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Approximations Of Pi
An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ''ad-'' (''ad-'' before ''p'' becomes ap- by assimilation) meaning ''to''. Words like ''approximate'', ''approximately'' and ''approximation'' are used especially in technical or scientific contexts. In everyday English, words such as ''roughly'' or ''around'' are used with a similar meaning. It is often found abbreviated as ''approx.'' The term can be applied to various properties (e.g., value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g., the approximate time was 10 o'clock). Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws. In science, approximation can refer to u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equality (mathematics)
In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between and is written , and pronounced equals . The symbol "" is called an "equals sign". Two objects that are not equal are said to be distinct. For example: * x=y means that and denote the same object. * The identity (x+1)^2=x^2+2x+1 means that if is any number, then the two expressions have the same value. This may also be interpreted as saying that the two sides of the equals sign represent the same function. * \ = \ if and only if P(x) \Leftrightarrow Q(x). This assertion, which uses set-builder notation, means that if the elements satisfying the property P(x) are the same as the elements satisfying Q(x), then the two uses of the set-builder notation define the same set. This property is often expressed as "two sets that have th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Significant Figures
Significant figures (also known as the significant digits, ''precision'' or ''resolution'') of a number in positional notation are digits in the number that are reliable and necessary to indicate the quantity of something. If a number expressing the result of a measurement (e.g., length, pressure, volume, or mass) has more digits than the number of digits allowed by the measurement resolution, then only as many digits as allowed by the measurement resolution are reliable, and so only these can be significant figures. For example, if a length measurement gives 114.8 mm while the smallest interval between marks on the ruler used in the measurement is 1 mm, then the first three digits (1, 1, and 4, showing 114 mm) are certain and so they are significant figures. Digits which are uncertain but ''reliable'' are also considered significant figures. In this example, the last digit (8, which adds 0.8 mm) is also considered a significant figure even though ther ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Korean Language
Korean ( South Korean: , ''hangugeo''; North Korean: , ''chosŏnmal'') is the native language for about 80 million people, mostly of Korean descent. It is the official and national language of both North Korea and South Korea (geographically Korea), but over the past years of political division, the two Koreas have developed some noticeable vocabulary differences. Beyond Korea, the language is recognised as a minority language in parts of China, namely Jilin Province, and specifically Yanbian Prefecture and Changbai County. It is also spoken by Sakhalin Koreans in parts of Sakhalin, the Russian island just north of Japan, and by the in parts of Central Asia. The language has a few extinct relatives which—along with the Jeju language (Jejuan) of Jeju Island and Korean itself—form the compact Koreanic language family. Even so, Jejuan and Korean are not mutually intelligible with each other. The linguistic homeland of Korean is suggested to be somewhere in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taiwanese Mandarin
Taiwanese Mandarin, ''Guoyu'' ( zh, s=, t=國語, p=Guóyǔ, l=National Language, first=t) or ''Huayu'' ( zh, s=, t=華語, p=Huáyǔ, first=t, l=Mandarin Language, labels=no) refers to Mandarin Chinese spoken in Taiwan. A large majority of the Taiwanese population is fluent in Mandarin, though many also speak Taiwanese Hokkien, commonly called ''Minnanyu'' ( ''Mǐnnányǔ'') or Southern Min, a variety of Min Chinese. This language has had significant influence on Mandarin as spoken on the island. ''Guoyu'' is not the indigenous language of Taiwan. Chinese settlers came to Taiwan in the 16th century, but spoke other Chinese languages, primarily Southern Min. Japan annexed Taiwan in 1895 and governed the island as a colony for the next 50 years, during which time Japanese was introduced and taught in schools, while non-Mandarin languages were spoken at home. With the defeat of Imperial Japan in World War II, Taiwan was returned to the Republic of China under the Kuomintang (KMT), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Language
is spoken natively by about 128 million people, primarily by Japanese people and primarily in Japan, the only country where it is the national language. Japanese belongs to the Japonic or Japanese- Ryukyuan language family. There have been many attempts to group the Japonic languages with other families such as the Ainu, Austroasiatic, Koreanic, and the now-discredited Altaic, but none of these proposals has gained widespread acceptance. Little is known of the language's prehistory, or when it first appeared in Japan. Chinese documents from the 3rd century AD recorded a few Japanese words, but substantial Old Japanese texts did not appear until the 8th century. From the Heian period (794–1185), there was a massive influx of Sino-Japanese vocabulary into the language, affecting the phonology of Early Middle Japanese. Late Middle Japanese (1185–1600) saw extensive grammatical changes and the first appearance of European loanwords. The basis of the standard dialect moved f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Limit (mathematics)
