LCD Monitor and LCD Projector

LCD Monitor

A monitor that uses LCD technologies rather than the conventional CRT technologies used by most desktop monitors. Until recently, LCD panels were used exclusively on notebook computers and other portable devices. In 1997, however, several manufacturers began offering full-size LCD monitors as alternatives to CRT monitors. The main advantage of LCD displays is that they take up less desk space and are lighter. Currently, however, they are also much more expensive.

LCD Projector

Short for liquid crystal display, a type of display used in digital watches and many portable computers. LCD displays utilize two sheets of polarizing material with a liquid crystal solution between them. An electric current passed through the liquid causes the crystals to align so that light cannot pass through them. Each crystal, therefore, is like a shutter, either allowing light to pass through or blocking the light.

Monochrome LCD images usually appear as blue or dark gray images on top of a grayish-white background. Color LCD displays use two basic techniques for producing color: Passive matrix is the less expensive of the two technologies. The other technology, called thin film transistor (TFT) or active-matrix, produces color images that are as sharp as traditional CRT displays, but the technology is expensive. Recent passive-matrix displays using new CSTN and DSTN technologies produce sharp colors rivaling active-matrix displays.

Most LCD screens used in notebook computers are backlit, or transmissive, to make them easier to read.

Sources: www.webopedia.com, en.wikipedia.org, www.npl.lib.va.us
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IT, Digital, Bot, Bioinformatics

IT
Short for Information Technology, and pronounced as separate letters, the broad subject concerned with all aspects of managing and processing information, especially within a large organization or company. Because computers are central to information management, computer departments within companies and universities are often called IT departments. Some companies refer to this department as IS (Information Services) or MIS (Management Information Services).

Digital
Describes any system based on discontinuous data or events. Computers are digital machines because at their most basic level they can distinguish between just two values, 0 and 1, or off and on. There is no simple way to represent all the values in between, such as 0.25. All data that a computer processes must be encoded digitally, as a series of zeroes and ones.

The opposite of digital is analog. A typical analog device is a clock in which the hands move continuously around the face. Such a clock is capable of indicating every possible time of day. In contrast, a digital clock is capable of representing only a finite number of times (every tenth of a second, for example).

In general, humans experience the world analogically. Vision, for example, is an analog experience because we perceive infinitely smooth gradations of shapes and colors. Most analog events, however, can be simulated digitally. Photographs in newspapers, for instance, consist of an array of dots that are either black or white. From afar, the viewer does not see the dots (the digital form), but only lines and shading, which appear to be continuous. Although digital representations are approximations of analog events, they are useful because they are relatively easy to store and manipulate electronically. The trick is in converting from analog to digital, and back again.

Bot
Short for robot, a computer program that runs automatically.

Bioinformatics
The application of computer technology to the management of biological information. Specifically, it is the science of developing computer databases and algorithms to facilitate and expedite biological research. Bioinformatics is being used largely in the field of human genome research by the Human Genome Project that has been determining the sequence of the entire human genome (about 3 billion base pairs) and is essential in using genomic information to understand diseases. It is also used largely for the identification of new molecular targets for drug discovery.

Many universities have recognized the importance of this endeavor and have instituted academic and training programs in bioinformatics that combine backgrounds in molecular biology with a strong foundation in computer science. Specialists in the field are referred to as computational biologists or bioinformatics computer scientists.

Sources: www.webopedia.com, en.wikipedia.org, www.npl.lib.va.us

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Networking

Routing

In internetworking, the process of moving a packet of data from source to destination. Routing is usually performed by a dedicated device called a router. Routing is a key feature of the Internet because it enables messages to pass from one computer to another and eventually reach the target machine. Each intermediary computer performs routing by passing along the message to the next computer. Part of this process involves analyzing a routing table to determine the best path.

Routing is often confused with bridging, which performs a similar function. The principal difference between the two is that bridging occurs at a lower level and is therefore more of a hardware function whereas routing occurs at a higher level where the software component is more important. And because routing occurs at a higher level, it can perform more complex analysis to determine the optimal path for the packet.


Network

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A group of two or more computer systems linked together. There are many types of computer networks, including:
# local-area networks (LANs) : The computers are geographically close together (that is, in the same building).
# wide-area networks (WANs) : The computers are farther apart and are connected by telephone lines or radio waves.
# campus-area networks (CANs): The computers are within a limited geographic area, such as a campus or military base.
# metropolitan-area networks MANs): A data network designed for a town or city.
# home-area networks (HANs): A network contained within a user's home that connects a person's digital devices.

In addition to these types, the following characteristics are also used to categorize different types of networks:
# topology : The geometric arrangement of a computer system. Common topologies include a bus, star, and ring. See the Network topology diagrams in the Quick Reference section of Webopedia.
# protocol : The protocol defines a common set of rules and signals that computers on the network use to communicate. One of the most popular protocols for LANs is called Ethernet. Another popular LAN protocol for PCs is the IBM token-ring network .
# architecture : Networks can be broadly classified as using either a peer-to-peer or client/server architecture.

Computers on a network are sometimes called nodes. Computers and devices that allocate resources for a network are called servers.

To connect two or more computers together with the ability to communicate with each other.


IP Masquerade

A Linux networking function. IP Masquerade, also called IPMASQ or MASQ, allows one or more computers in a network without assigned IP addresses to communicate with the Internet using the Linux server's assigned IP address. The IPMASQ server acts as a gateway, and the other devices are invisible behind it, so to other machines on the Internet the outgoing traffic appears to be coming from the IPMASQ server and not the internal PCs.

Since IPMASQ is a generic technology the server can be connected to other computers through LAN technologies like Ethernet, Token Ring, and FDDI, as well as dialup connections like PPP or SLIP.

Sources: www.webopedia.com, en.wikipedia.org, www.npl.lib.va.us
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Local Area Network

A computer network that spans a relatively small area. Most LANs are confined to a single building or group of buildings. However, one LAN can be connected to other LANs over any distance via telephone lines and radio waves. A system of LANs connected in this way is called a wide-area network (WAN).

Most LANs connect workstations and personal computers. Each node (individual computer ) in a LAN has its own CPU with which it executes programs, but it also is able to access data and devices anywhere on the LAN. This means that many users can share expensive devices, such as laser printers, as well as data. Users can also use the LAN to communicate with each other, by sending e-mail or engaging in chat sessions.

There are many different types of LANs Ethernets being the most common for PCs. Most Apple Macintosh networks are based on Apple's AppleTalk network system, which is built into Macintosh computers.

