- UID
- 637277
- 在线时间
- 小时
- 注册时间
- 2011-6-4
- 最后登录
- 1970-1-1
- 主题
- 帖子
- 性别
- 保密
|
每日阅读汇总贴http://forum.chasedream.com/GMAT_RC/thread-562296-1-1.html
逻辑姊妹篇：http://forum.chasedream.com/GMAT_CR/thread-580862-1-1.html
【速度4-4】
Pierre de Fermat
From Wikipedia, the free encyclopedia
计时1
Pierre de Fermat (French pronunciation: [pj??? d?f???ma]; 17[1] August 1601 or 1607/8[2] – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and an amateur mathematician who is given credit for early developments that led to infinitesimal calculus, including his adequality. In particular, he is recognized for his discovery of an original method of finding the greatest and the smallest ordinates of curved lines, which is analogous to that of the then unknown differential calculus, and his research into number theory. He made notable contributions to analytic geometry, probability, and optics. He is best known for Fermat's Last Theorem, which he described in a note at the margin of a copy of Diophantus' Arithmetica.
Life and work
Fermat was born in Beaumont-de-Lomagne, Tarn-et-Garonne, France; the late 15th century mansion where Fermat was born is now a museum. He was of Basque origin. Fermat's father was a wealthy leather merchant and second consul of Beaumont-de-Lomagne. Pierre had a brother and two sisters and was almost certainly brought up in the town of his birth. There is little evidence concerning his school education, but it may have been at the local Franciscan monastery.
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.
字数289
计时2
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]
Work
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]
字数221
计时3
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.
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.
字数253
计时4
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]
Death
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.
字数295
计时5
Assessment of his work
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.
字数278
【越障4-4】
Can Suburbs Be Designed to Do Away with the Car?
The public-transit goals of a "new urbanism" town can fail if residents don't foresee true travel benefits
By David Biello | August 17, 2011
The new kind of suburb wasn't supposed to be so suburban. Packed into 180 hectares, King Farm in Rockville, Md., filled in a patch of lingering farmland just outside Washington, D.C. The village planners left a broad swath of green down the main road, dubbed King Farm Boulevard, that sported along its sides a mix of different types of housing and amenities, such as shops, within walking distance. Down the middle of the boulevard would be the forthcoming train system that would efficiently shuttle new residents to the Washington Metro's Red Line, thereby linking them with the regional public transit system.
As a result of the new design sensibilities, the Congress for the New Urbanism highlighted King Farm in 2008 as an "exciting" development, and the U.S. Environmental Protection Agency cited it as an example of "smart growth." The planned community checked off all the boxes of the "new urbanist" manifesto: a mix of housing types paired with centrally located amenities, designed for pedestrians and cars as well as public transport–oriented.
Instead of embracing that transportation vision, however, the residents of King Farm and the Rockville City Council recently rejected the proposed transit plan—specifically, any light-rail line that would travel down the swath of green explicitly designed to host such a system.
Transit-ready development may mean nothing if local residents are not ready for public transit. And King Farm residents seem prepared to fight the State of Maryland, which bears ultimate responsibility for the decision and still wants to route any transit system through the community. The battle highlights one of the challenges facing so-called new urbanism as it attempts to steer American life away from the car, which has dominated city planning since at least the 1950s.
The new urbanist movement disdained the automobile-centric sprawl, which locked residents into the use of polluting cars for even the most basic trips. The logic of sprawl saw cities eat up a larger and larger share of the surrounding real estate, fueling habitat destruction, smog from tailpipe emissions, runoff from impermeable pavement and other environmental ills.
Communities inspired by a return to the walkable cities of most of human history have sprung up from coast to coast, including places where one might least expect it, such as Los Angeles, Denver and even Salt Lake City, the latter of which has shifted growth patterns away from sprawl. But, as the example of King Farm shows, new urbanism can devolve into the kind of central planning criticized by the very founders of the urban planning school of thought—and can also result in what is essentially a style without substance. "It is more about lifestyle than ecologically sound cities," says sociologist Saskia Sassen of Columbia University, a member of the U.S. National Academy of Sciences panel on cities.
Planner and developer Jonathan Rose of Jonathan Rose Companies of New York City echoes that sentiment. Not owning a car reduces consumption, he notes, but "that reduction in consumption has to come with an increase in happiness. If it comes with suffering—it takes three buses to get where you want to go—then it's not sustainable."
Such suffering seems to be the case for residents of King Farm, some of whom would choose the freedom to be stuck in Beltway traffic rather than face the peril of a community divided by train tracks. "We've come a long way from an era where many cities produced affordable housing through what gets endearingly called 'drive 'til you qualify' strategies," says Uwe Brandes, vice president of initiatives at the Urban Land Institute, a nonprofit research and education think tank focused on land use. "The area of caution associated with transit-oriented development is there's a danger that these areas in cities can become economic and social enclaves. That's a yellow, blinking light." |
|
京公网安备11010202008513号 京ICP证101109号 京ICP备12012021号
发表于 2011-8-17 19:26:32
收藏
收藏
楼主
发表于 2011-8-17 20:13:24
晕了。。