerly sought regarding the emendation of Greek texts.
He communicated most of his work in letters to friends, often with little or no proof of his theorems. This allowed him to preserve his status as an "amateur" while gaining the recognition he desired. This naturally led to priority disputes with fellow contemporaries such as Descartes and Wallis. He developed a close relationship with Blaise Pascal.[3]
Anders Hald writes that, "The basis of Fermat's mathematics was the classical Greek treatises combined with Vieta's new algebraic methods."[4]
Fermat's pioneering work in analytic geometry was circulated in manuscript form in 1636, predating the publication of Descartes' famous La géométrie. This manuscript was published posthumously in 1679 in "Varia opera mathematica", as Ad Locos Planos et Solidos Isagoge, ("Introduction to Plane and Solid Loci").[5]
In Methodus ad disquirendam maximam et minima and in De tangentibus linearum curvarum, Fermat developed a method for determining maxima, minima, and tangents to various curves that was equivalent to differentiation.[6] In these works, Fermat obtained a technique for finding the centers of gravity of various plane and solid figures, which led to his further work in quadrature.
Fermat was the first person known to have evaluated the integral of general power functions. Using an ingenious trick, he was able to reduce this evaluation to the sum of geometric series.[7] The resulting formula was helpful to Newton, and then Leibniz, when they independently developed the fundamental theorem of calculus.[citation needed]
In number theory, Fermat studied Pell's equation, perfect numbers, amicable numbers and what would later become Fermat numbers. It was while researching perfect numbers that he discovered the little theorem. He invented a factorization method - Fermat's factorization method - as well as the proof technique of infinite descent, which he used to prove Fermat's Last Theorem for the case n = 4. Fermat developed the two-square theorem, and the polygonal number theorem, which states that each number is a sum of three triangular numbers, four square numbers, five pentagonal numbers, and so on.
Although Fermat claimed to have proved all his arithmetic theorems, few records of his proofs have survived. Many mathematicians, including Gauss, doubted several of his claims, especially given the difficulty of some of the problems and the limited mathematical tools available to Fermat. His famous Last Theorem was first discovered by his son in the margin on his father's copy of an edition of Diophantus, and included the statement that the margin was too small to include the proof. He had not bothered to inform even Marin Mersenne of it. It was not proved until 1994, using techniques unavailable to Fermat.
Although he carefully studied, and drew inspiration from Diophantus, Fermat began a different tradition. Diophantus was content to find a single solution to his equations, even if it were an undesired fractional one. Fermat was interested only in integer solutions to his Diophantine equations, and he looked for all possible general solutions. He often proved that certain equations had no solution, which usually baffled his contemporaries.
Through his correspondence with Pascal in 1654, Fermat and Pascal helped lay the fundamental groundwork for the theory of probability. From this brief but productive collaboration on the problem of points, they are now regarded as joint founders of probability theory.[8] Fermat is credited with carrying out the first ever rigorous probability calculation. In it, he was asked by a professional gambler why if he bet on rolling at least one six in four throws of a die he won in the long term, whereas betting on throwing at least one double-six in 24 throws of two dice resulted in him losing. Fermat subsequently proved why this was the case mathematically.[9]
Fermat's principle of least time (which he used to derive Snell's law in 1657) was the first variational principle[10] enunciated in physics since Hero of Alexandria described a principle of least distance in the first century CE. In this way, Fermat is recognized as a key figure in the historical development of the fundamental principle of least action in physics. The term Fermat functional was named in recognition of this role.[11]
Plaque at the place of burial of Pierre de Fermat
Place of burial of Pierre de Fermat in Place Jean Jaurés, Castres, France. Translation of the plaque: in this place was buried on January 13, 1665, Pierre de Fermat, councilor of the chamber of Edit and mathematician of great renown, celebrated for his theorem (sic),
an + bn ≠ cn for n>2
He died at Castres, Tarn.[2] The oldest, and most prestigious, high school in Toulouse is named after him: the Lycée Pierre de Fermat. French sculptor Théophile Barrau made a marble statue named Hommage à Pierre Fermat as tribute to Fermat, now at the Capitole of Toulouse.
Holographic will handwritten by Fermat on 4 March 1660 — kept at the Departmental Archives of Haute-Garonne, in Toulouse
Together with René Descartes, Fermat was one of the two leading mathematicians of the first half of the 17th century. According to Peter L. Bernstein, in his book Against the Gods, Fermat "was a mathematician of rare power. He was an independent inventor of analytic geometry, he contributed to the early development of calculus, he did research on the weight of the earth, and he worked on light refraction and optics. In the course of what turned out to be an extended correspondence with Pascal, he made a significant contribution to the theory of probability. But Fermat's crowning achievement was in the theory of numbers."[12]
Regarding Fermat's work in analysis, Isaac Newton wrote that his own early ideas about calculus came directly from "Fermat's way of drawing tangents."[13]
Of Fermat's number theoretic work, the great 20th century mathematician André Weil wrote that "... what we possess of his methods for dealing with curves of genus 1 is remarkably coherent; it is still the foundation for the modern theory of such curves. It naturally falls into two parts; the first one ... may conveniently be termed a method of ascent, in contrast with the descent which is rightly regarded as Fermat's own."[14] Regarding Fermat's use of ascent, Weil continued "The novelty consisted in the vastly extended use which Fermat made of it, giving him at least a partial equivalent of what we would obtain by the systematic use of the group theoretical properties of the rational points on a standard cubic."[15] With his gift for number relations and his ability to find proofs for many of his theorems, Fermat essentially created the modern theory of numbers.
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