The following characteristics differentiate one LAN from another:

  • topology : The geometric arrangement of devices on the network. For example, devices can be arranged in a ring or in a straight line.
  • protocols : The rules and encoding specifications for sending data. The protocols also determine whether the network uses a peer-to-peer or client/server architecture.
  • media : Devices can be connected by twisted-pair wire, coaxial cables, or fiber optic cables. Some networks do without connecting media altogether, communicating instead via radio waves.
  • LANs are capable of transmitting data at very fast rates, much faster than data can be transmitted over a telephone line; but the distances are limited, and there is also a limit on the number of computers that can be attached to a single LAN.


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    Computer Components

    Processor

    Processor is part of the computer who is managing all activity of computer, in human maybe this like a brain. Abbreviation for central processing unit, and pronounced as separate letters. The CPU is the brains of the computer. Sometimes referred to simply as the central processor,but more commonly called processor, the CPU is where most calculations take place. In terms of computing power, the CPU is the most important element of a computer system.
    On large machines, CPUs require one or more printed circuit boards. On personal computers and small workstations, the CPU is housed in a single chip called a microprocessor. Since the 1970's the microprocessor class of CPUs has almost completely overtaken all other CPU implementations.

    The CPU itself is an internal component of the computer. Modern CPUs are small and square and contain multiple metallic connectors or pins on the underside. The CPU is inserted directly into a CPU socket, pin side down, on the motherboard. Each motherboard will support only a specific type or range of CPU so you must check the motherboard manufacturer's specifications before attempting to replace or upgrade a CPU. Modern CPUs also have an attached heat sink and small fan that go directly on top of the CPU to help dissipate heat.

    Two typical components of a CPU are the following:

    * The arithmetic logic unit (ALU), which performs arithmetic and logical operations.
    * The control unit (CU), which extracts instructions from memory and decodes and executes them, calling on the ALU when necessary.


    Mainboard
    The main circuit board of a microcomputer interfaces, . The motherboard contains the connectors for attaching additional boards. Typically, the motherboard contains the CPU, BIOS, memory, mass storageserial and parallel ports, expansion slots, and all the controllers required to control standard peripheral devices, such as the display screen, keyboard, and disk drive. Collectively, all these chips that reside on the motherboard are known as the motherboard's chipset. On most PCs, it is possible to add memory chips directly to the motherboard. You may also be able to upgrade to a faster PC by replacing the CPU chip. To add additional core features, you may need to replace the motherboard entirely.


    Memory/Storage
    Memory is the internal storage areas in the computer. The term identifies data storage that comes in the form of chips, and the word storage is used for the memory that exists on tapes or disks. Moreover, the term memory is usually used as shorthand for physical memory, which refers to the actual chips capable of holding data. Therefore, memory is both hardware and software.


    Read-Only Memory (ROM)
    ROM is computer memory on which data has been prerecorded. Once data has been written on a ROM chip, it cannot be removed and can only be read. ROM retains its contents even when the computer is turned off. ROM is referred to as being nonvolatile. Most personal computers contain a small amount of ROM that stores critical programs such as the program that boots the computer. In addition, ROM is used extensively in calculators and peripheral devices such as laser printers, whose fonts are often stored in ROM.


    Random-Access Memory (RAM)
    RAM is a type of memory that can be accessed randomly and is the most common type of memory found in computers and other devices, such as printers. Also called the main memory.





    VGA Card
    Abbreviation of video graphics array, a graphics display system for PCs developed by IBM. VGA has become one of the de facto standards for PCs. In text mode, VGA systems provide a resolution of 720 by 400 pixels. In graphics mode, the resolution is either 640 by 480 (with 16 colors) or 320 by 200 (with 256 colors). The total palette of colors is 262,144.
    Unlike earlier graphics standards for PCs -- MDA, CGA, and EGA -- VGA uses analog signals rather than digital signals. Consequently, a monitor designed for one of the older standards will not be able to use VGA.
    Since its introduction in 1987, several other standards have been developed that offer greater resolution and more colors (see SVGA , 8514/A graphics standard, and XGA), but VGA remains the lowest common denominator. All PCs made today support VGA, and possibly some other more advanced standard.

    Sources: www.webopedia.com, en.wikipedia.org, www.npl.lib.va.us
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    Albert Einstein

    Einstein in 1947

    Albert Einstein (German: IPA: [ˈalbɐt ˈaɪ̯nʃtaɪ̯n] (Audio file) ; English: IPA: /ˈælbɝt ˈaɪnstaɪn/) (March 14, 1879 – April 18, 1955) was a German-born theoretical physicist. He is best known for his theory of relativity and specifically mass–energy equivalence, E = mc2. Einstein received the 1921 Nobel Prize in Physics "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect."

    Einstein's many contributions to physics include his special theory of relativity, which reconciled mechanics with electromagnetism, and his general theory of relativity, which extended the principle of relativity to non-uniform motion, creating a new theory of gravitation. His other contributions include relativistic cosmology, capillary action, critical opalescence, classical problems of statistical mechanics and their application to quantum theory, an explanation of the Brownian movement of molecules, atomic transition probabilities, the quantum theory of a monatomic gas, thermal properties of light with low radiation density (which laid the foundation for the photon theory), a theory of radiation including stimulated emission, the conception of a unified field theory, and the geometrization of physics.

    Works by Albert Einstein include more than fifty scientific papers and also non-scientific books. Einstein is revered by the physics community, and in 1999 Time magazine named him the "Person of the Century". In wider culture the name "Einstein" has become synonymous with genius.

    Youth and Schooling

    Albert Einstein was born into a Jewish family in Ulm, Württemberg, Germany on March 14, 1879. His father was Hermann Einstein, a salesman and engineer. His mother was Pauline Einstein (née Koch). In 1880, the family moved to Munich, where his father and his uncle founded a company, Elektrotechnische Fabrik J. Einstein & Cie, that manufactured electrical equipment.

    The Einsteins were not observant of Jewish religious practices, and Albert attended a Catholic elementary school. Although Einstein had early speech difficulties, he was a top student in elementary school.

    When Einstein was five, his father showed him a pocket compass. Einstein realized that something in empty space was moving the needle and later stated that this experience made "a deep and lasting impression". At his mother's insistence, he took violin lessons starting at age six, and although he disliked them and eventually quit, he later took great pleasure in Mozart's violin sonatas. As he grew, Einstein built models and mechanical devices for fun, and began to show a talent for mathematics.

    In 1889, family friend Max Talmud, a medical student, introduced the ten-year-old Einstein to key science, mathematics, and philosophy texts, including Kant's Critique of Pure Reason and Euclid's Elements (Einstein called it the "holy little geometry book"). From Euclid, Einstein began to understand deductive reasoning, and by the age of twelve, he had learned Euclidean geometry. Soon thereafter he began to investigate calculus.

