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History Of Computing
The history of computing is longer than the history of computing hardware and modern computing technology and includes the history of methods intended for pen and paper or for chalk and slate, with or without the aid of tables. Concrete devices Digital computing is intimately tied to the representation of numbers. But long before abstractions like ''the number'' arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as: *''One-to-one correspondence'', a rule to count ''how many'' items, e.g. on a tally stick, eventually abstracted into ''numbers''. *''Comparison to a standard'', a method for assuming ''reproducibility'' in a measurement, for example, the number of coins. *The ''3-4-5'' right triangle was a device for assuring a ''right angle'', using ropes with 12 evenly spaced knots, for example. Numbers Eventually, the concept of numbers became concrete and familiar enough for counting to arise, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Computing Hardware
The history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers. Before the 20th century, most calculations were done by humans. The first aids to computation were purely mechanical devices which required the operator to set up the initial values of an elementary arithmetic operation, then manipulate the device to obtain the result. Later, computers represented numbers in a continuous form (e.g. distance along a scale, rotation of a shaft, or a voltage). Numbers could also be represented in the form of digits, automatically manipulated by a mechanism. Although this approach generally required more complex mechanisms, it greatly increased the precision of results. The development of transistor technology and then the integrated circuit chip led to a series of breakthroughs, starting with transistor computers and then integrated circuit computers, causing digital computers to largely replace analog computers. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Blackbird
The common blackbird (''Turdus merula'') is a species of true thrush. It is also called the Eurasian blackbird (especially in North America, to distinguish it from the unrelated New World blackbirds), or simply the blackbird where this does not lead to confusion with a local species. It breeds in Europe, Asiatic Russia, and North Africa, and has been introduced to Australia and New Zealand. It has a number of subspecies across its large range; a few of the Asian subspecies are sometimes considered to be full species. Depending on latitude, the common blackbird may be resident, partially migratory, or fully migratory. The adult male of the common blackbird (''Turdus merula merula'', the nominate subspecies), which is found throughout most of Europe, is all black except for a yellow eye-ring and bill and has a rich, melodious song; the adult female and juvenile have mainly dark brown plumage. This species breeds in woods and gardens, building a neat, cup-shaped nest, bound ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Logarithm
In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as standard logarithm. Historically, it was known as ''logarithmus decimalis'' or ''logarithmus decadis''. It is indicated by , , or sometimes with a capital (however, this notation is ambiguous, since it can also mean the complex natural logarithmic multi-valued function). On calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base e ≈ 2.71828) rather than common logarithm when they write "log". To mitigate this ambiguity, the ISO 80000 specification recommends that should be written , and should be . Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because . Every nonnegative real number has a unique nonnegative square root, called the ''principal square root'', which is denoted by \sqrt, where the symbol \sqrt is called the '' radical sign'' or ''radix''. For example, to express the fact that the principal square root of 9 is 3, we write \sqrt = 3. The term (or number) whose square root is being considered is known as the ''radicand''. The radicand is the number or expression underneath the radical sign, in this case 9. For nonnegative , the principal square root can also be written in exponent notation, as . Every positive number has two square roots: \sqrt, which is positive, and -\sqrt, which is negative. The two roots can be written more concisely using the ± sign as \plusmn\sq ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Function
In mathematics, a function from a set to a set assigns to each element of exactly one element of .; the words map, mapping, transformation, correspondence, and operator are often used synonymously. The set is called the domain of the function and the set is called the codomain of the function.Codomain ''Encyclopedia of Mathematics'Codomain. ''Encyclopedia of Mathematics''/ref> The earliest known approach to the notion of function can be traced back to works of Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a ''function'' of time. Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). The concept of a function was formalized at the end of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Expression
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Mathematical symbols can designate numbers ( constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax. Many authors distinguish an expression from a ''formula'', the former denoting a mathematical object, and the latter denoting a statement about mathematical objects. For example, 8x-5 is an expression, while 8x-5 \geq 5x-8 is a formula. However, in modern mathematics, and in particular in computer algebra, formulas are viewed as expressions that can be evaluated to ''true'' or ''false'', depending on the values that are given to the variables occurring in the expressions. For example 8x-5 \geq 5x-8 takes the value ''false'' if is given a value less than –1, and the value ''true'' otherwise. Examples The use of express ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paper
Paper is a thin sheet material produced by mechanically or chemically processing cellulose fibres derived from wood, Textile, rags, poaceae, grasses or other vegetable sources in water, draining the water through fine mesh leaving the fibre evenly distributed on the surface, followed by pressing and drying. Although paper was originally made in single sheets by hand, almost all is now made on large machines—some making reels 10 metres wide, running at 2,000 metres per minute and up to 600,000 tonnes a year. It is a versatile material with many uses, including printing, painting, graphics, signage, design, packaging, decorating, writing, and Housekeeping, cleaning. It may also be used as filter paper, wallpaper, book endpaper, conservation paper, laminated worktops, toilet tissue, or currency and security paper, or in a number of industrial and construction processes. The papermaking process developed in east Asia, probably China, at least as early as 105 Common Era, CE, by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Europe
Europe is a large peninsula conventionally considered a continent in its own right because of its great physical size and the weight of its history and traditions. Europe is also considered a subcontinent of Eurasia and it is located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere. Comprising the westernmost peninsulas of Eurasia, it shares the continental landmass of Afro-Eurasia with both Africa and Asia. It is bordered by the Arctic Ocean to the north, the Atlantic Ocean to the west, the Mediterranean Sea to the south and Asia to the east. Europe is commonly considered to be separated from Asia by the watershed of the Ural Mountains, the Ural River, the Caspian Sea, the Greater Caucasus, the Black Sea and the waterways of the Turkish Straits. "Europe" (pp. 68–69); "Asia" (pp. 90–91): "A commonly accepted division between Asia and Europe ... is formed by the Ural Mountains, Ural River, Caspian Sea, Caucasus Mountains, and the Blac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hindu–Arabic Numeral System
The Hindu–Arabic numeral system or Indo-Arabic numeral system Audun HolmeGeometry: Our Cultural Heritage 2000 (also called the Hindu numeral system or Arabic numeral system) is a positional decimal numeral system, and is the most common system for the symbolic representation of numbers in the world. It was invented between the 1st and 4th centuries by Indian mathematicians. The system was adopted in Arabic mathematics by the 9th century. It became more widely known through the writings of the Persian mathematician Al-Khwārizmī: "Historians have speculated on al-Khwarizmi's native language. Since he was born in a former Persian province, he may have spoken the Persian language. It is also possible that he spoke Khwarezmian, a language of the region that is now extinct." (''On the Calculation with Hindu Numerals'', ) and Arab mathematician Al-Kindi (''On the Use of the Hindu Numerals'', ). The system had spread to medieval Europe by the High Middle Ages. The system is ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the decimal, decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian Numerals, Babylonian numeral system, base 60, was the first positional system to be deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euclidean Algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder. It is named after the ancient Greek mathematician Euclid, who first described it in his ''Elements'' (c. 300 BC). It is an example of an ''algorithm'', a step-by-step procedure for performing a calculation according to well-defined rules, and is one of the oldest algorithms in common use. It can be used to reduce fractions to their simplest form, and is a part of many other number-theoretic and cryptographic calculations. The Euclidean algorithm is based on the principle that the greatest common divisor of two numbers does not change if the larger number is replaced by its difference ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an Inference, inferential Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for furthe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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