In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value. Limits are essential to calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals. The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory. In formulas, a limit of a function is usually written as : \lim_ f(x) = L, (although a few authors may use "Lt" instead of "lim") and is read as "the limit of of as approaches equals ". The fact that a function approaches the limit as approaches is sometimes denoted by a right arrow (→ or \rightarrow), as in :f(x) \to L \text x \to c, which reads "f of x tends to L as x tends to c". History Grégoire de Saint-Vincent gave the first definition of limit (terminus) of a geometric series in his work ''Opus Geometricum'' (1647): "The ''terminus'' of a pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Congruence Relation
In abstract algebra, a congruence relation (or simply congruence) is an equivalence relation on an algebraic structure (such as a group, ring, or vector space) that is compatible with the structure in the sense that algebraic operations done with equivalent elements will yield equivalent elements. Every congruence relation has a corresponding quotient structure, whose elements are the equivalence classes (or congruence classes) for the relation. Basic example The prototypical example of a congruence relation is congruence modulo n on the set of integers. For a given positive integer n, two integers a and b are called congruent modulo n, written : a \equiv b \pmod if a - b is divisible by n (or equivalently if a and b have the same remainder when divided by n). For example, 37 and 57 are congruent modulo 10, : 37 \equiv 57 \pmod since 37 - 57 = -20 is a multiple of 10, or equivalently since both 37 and 57 have a remainder of 7 when divided by 10. Congruence modulo n (for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isomorphism
In mathematics, an isomorphism is a structure-preserving mapping between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them. The word isomorphism is derived from the Ancient Greek: ἴσος ''isos'' "equal", and μορφή ''morphe'' "form" or "shape". The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties (excluding further information such as additional structure or names of objects). Thus isomorphic structures cannot be distinguished from the point of view of structure only, and may be identified. In mathematical jargon, one says that two objects are . An automorphism is an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if there is only one isomorphism between the two structures (as it is the case for solutions of a univer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proportionality (mathematics)
In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality. This definition is commonly extended to related varying quantities, which are often called ''variables''. This meaning of ''variable'' is not the common meaning of the term in mathematics (see variable (mathematics)); these two different concepts share the same name for historical reasons. Two functions f(x) and g(x) are ''proportional'' if their ratio \frac is a constant function. If several pairs of variables share the same direct proportionality constant, the equation expressing the equality of these ratios is called a proportion, e.g., (for details see Ratio). Proportionality is closely rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LaTeX
Latex is an emulsion (stable dispersion) of polymer microparticles in water. Latexes are found in nature, but synthetic latexes are common as well. In nature, latex is found as a milky fluid found in 10% of all flowering plants (angiosperms). It is a complex emulsion that coagulates on exposure to air, consisting of proteins, alkaloids, starches, sugars, oils, tannins, resins, and gums. It is usually exuded after tissue injury. In most plants, latex is white, but some have yellow, orange, or scarlet latex. Since the 17th century, latex has been used as a term for the fluid substance in plants, deriving from the Latin word for "liquid". It serves mainly as defense against herbivorous insects. Latex is not to be confused with plant sap; it is a distinct substance, separately produced, and with different functions. The word latex is also used to refer to natural latex rubber, particularly non-vulcanized rubber. Such is the case in products like latex gloves, latex condoms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alfred Greenhill
Sir Alfred George Greenhill, FRS FRAeS (29 November 1847 in London – 10 February 1927 in London), was a British mathematician. George Greenhill was educated at Christ's Hospital School and from there he went to St John's College, Cambridge in 1866. In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK. He held this chair until his retirement in 1908. His 1892 textbook on applications of elliptic functions is of acknowledged excellence. He was one of the world's leading experts on applications of elliptic integrals in electromagnetic theory. He was a Plenary Speaker of the ICM in 1904 at Heidelberg (where he also gave a section talk) and an Invited Speaker of the ICM in 1908 at Rome, in 1920 at Strasbourg, and in 1924 at Toronto. Greenhill formula In 1879, Greenhill developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowance ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Asymptotic Analysis
In mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function as becomes very large. If , then as becomes very large, the term becomes insignificant compared to . The function is said to be "''asymptotically equivalent'' to , as ". This is often written symbolically as , which is read as " is asymptotic to ". An example of an important asymptotic result is the prime number theorem. Let denote the prime-counting function (which is not directly related to the constant pi), i.e. is the number of prime numbers that are less than or equal to . Then the theorem states that \pi(x)\sim\frac. Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there in terms of big O notation. Definition Formally, given functions and , we define a binary relation f(x) \sim g(x) \qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