    In his early teens, Einstein attended the progressive Luitpold Gymnasium. His father intended for him to pursue electrical engineering, but Einstein clashed with authorities and resented the school regimen. He later wrote that the spirit of learning and creative thought were lost in strict rote learning.

    In 1894, when Einstein was fifteen, his father's business failed, and the Einstein family moved to Italy, first to Milan and then, after a few months, to Pavia. During this time, Einstein wrote his first scientific work, "The Investigation of the State of Aether in Magnetic Fields". Einstein had been left behind in Munich to finish high school, but in the spring of 1895, he withdrew to join his family in Pavia, convincing the school to let him go by using a doctor's note.

    Rather than completing high school, Einstein decided to apply directly to the ETH Zurich, the Swiss Federal Institute of Technology in Zürich, Switzerland. Lacking a school certificate, he was required to take an entrance examination, which he did not pass, although he got exceptional marks in mathematics and physics. Einstein wrote that it was in that same year, at age 16, that he first performed his famous thought experiment visualizing traveling alongside a beam of light (Einstein 1979).

    The Einsteins sent Albert to Aarau, Switzerland to finish secondary school. While lodging with the family of Professor Jost Winteler, he fell in love with the family's daughter, Marie. (Albert's sister Maja later married Paul Winteler.) In Aarau, Einstein studied Maxwell's electromagnetic theory. In 1896, he graduated at age 17, renounced his German citizenship to avoid military service (with his father's approval), and finally enrolled in the mathematics program at ETH. Marie moved to Olsberg, Switzerland for a teaching post.

    In 1896, Einstein's future wife, Mileva Marić, also enrolled at ETH, as the only woman studying mathematics. During the next few years, Einstein and Marić's friendship developed into romance. Einstein graduated in 1900 from ETH with a degree in physics. That same year, Einstein's friend Michele Besso introduced him to the work of Ernst Mach. The next year, Einstein published a paper in the prestigious Annalen der Physik on the capillary forces of a straw (Einstein 1901). On February 21, 1901, he gained Swiss citizenship, which he never revoked.

    Patent office

    Following graduation, Einstein could not find a teaching post. After almost two years of searching, a former classmate's father helped him get a job in Berne, at the Federal Office for Intellectual Property, the patent office, as an assistant examiner. His responsibility was evaluating patent applications for electromagnetic devices. In 1903, Einstein's position at the Swiss Patent Office was made permanent, although he was passed over for promotion until he "fully mastered machine technology".

    With friends he met in Bern, Einstein formed a weekly discussion club on science and philosophy, jokingly named "The Olympia Academy". Their readings included Poincaré, Mach, and Hume, who influenced Einstein's scientific and philosophical outlook.

    During this period Einstein had almost no personal contact with the physics community. Much of his work at the patent office related to questions about transmission of electric signals and electrical-mechanical synchronization of time: two technical problems that show up conspicuously in the thought experiments that eventually led Einstein to his radical conclusions about the nature of light and the fundamental connection between space and time.

    Marriage and family life

    Einstein and Mileva Marić had a daughter, Lieserl Einstein, born in early 1902. Her fate is unknown.

    Einstein married Mileva on January 6, 1903, although Einstein's mother had objected to the match because she had a prejudice against Serbs and thought Marić "too old" and "physically defective." Their relationship was for a time a personal and intellectual partnership. In a letter to her, Einstein called Marić "a creature who is my equal and who is as strong and independent as I am." There has been debate about whether Marić influenced Einstein's work; however, most historians do not think she made major contributions. On May 14, 1904, Albert and Mileva's first son, Hans Albert Einstein, was born in Berne, Switzerland. Their second son, Eduard, was born in Munich on July 28, 1910.

    Einstein and Marić divorced on February 14, 1919, having lived apart for five years. On June 2 of that year, Einstein married Elsa Löwenthal, who had nursed him through an illness. Elsa was Albert's first cousin maternally and his second cousin paternally. Together the Einsteins raised Margot and Ilse, Elsa's daughters from her first marriage. Their union produced no children.

    Annus Mirabilis

    In 1905, while he was working in the patent office, Einstein had four papers published in the Annalen der Physik, the leading German physics journal. These are the papers that history has come to call the Annus Mirabilis Papers:

    • His paper on the particulate nature of light put forward the idea that certain experimental results, notably the photoelectric effect, could be simply understood from the postulate that light interacts with matter as discrete "packets" (quanta) of energy, an idea that had been introduced by Max Planck in 1900 as a purely mathematical manipulation, and which seemed to contradict contemporary wave theories of light.(Einstein 1905a) This was the only work of Einstein's that he himself called "revolutionary."
    • His paper on Brownian motion explained the random movement of very small objects as direct evidence of molecular action, thus supporting the atomic theory. (Einstein 1905c)
    • His paper on the electrodynamics of moving bodies introduced the radical theory of special relativity, which showed that the observed independence of the speed of light on the observer's state of motion required fundamental changes to the notion of simultaneity. Consequences of this include the time-space frame of a moving body slowing down and contracting (in the direction of motion) relative to the frame of the observer. This paper also argued that the idea of a luminiferous aether—one of the leading theoretical entities in physics at the time—was superfluous. (Einstein 1905d)
    • In his paper on mass–energy equivalence (previously considered to be distinct concepts), Einstein deduced from his equations of special relativity what later became the well-known expression: E = mc2, suggesting that tiny amounts of mass could be converted into huge amounts of energy. (Einstein 1905e)

    All four papers are today recognized as tremendous achievements—and hence 1905 is known as Einstein's "Wonderful Year". At the time, however, they were not noticed by most physicists as being important, and many of those who did notice them rejected them outright. Some of this work—such as the theory of light quanta—remained controversial for years.

    At the age of 26, having studied under Alfred Kleiner, Professor of Experimental Physics, Einstein was awarded a PhD by the University of Zurich. His dissertation was entitled A New Determination of Molecular Dimensions. (Einstein 1905b)

    Light and general relativity

    In 1906, the patent office promoted Einstein to Technical Examiner Second Class, but he had not given up on academia. In 1908, he became a privatdozent at the University of Bern. In 1910, he wrote a paper on critical opalescence that described the cumulative effect of light scattered by individual molecules in the atmosphere, i.e. why the sky is blue.

