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Napierian Logarithm
The term Napierian logarithm or Naperian logarithm, named after John Napier, is often used to mean the natural logarithm. Napier did not introduce this ''natural'' logarithmic function, although it is named after him. However, if it is taken to mean the "logarithms" as originally produced by Napier, it is a function given by (in terms of the modern natural logarithm): : \mathrm(x) = -10^7 \ln (x/10^7) The Napierian logarithm satisfies identities quite similar to the modern logarithm, such as : \mathrm(xy) \approx \mathrm(x)+\mathrm(y)-161180956 or :\mathrm(xy/10^7) = \mathrm(x)+\mathrm(y) In Napier's 1614 ''Mirifici Logarithmorum Canonis Descriptio'', he provides tables of logarithms of sines for 0 to 90°, where the values given (columns 3 and 5) are : \mathrm(\theta) = -10^7 \ln (\sin(\theta)) Properties Napier's "logarithm" is related to the natural logarithm by the relation : \mathrm (x) \approx 10000000 (16.11809565 - \ln x) and to the common logarithm In mat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Napier
John Napier of Merchiston ( ; Latinisation of names, Latinized as Ioannes Neper; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. John Napier is best known as the discoverer of logarithms. He also invented the so-called "Napier's bones" and made common the use of the decimal point in arithmetic and mathematics. Napier's birthplace, Merchiston Castle, Merchiston Tower in Edinburgh, is now part of the facilities of Edinburgh Napier University. There is a memorial to him at St Cuthbert's Parish Church, St Cuthbert's at the west side of Edinburgh.Monuments and monumental inscriptions in Scotland: The Grampian Society, 1871 Life Napier's father was Archibald Napier (landowner), Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of the politician and judge Francis Bothwell, and a sister of Adam Bothwell who bec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Logarithm
The natural logarithm of a number is its logarithm to the base of a logarithm, base of the e (mathematical constant), mathematical constant , which is an Irrational number, irrational and Transcendental number, transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if the base is implicit, simply . Parentheses are sometimes added for clarity, giving , , or . This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity. The natural logarithm of is the exponentiation, power to which would have to be raised to equal . For example, is , because . The natural logarithm of itself, , is , because , while the natural logarithm of is , since . The natural logarithm can be defined for any positive real number as the Integral, area under the curve from to (with the area being negative when ). The simplicity of this definition, which is matched in many other formulas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , then is the logarithm of to base , written , so . As a single-variable function, the logarithm to base is the inverse of exponentiation with base . The logarithm base is called the ''decimal'' or ''common'' logarithm and is commonly used in science and engineering. The ''natural'' logarithm has the number as its base; its use is widespread in mathematics and physics because of its very simple derivative. The ''binary'' logarithm uses base and is widely used in computer science, information theory, music theory, and photography. When the base is unambiguous from the context or irrelevant it is often omitted, and the logarithm is written . Logarithms were introduced by John Napier in 1614 as a means of simplifying calculation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirifici Logarithmorum Canonis Descriptio
''Mirifici Logarithmorum Canonis Descriptio'' (Description of the Wonderful Canon of Logarithms, 1614) and ''Mirifici Logarithmorum Canonis Constructio'' (Construction of the Wonderful Canon of Logarithms, 1619) are two books in Latin by John Napier expounding the method of logarithms. While others had approached the idea of logarithms, notably Jost Bürgi, it was Napier who first published the concept, along with easily used Mathematical table, precomputed tables, in his ''Mirifici Logarithmorum Canonis Descriptio.'' Prior to the introduction of logarithms, high accuracy numerical calculations involving multiplication, division and root extraction were laborious and error prone. Logarithms greatly simplify such calculations. As Napier put it: “…nothing is more tedious, fellow mathematicians, in the practice of the mathematical arts, than the great delays suffered in the tedium of lengthy multiplications and divisions, the finding of ratios, and in the extraction of square ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Common Logarithm
In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian logarithm. The name "Briggsian logarithm" is in honor of the British mathematician Henry Briggs who conceived of and developed the values for the "common logarithm". Historically', the "common logarithm" was known by its Latin name ''logarithmus decimalis'' or ''logarithmus decadis''. The mathematical notation for using the common logarithm is , , or sometimes with a capital ; on calculators, it is printed as "log", but mathematicians usually mean natural logarithm (logarithm with base ≈ 2.71828) rather than common logarithm when writing "log". Before the early 1970s, handheld electronic calculators were not available, and mechanical calculators capable of multiplication were bulky, expensive and not widely available. Instead, tables of base-10 logarithms were used in science, engineering and navi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Logarithms
History is the systematic study of the past, focusing primarily on the human past. As an academic discipline, it analyses and interprets evidence to construct narratives about what happened and explain why it happened. Some theorists categorize history as a social science, while others see it as part of the humanities or consider it a hybrid discipline. Similar debates surround the purpose of history—for example, whether its main aim is theoretical, to uncover the truth, or practical, to learn lessons from the past. In a more general sense, the term ''history'' refers not to an academic field but to the past itself, times in the past, or to individual texts about the past. Historical research relies on primary and secondary sources to reconstruct past events and validate interpretations. Source criticism is used to evaluate these sources, assessing their authenticity, content, and reliability. Historians strive to integrate the perspectives of several sources to develop a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