    During 1909, Einstein published "Über die Entwicklung unserer Anschauungen über das Wesen und die Konstitution der Strahlung" ("The Development of Our Views on the Composition and Essence of Radiation"), on the quantization of light. In this and in an earlier 1909 paper, Einstein showed that Max Planck's energy quanta must have well-defined momenta and act in some respects as independent, point-like particles. This paper introduced the photon concept (although the term itself was introduced by Gilbert N. Lewis in 1926) and inspired the notion of wave–particle duality in quantum mechanics.

    In 1911, Einstein became an associate professor at the University of Zurich. However, shortly afterward, he accepted a full professorship at the Charles University of Prague. While in Prague, Einstein published a paper about the effects of gravity on light, specifically the gravitational redshift and the gravitational deflection of light. The paper appealed to astronomers to find ways of detecting the deflection during a solar eclipse. German astronomer Erwin Finlay-Freundlich publicized Einstein's challenge to scientists around the world.

    In 1912, Einstein returned to Switzerland to accept a professorship at his alma mater, the ETH. There he met mathematician Marcel Grossmann who introduced him to Riemannian geometry, and at the recommendation of Italian mathematician Tullio Levi-Civita, Einstein began exploring the usefulness of general covariance (essentially the use of tensors) for his gravitational theory. Although for a while Einstein thought that there were problems with that approach, he later returned to it and by late 1915 had published his general theory of relativity in the form that is still used today (Einstein 1915). This theory explains gravitation as distortion of the structure of spacetime by matter, affecting the inertial motion of other matter.

    After many relocations, Mileva established a permanent home with the children in Zurich in 1914, just before the start of World War I. Einstein continued on alone to Berlin, where he became a member of the Prussian Academy of Sciences. As part of the arrangements for his new position, he also became a professor at the Humboldt University of Berlin, although with a special clause freeing him from most teaching obligations. From 1914 to 1932 he was also director of the Kaiser Wilhelm Institute for Physics.

    During World War I, the speeches and writings of Central Powers scientists were available only to Central Powers academics, for national security reasons. Some of Einstein's work did reach the United Kingdom and the United States through the efforts of the Austrian Paul Ehrenfest and physicists in the Netherlands, especially 1902 Nobel Prize-winner Hendrik Lorentz and Willem de Sitter of the Leiden University. After the war ended, Einstein maintained his relationship with the Leiden University, accepting a contract as an Extraordinary Professor; he travelled to Holland regularly to lecture there between 1920 and 1930.

    In 1917, Einstein published an article in Physikalische Zeitschrift that proposed the possibility of stimulated emission, the physical process that makes possible the maser and the laser (Einstein 1917b). He also published a paper introducing a new notion, the cosmological constant, into the general theory of relativity in an attempt to model the behavior of the entire universe (Einstein 1917a).

    1917 was the year astronomers began taking Einstein up on his 1911 challenge from Prague. The Mount Wilson Observatory in California, U.S., published a solar spectroscopic analysis that showed no gravitational redshift. In 1918, the Lick Observatory, also in California, announced that they too had disproven Einstein's prediction, although their findings were not published.

    However, in May 1919, a team led by British astronomer Arthur Stanley Eddington claimed to have confirmed Einstein's prediction of gravitational deflection of starlight by the Sun while photographing a solar eclipse in Sobral, northern Brazil, and Príncipe. On November 7, 1919, leading British newspaper The Times printed a banner headline that read: "Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown". In an interview Nobel laureate Max Born praised general relativity as the "greatest feat of human thinking about nature"; fellow laureate Paul Dirac was quoted saying it was "probably the greatest scientific discovery ever made".

    In their excitement, the world media made Albert Einstein world-famous. Ironically, later examination of the photographs taken on the Eddington expedition showed that the experimental uncertainty was of about the same magnitude as the effect Eddington claimed to have demonstrated, and in 1962 a British expedition concluded that the method used was inherently unreliable. The deflection of light during a solar eclipse has, however, been more accurately measured (and confirmed) by later observations.

    There was some resentment toward the newcomer Einstein's fame in the scientific community, notably among German physicists, who later started the Deutsche Physik (German Physics) movement.

    Nobel Prize

    In 1921 Einstein was awarded the Nobel Prize in Physics, "for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect". This refers to his 1905 paper on the photoelectric effect: "On a Heuristic Viewpoint Concerning the Production and Transformation of Light", which was well supported by the experimental evidence by that time. The presentation speech began by mentioning "his theory of relativity [which had] been the subject of lively debate in philosophical circles [and] also has astrophysical implications which are being rigorously examined at the present time." (Einstein 1923) As stipulated in their 1919 divorce settlement, Einstein gave the Nobel prize money to his first wife, Mileva Marić.

    Einstein traveled to New York City in the United States for the first time on April 2, 1921. When asked where he got his scientific ideas, Einstein explained that he believed scientific work best proceeds from an examination of physical reality and a search for underlying axioms, with consistent explanations that apply in all instances and avoid contradicting each other. He also recommended theories with visualizable results (Einstein 1954).

    Unified field theory

    Einstein's research after general relativity consisted primarily of a long series of attempts to generalize his theory of gravitation in order to unify and simplify the fundamental laws of physics, particularly gravitation and electromagnetism. In 1950, he described this "unified field theory" in a Scientific American article entitled "On the Generalized Theory of Gravitation" (Einstein 1950).

    Although he continued to be lauded for his work in theoretical physics, Einstein became increasingly isolated in his research, and his attempts were ultimately unsuccessful. In his pursuit of a unification of the fundamental forces, he ignored some mainstream developments in physics (and vice versa), most notably the strong and weak nuclear forces, which were not well understood until many years after Einstein's death. Einstein's goal of unifying the laws of physics under a single model survives in the current drive for the grand unification theory.

    Collaboration and conflict

    Bose–Einstein statistics

    In 1924, Einstein received a description of a statistical model from Indian physicist Satyendra Nath Bose which showed that light could be understood as a gas. Bose's statistics applied to some atoms as well as to the proposed light particles, and Einstein submitted his translation of Bose's paper to the Zeitschrift für Physik. Einstein also published his own articles describing the model and its implications, among them the Bose–Einstein condensate phenomenon that should appear at very low temperatures (Einstein 1924). It was not until 1995 that the first such condensate was produced experimentally by Eric Allin Cornell and Carl Wieman using ultra-cooling equipment built at the NIST-JILA laboratory at the University of Colorado at Boulder. Bose–Einstein statistics are now used to describe the behaviors of any assembly of "bosons". Einstein's sketches for this project may be seen in the Einstein Archive in the library of the Leiden University.

    Schrödinger gas model

    Einstein suggested to Erwin Schrödinger an application of Max Planck's idea of treating energy levels for a gas as a whole rather than for individual molecules, and Schrödinger applied this in a paper using the Boltzmann distribution to derive the thermodynamic properties of a semiclassical ideal gas. Schrödinger urged Einstein to add his name as co-author, although Einstein declined the invitation.

    Einstein refrigerator

    In 1926, Einstein and his former student Leó Szilárd, a Hungarian physicist who later worked on the Manhattan Project and is credited with the discovery of the chain reaction, co-invented (and in 1930, patented) the Einstein refrigerator, revolutionary for having no moving parts and using only heat, not ice, as an input.

    Bohr versus Einstein

    In the 1920s, quantum mechanics developed into a more complete theory. Einstein was unhappy with the "Copenhagen interpretation" of quantum theory developed by Niels Bohr and Werner Heisenberg, wherein quantum phenomena are inherently probabilistic, with definite states resulting only upon interaction with classical systems. A public debate between Einstein and Bohr followed, lasting for many years (including during the Solvay Conferences). Einstein formulated thought experiments against the Copenhagen interpretation, which were all rebutted by Bohr. In a 1926 letter to Max Born, Einstein wrote: "I, at any rate, am convinced that He [God] does not throw dice." (Einstein 1969).

    Einstein was never satisfied by what he perceived to be quantum theory's intrinsically incomplete description of nature, and in 1935 he further explored the issue in collaboration with Boris Podolsky and Nathan Rosen, noting that the theory seems to require non-local interactions; this is known as the EPR paradox (Einstein 1935). The EPR experiment has since been performed, with results confirming quantum theory's predictions.

    Einstein's disagreement with Bohr revolved around the idea of scientific determinism. For this reason the repercussions of the Einstein-Bohr debate have found their way into philosophical discourse as well.

    Religious views

    The question of scientific determinism gave rise to questions about Einstein's position on theological determinism, and even whether or not he believed in God. In 1929, Einstein told Rabbi Herbert S. Goldstein "I believe in Spinoza's God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind." In a 1950 letter to M. Berkowitz, Einstein stated that "My position concerning God is that of an agnostic. I am convinced that a vivid consciousness of the primary importance of moral principles for the betterment and ennoblement of life does not need the idea of a law-giver, especially a law-giver who works on the basis of reward and punishment." Einstein also stated: "I have repeatedly said that in my opinion the idea of a personal God is a childlike one. You may call me an agnostic, but I do not share the crusading spirit of the professional atheist whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth," and "In view of such harmony in the cosmos which I, with my limited human mind, am able to recognize, there are yet people who say there is no God. But what really makes me angry is that they quote me for the support of such views." Einstein clarified his religious views in a letter he wrote in response to those who claimed that he worshipped a Judeo-Christian god: "It was, of course, a lie what you read about my religious convictions, a lie which is being systematically repeated. I do not believe in a personal god and I have never denied this but have expressed it clearly. If something is in me which can be called religious then it is the unbounded admiration for the structure of the world so far as our science can reveal it." In his book The World as I See It, he wrote: "A knowledge of the existence of something we cannot penetrate, of the manifestations of the profoundest reason and the most radiant beauty, which are only accessible to our reason in their most elementary forms—it is this knowledge and this emotion that constitute the truly religious attitude; in this sense, and in this alone, I am a deeply religious man."

    Einstein published a paper in Nature in 1940 entitled "Science and Religion" which gave his views on the subject. He says that: "a person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings and aspirations to which he clings because of their super-personal value … regardless of whether any attempt is made to unite this content with a Divine Being, for otherwise it would not be possible to count Buddha and Spinoza as religious personalities. Accordingly a religious person is devout in the sense that he has no doubt of the significance of those super-personal objects and goals which neither require nor are capable of rational foundation … In this sense religion is the age-old endeavour of mankind to become clearly and completely conscious of these values and goals, and constantly to strengthen their effects." He argued that conflicts between science and religion "have all sprung from fatal errors." "ven though the realms of religion and science in themselves are clearly marked off from each other" there are "strong reciprocal relationships and dependencies … science without religion is lame, religion without science is blind … a legitimate conflict between science and religion cannot exist." In Einstein's view, "neither the rule of human nor Divine Will exists as an independent cause of natural events. To be sure, the doctrine of a personal God interfering with natural events could never be refuted … by science, for can always take refuge in those domains in which scientific knowledge has not yet been able to set foot." (Einstein 1940, pp. 605–607)

    His friend Max Jammer explored Einstein's views on religion thoroughly in the 1999 book Einstein and Religion: Physics and Theology.

    Politics

    With increasing public demands, his involvement in political, humanitarian, and academic projects in various countries, and his new acquaintances with scholars and political figures from around the world, Einstein was less able to achieve the productive isolation that he needed in order to work. Due to his fame and genius, Einstein found himself called on to give conclusive judgments on matters that had nothing to do with theoretical physics or mathematics. He was not timid, and he was aware of the world around him, with no illusion that ignoring politics would make world events fade away. His very visible position allowed him to speak and write frankly, even provocatively, at a time when many people of conscience could only flee to the underground or keep doubts about developments within their own movements to themselves for fear of internecine fighting. Einstein flouted the ascendant Nazi movement, tried to be a voice of moderation in the tumultuous formation of the State of Israel and braved anti-communist politics and resistance to the civil rights movement in the United States. He participated in the 1927 congress of the League against Imperialism in Brussels.

    Zionism

    Einstein was a cultural Zionist. In 1931, The Macmillan Company published About Zionism: Speeches and Lectures by Professor Albert Einstein. Querido, an Amsterdam publishing house, collected eleven of Einstein's essays into a 1933 book entitled Mein Weltbild, translated to English as The World as I See It; Einstein's foreword dedicates the collection "to the Jews of Germany". In the face of Germany's rising militarism, Einstein wrote and spoke for peace.

    Despite his years of Zionist efforts, Einstein publicly stated reservations about the proposal to partition the British-supervised British Mandate of Palestine into independent Arab and Jewish countries. In a 1938 speech, "Our Debt to Zionism", he said: "I am afraid of the inner damage Judaism will sustain—especially from the development of a narrow nationalism within our own ranks, against which we have already had to fight strongly, even without a Jewish state. ... If external necessity should after all compel us to assume this burden [of a state], let us bear it with tact and patience."

    The United Nations did divide the mandate, demarcating the borders of several new countries including the State of Israel, and war broke out immediately. Einstein was one of the authors of a 1948 letter to the New York Times criticizing Menachem Begin's Revisionist Herut (Freedom) Party for the Deir Yassin massacre (Einstein et al. 1948).

    Einstein served on the Board of Governors of The Hebrew University of Jerusalem. In his Will of 1950, Einstein bequeathed literary rights to his writings to The Hebrew University, where many of his original documents are held in the Albert Einstein Archives.

    When President Chaim Weizmann died in 1952, Einstein was asked to be Israel's second president, but he declined. He wrote: "I am deeply moved by the offer from our State of Israel, and at once saddened and ashamed that I cannot accept it."

    Anti-Nazism

    In January 1933, Adolf Hitler was appointed Chancellor of Germany. One of the first actions of Hitler's administration was the Law for the Restoration of the Professional Civil Service which removed Jews and politically suspect government employees (including university professors) from their jobs, unless they had demonstrated their loyalty to Germany by serving in World War I. In December 1932, in response to this growing threat, Einstein had prudently traveled to the U.S. For several years he had been wintering at the California Institute of Technology in Pasadena, California, and also was a guest lecturer at Abraham Flexner's newly founded Institute for Advanced Study in Princeton, New Jersey.

    The Einsteins bought a house in Princeton (where Elsa died in 1936), and Einstein remained an integral contributor to the Institute for Advanced Study until his death in 1955. During the 1930s and into World War II, Einstein wrote affidavits recommending United States visas for a huge number of Jews from Europe trying to flee persecution, raised money for Zionist organizations and was in part responsible for the formation, in 1933, of the International Rescue Committee.

    Meanwhile in Germany, a campaign to eliminate Einstein's work from the German lexicon as unacceptable "Jewish physics" (Jüdische physik) was led by Nobel laureates Philipp Lenard and Johannes Stark. Deutsche Physik activists published pamphlets and even textbooks denigrating Einstein, and instructors who taught his theories were blacklisted—including Nobel laureate Werner Heisenberg, who had debated quantum probability with Bohr and Einstein. Philipp Lenard claimed that the mass–energy equivalence formula needed to be credited to Friedrich Hasenöhrl to make it an Aryan creation.

    Einstein became a citizen of the United States in 1940, although he retained his Swiss citizenship.

    Atomic bomb

    Concerned scientists, many of them refugees from European anti-Semitism in the U.S., recognized the danger of German scientists developing an atomic bomb based on the newly-discovered phenomena of nuclear fission. In 1939, the Hungarian émigré Leó Szilárd, having failed to arouse U.S. government interest on his own, convinced Einstein to sign a letter to U.S. President Franklin Delano Roosevelt urging U.S. development of such a weapon. In August 1939, Roosevelt received the Einstein-Szilárd letter and authorized secret research into the harnessing of nuclear fission for military purposes.

    By 1942 this effort had become the Manhattan Project, the largest secret scientific endeavor undertaken up to that time. By late 1945, the U.S. had developed operational nuclear weapons, and used them on the Japanese cities of Hiroshima and Nagasaki. Einstein himself did not play a role in the development of the atomic bomb other than signing the letter. He did help the United States Navy with some unrelated theoretical questions it was working on during the war.

    According to Linus Pauling, Einstein later expressed regret about his letter to Roosevelt. In 1947, Einstein wrote an article for The Atlantic Monthly arguing that the United States should not try to pursue an atomic monopoly, and instead should equip the United Nations with nuclear weapons for the sole purpose of maintaining deterrence.

    Cold War era

    When he was a visible figure working against the rise of Nazism, Einstein had sought help and developed working relationships in both the West and what was to become the Soviet bloc. After World War II, enmity between the former allies became a very serious issue for people with international résumés. To make things worse, during the first days of McCarthyism Einstein was writing about a single world government; it was at this time that he wrote, "I do not know how the third World War will be fought, but I can tell you what they will use in the Fourth—rocks!" In a 1949 Monthly Review article entitled "Why Socialism?" Albert Einstein described a chaotic capitalist society, a source of evil to be overcome, as the "predatory phase of human development" (Einstein 1949). With Albert Schweitzer and Bertrand Russell, Einstein lobbied to stop nuclear testing and future bombs. Days before his death, Einstein signed the Russell-Einstein Manifesto, which led to the Pugwash Conferences on Science and World Affairs.

    Einstein was a member of several civil rights groups, including the Princeton chapter of the NAACP. When the aged W. E. B. Du Bois was accused of being a Communist spy, Einstein volunteered as a character witness, and the case was dismissed shortly afterward. Einstein's friendship with activist Paul Robeson, with whom he served as co-chair of the American Crusade to End Lynching, lasted twenty years.

    In 1946, Einstein collaborated with Rabbi Israel Goldstein, Middlesex heir C. Ruggles Smith, and activist attorney George Alpert on the Albert Einstein Foundation for Higher Learning, Inc., which was formed to create a Jewish-sponsored secular university, open to all students, on the grounds of the former Middlesex College in Waltham, Massachusetts. Middlesex was chosen in part because it was accessible from both Boston and New York City, Jewish cultural centers of the U.S. Their vision was a university "deeply conscious both of the Hebraic tradition of Torah looking upon culture as a birthright, and of the American ideal of an educated democracy." The collaboration was stormy, however. Finally, when Einstein wanted to appoint British economist Harold Laski as the university's president, Alpert wrote that Laski was "a man utterly alien to American principles of democracy, tarred with the Communist brush." Einstein withdrew his support and barred the use of his name. The university opened in 1948 as Brandeis University. In 1953, Brandeis offered Einstein an honorary degree, but he declined.

    Given Einstein's links to Germany and Zionism, his socialistic ideals, and his links to Communist figures, the U.S. Federal Bureau of Investigation kept a file on Einstein that grew to 1,427 pages. Many of the documents in the file were sent to the FBI by concerned citizens: some objecting to his immigration, while others asked the FBI to protect him.

    Although Einstein had long been sympathetic to the notion of vegetarianism, it was only near the start of 1954 that he adopted a strict vegetarian diet.

    Death

    On April 17, 1955, Albert Einstein experienced internal bleeding caused by the rupture of an aortic aneurysm. He took a draft of a speech he was preparing for a television appearance commemorating the State of Israel's seventh anniversary with him to the hospital, but he did not live long enough to complete it. He died in Princeton Hospital early the next morning at the age of 76. Einstein's remains were cremated and his ashes were scattered.

    Before the cremation, Princeton Hospital pathologist Thomas Stoltz Harvey removed Einstein's brain for preservation, in hope that the neuroscience of the future would be able to discover what made Einstein so intelligent.

    Legacy

    While travelling, Einstein had written daily to his wife Elsa and adopted stepdaughters, Margot and Ilse, and the letters were included in the papers bequeathed to The Hebrew University. Margot Einstein permitted the personal letters to be made available to the public, but requested that it not be done until twenty years after her death (she died in 1986). Barbara Wolff, of The Hebrew University's Albert Einstein Archives, told the BBC that there are about 3,500 pages of private correspondence written between 1912 and 1955.

    The United States' National Academy of Sciences commissioned the Albert Einstein Memorial, a monumental bronze and marble sculpture by Robert Berks, dedicated in 1979 at its Washington, D.C. campus adjacent to the National Mall.

    Einstein bequeathed the royalties from use of his image to The Hebrew University of Jerusalem. The Roger Richman Agency licenses the use of his name and associated imagery, as agent for the Hebrew University.

    Honors

    See also: List of things named after Albert Einstein

    In 1999, Albert Einstein was named "Person of the Century" by Time magazine, the Gallup poll recorded him as the fourth most admired person of the 20th century and according to The 100: A Ranking of the Most Influential Persons in History, Einstein is "the greatest scientist of the twentieth century and one of the supreme intellects of all time."

    A partial list of his memorials:

    • The International Union of Pure and Applied Physics named 2005 the "World Year of Physics" in commemoration of the 100th anniversary of the publication of the Annus Mirabilis Papers.
    • The Albert Einstein Memorial by Robert Berks
    • A unit used in photochemistry, the einstein
    • The chemical element 99, einsteinium
    • The asteroid 2001 Einstein
    • The Albert Einstein Award
    • The Albert Einstein Peace Prize

    In 1990, his name was added to the Walhalla temple.

    Impact on popular culture

    Main article: Albert Einstein in popular culture

    In the period before World War II, Albert Einstein was so well-known in America that he would be stopped on the street by people wanting him to explain "that theory". He finally figured out a way to handle the incessant inquiries. He told his inquirers "Pardon me, sorry! Always I am mistaken for Professor Einstein."

    Albert Einstein has been the subject of or inspiration for many novels, films, and plays. Einstein is a favorite model for depictions of mad scientists and absent-minded professors; his expressive face and distinctive hairstyle have been widely copied and exaggerated. Time magazine's Frederic Golden wrote that Einstein was "a cartoonist's dream come true."

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    Archimedes


    Archimedes Thoughtful by Fetti (1620)

    Archimedes of Syracuse (Ancient Greek: Ἀρχιμήδης) (c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Among his advances in physics are the foundations of hydrostatics and the explanation of the principle of the lever. He is credited with designing innovative machines, including siege engines and the screw pump that bears his name. Modern experiments have tested claims that Archimedes designed machines capable of lifting attacking ships out of the water, and setting ships on fire using an array of mirrors.

    Archimedes is considered to be one of the greatest mathematicians of all time. He used the method of exhaustion to calculate the area under the arc of a parabola with the summation of an infinite series, and gave a remarkably accurate approximation of Pi. He also defined the spiral bearing his name, formulas for the volumes of surfaces of revolution and an ingenious system for expressing very large numbers.

    Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting the tomb of Archimedes, which was surmounted by a sphere inscribed within a cylinder. Archimedes had proved that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter), and regarded this as the greatest of his mathematical achievements.

    Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was made only by Isidore of Miletus (c. 530 AD), while commentaries on the works of Archimedes written by Eutocius in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance, while the discovery in 1906 of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.

    Biography

    Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia. The date of birth is based on a statement by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years. In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children. During his youth Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred to Conon of Samos as his friend, while two of his works (The Sand Reckoner and the Cattle Problem) have introductions addressed to Eratosthenes.

    Archimedes died c. 212 BC during the Second Punic War, when Roman forces under General Marcus Claudius Marcellus captured the city of Syracuse after a two-year-long siege. According to the popular account given by Plutarch, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives a lesser-known account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he had ordered him not to be harmed.

    The last words attributed to Archimedes are "Do not disturb my circles" (Greek: μή μου τούς κύκλους τάραττε), a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is often given in Latin as "Noli turbare circulos meos", but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch.

    Discoveries and inventions

    The most commonly related anecdote about Archimedes tells how he invented a method for measuring the volume of an object with an irregular shape. According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its density as a cube, which would have been the simplest solution. While taking a bath, he noticed that the level of the water rose as he got in. He realized that this effect could be used to determine the volume of the crown. For practical purposes water is incompressible, so the crown would displace an amount of water equal to its own volume. By dividing the weight of the crown by the volume of water displaced, its density could be obtained. The density of the crown would be lower if cheaper and less dense metals had been added. Archimedes then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" "I have found it!" (Greek: "εύρηκα!")

    The story about the golden crown does not appear in the known works of Archimedes, but in his treatise On Floating Bodies he gives the principle known in hydrostatics as Archimedes' Principle. This states that a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.

    While Archimedes did not invent the lever, he wrote the earliest known rigorous explanation of the principle involved. According to Pappus of Alexandria, his work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." (Greek: "δος μοι πα στω και ταν γαν κινάσω") Plutarch describes how Archimedes designed block and tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move.

    A large part of Archimedes' work in engineering arose from fulfilling the needs of his home city of Syracuse. The Greek writer Athenaeus of Naucratis described how King Hieron II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship. The Syracusia is said to have been the largest ship built in classical antiquity. According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes screw was purportedly developed in order to remove the bilge water. Archimedes' machine was a device with a revolving screw shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. The Archimedes screw is still in use today for pumping liquids and semifluid solids such as coal and grain.

    The Archimedes screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon.

    The Claw of Archimedes is another weapon that he is said to have designed in order to defend the city of Syracuse. Also known as "the ship shaker", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped on to an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.

    Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.

    Cicero (106 BC–43 BC) mentions Archimedes briefly in his dialogue De re publica, which portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome. Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus:

    Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. — When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.

    This is a description of a planetarium or orrery. Pappus of Alexandria stated that Archimedes had written a manuscript (now lost) on the construction of these mechanisms entitled On Sphere-Making. Modern research in this area has been focused on the Antikythera mechanism, another device from classical antiquity that was probably designed for the same purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.

    Lucian wrote that during the Siege of Syracuse (c. 214–212 BC), Archimedes repelled an attack by Roman forces with a burning-glass. The device was used to focus sunlight on to the approaching ships, causing them to catch fire. This claim, sometimes called the "Archimedes heat ray", has been the subject of ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes. It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight on to a ship. This would have used the principle of the parabolic reflector in a manner similar to a solar furnace.

    A test of the Archimedes heat ray was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which may have aided combustion.

    In October 2005 a group of students from the Massachusetts Institute of Technology carried out an experiment with 127 one-foot (30 cm) square mirror tiles, focused on a mocked-up wooden ship at a range of around 100 feet (30 m). Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the weapon was a feasible device under these conditions. The MIT group repeated the experiment for the television show MythBusters, using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its flash point, which is around 300 degrees Celsius (570 °F). When MythBusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (or failed) because of the length of time and the ideal weather conditions required for combustion to occur. It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors. MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances.

    The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a sphere and a cylinder of the same height and diameter. Archimedes had proved that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. In 75 BC, 137 years after his death, the Roman orator Cicero was serving as quaestor in Sicily. He had heard stories about the tomb of Archimedes, but none of the locals was able to give him the location. Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.

    The standard versions of the life of Archimedes were written long after his death by the historians of Ancient Rome. The account of the siege of Syracuse given by Polybius in his Universal History was written around seventy years after Archimedes' death, and was used subsequently as a source by Plutarch and Livy. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city.

    Mathematics

    While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote: “He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.”

    Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus. By assuming a proposition to be true and showing that this would lead to a contradiction, he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of π (Pi). He did this by drawing a larger polygon outside a circle and a smaller polygon inside the circle. As the number of sides of the polygon increases, it becomes a more accurate approximation of a circle. When the polygons had 96 sides each, he calculated the lengths of their sides and showed that the value of π lay between 3 + 1/7 (approximately 3.1429) and 3 + 10/71 (approximately 3.1408). He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle.

    In The Measurement of a Circle, Archimedes gives the value of the square root of 3 as being more than 265/153 (approximately 1.7320261) and less than 1351/780 (approximately 1.7320512). The actual value is approximately 1.7320508, making this a very accurate estimate. He introduced this result without offering any explanation of the method used to obtain it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."

    Image:Parabola-and-inscribed triangle text.png

    In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He expressed the solution to the problem as a geometric series that summed to infinity with the ratio 1/4:

    \sum_{n=0}^\infty 4^{-n} = 1 + 4^{-1} + 4^{-2} + 4^{-3} + \cdots = {4\over 3}. \;

    If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on. This proof is a variation of the infinite series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 1/3.

    In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based around the myriad. The word is based on the Greek for uncountable, murious, and was also used to denote the number 10,000. He proposed a number system using powers of myriad myriads (100 million) and concluded that the number of grains of sand required to fill the universe would be 8×1063, which can also be expressed as eight vigintillions.

    Writings

    The written work of Archimedes has not survived as well as that of Euclid, and seven of his treatises are known to exist only through references made to them by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra, while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica. During his lifetime, Archimedes made his work known through correspondence with the mathematicians in Alexandria. The writings of Archimedes were collected by the Byzantine architect Isidore of Miletus (c. 530 AD), while commentaries on the works of Archimedes written by Eutocius in the sixth century AD helped to bring his work a wider audience. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD). During the Renaissance, the Editio Princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin. Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.

    Surviving works

    • On the Equilibrium of Planes (two volumes)
    The first book is in fifteen propositions with seven postulates, while the second book is in ten propositions. In this work Archimedes explains the Law of the Lever, stating:
    Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.
    Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, paraboloids, and hemispheres.
    • On the Measurement of the Circle
    This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes shows that the value of π (Pi) is greater than 223/71 and less than 22/7. The latter figure was used as an approximation of π throughout the Middle Ages and is still used today when a rough figure is required.
    • On Spirals
    This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation
    \, r=a+b\theta
    with real numbers a and b. This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.
    • On the Sphere and the Cylinder (two volumes)
    In this treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is \tfrac{4}{3}\pi r^3 for the sphere, and r3 for the cylinder. The surface area is r2 for the sphere, and r2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. The sphere has a volume and surface area two-thirds that of the cylinder. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.
    • On Conoids and Spheroids
    This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
    • On Floating Bodies (two volumes)
    In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
    In the second part, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:
    Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
    • The Quadrature of the Parabola
    In this work of 24 propositions addressed to Dositheus, Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He achieves this by calculating the value of a geometric series that sums to infinity with the ratio 1/4.
    • Stomachion
    This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces of paper could be assembled into the shape of a square. The figure given by Dr. Netz is that the pieces can be made into a square in 17,152 ways. The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded. The Stomachion represents an example of an early problem in combinatorics. Stomachion is the Greek word for stomach, στομάχιον, and the reason for the name is unclear.
    • Archimedes' cattle problem
    This work was discovered by Gotthold Ephraim Lessing in a Greek manuscript consisting of a poem of 44 lines, in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians in Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. This version of the problem was first solved by a computer in 1965, and the answer is a very large number, approximately 7.760271×10206544.
    • The Sand Reckoner
    In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos, contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.
    • The Method of Mechanical Theorems
    This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.

    Apocryphal works

    Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in Arabic. The scholars T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The Lemmas may be based on an earlier work by Archimedes that is now lost.

    It has also been claimed by the Arab scholar Abu'l Raihan Muhammed al-Biruni that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes. However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century AD.

    Archimedes Palimpsest

    Main article: Archimedes Palimpsest

    The foremost document containing the work of Archimedes is the Archimedes Palimpsest. A palimpsest, from the Greek word palimpsestos meaning "scraped again", is a manuscript written on parchment that has another text written over it, leaving two or more layers of visible writing. Palimpsests were common in antiquity because parchment was scarce and costly. As certain kinds of texts went in and out of literary fashion the manuscripts were recycled and reused, with their original content being rubbed away and overwritten. In 1906, the Danish professor Johan Ludvig Heiberg realized that a 174-page goatskin parchment of prayers written in the 13th century AD also carried an older work written in the 10th century AD, which he identified as previously unknown copies of works by Archimedes. The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at Christie's in New York. The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek. It is the only known source of the Method of Mechanical Theorems, referred to by Suidas and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now stored at the Walters Art Museum in Baltimore, Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten text.

    The treatises in the Archimedes Palimpsest are: On the Equilibrium of Planes, On Spirals, The Measurement of the Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and Stomachion.

    Legacy

    There is a crater on the Moon named Archimedes (29.7° N, 4.0° W) in his honor, and a lunar mountain range, the Montes Archimedes (25.3° N, 4.6° W).

    The asteroid 3600 Archimedes is named after him.

    The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with his proof concerning the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).

    Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982), and Spain (1963).

    The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California Gold Rush.

    A movement for civic engagement targeting universal access to health care in the US state of Oregon has been named the "Archimedes Movement", headed by former Oregon Governor John Kitzhaber.

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