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Colin MacLaurin
Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for being the youngest professor. The Maclaurin series, a special case of the Taylor series, is named after him. Owing to changes in orthography since that time (his name was originally rendered as M'Laurine), his surname is alternatively written MacLaurin. Early life Maclaurin was born in Kilmodan, Argyll. His father, John Maclaurin, minister of Glendaruel, died when Maclaurin was in infancy, and his mother died before he reached nine years of age. He was then educated under the care of his uncle, Daniel Maclaurin, minister of Kilfinan. A child prodigy, he entered university at age 11. Academic career At eleven, Maclaurin, a child prodigy at the time, entered the University of Glasgow. He graduated Master of Arts three years later by defending ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David Erskine, 11th Earl Of Buchan
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maclaurin's Inequality
In mathematics, Maclaurin's inequality, named after Colin Maclaurin, is a refinement of the inequality of arithmetic and geometric means. Let ''a''1, ''a''2, ..., ''a''''n'' be positive real numbers, and for ''k'' = 1, 2, ..., ''n'' define the averages ''S''''k'' as follows: :S_k = \frac. The numerator of this fraction is the elementary symmetric polynomial of degree ''k'' in the ''n'' variables ''a''1, ''a''2, ..., ''a''''n'', that is, the sum of all products of ''k'' of the numbers ''a''1, ''a''2, ..., ''a''''n'' with the indices in increasing order. The denominator is the number of terms in the numerator, the binomial coefficient \scriptstyle. Maclaurin's inequality is the following chain of inequalities: :S_1 \geq \sqrt \geq \sqrt \geq \cdots \geq \sqrt /math> with equality if and only if all the ''a''''i'' are equal. For ''n'' = 2, this gives the usual inequality of arithmetic and geometric me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Glendaruel
Glendaruel (Gaelic: ''Gleann Dà Ruadhail'') is a glen in the Cowal peninsula in Argyll and Bute, Scotland. The main settlement in Glendaruel is the Clachan of Glendaruel. Features The present Kilmodan Church was built in the Clachan of Glendaruel in 1783. The Clachan of Glendaruel is the current location of Kilmodan Primary School, and the ground of Col-Glen Shinty Club. The ruined Dunans Castle is also located in Glendaruel, while Glendaruel Wood and Crags and the Ruel Estuary are both included in the List of Sites of Special Scientific Interest in Mid Argyll and Cowal. As the nearest Hospital is some miles away in Dunoon, a disused phone box in the village was converted to house a defibrillator. Just weeks before the installation, a tourist in Glendaruel had died from a heart attack. Decline The community is home to around 188 people as of 2008 and has been subject to a general decline in the late 20th century continuing into the early 21st century. The closure of the Gl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthography
An orthography is a set of conventions for writing a language, including norms of spelling, hyphenation, capitalization, word breaks, emphasis, and punctuation. Most transnational languages in the modern period have a writing system, and most of these systems have undergone substantial standardization, thus exhibiting less dialect variation than the spoken language. These processes can fossilize pronunciation patterns that are no longer routinely observed in speech (e.g., "would" and "should"); they can also reflect deliberate efforts to introduce variability for the sake of national identity, as seen in Noah Webster's efforts to introduce easily noticeable differences between American and British spelling (e.g., "honor" and "honour"). Some nations (e.g. France and Spain) have established language academies in an attempt to regulate orthography officially. For most languages (including English) however, there are no such authorities and a sense of 'correct' orthography evol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary algebra deals with the manipulation of variables (commonly represented by Roman letters) as if they were numbers and is therefore essential in all applications of mathematics. Abstract algebra is the name given, mostly in education, to the study of algebraic structures such as groups, rings, and fields (the term is no more in common use outside educational context). Linear algebra, which deals with linear equations and linear mappings, is used for modern presentations of geometry, and has many practical applications (in weather forecasting, for example). There are many areas of mathematics that belong to algebra, some having "algebra" in their name, such as commutative algebra, and some not, such as Galois theory. The word ''algebra'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a ''geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that geometries ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scottish People
The Scots ( sco, Scots Fowk; gd, Albannaich) are an ethnic group and nation native to Scotland. Historically, they emerged in the early Middle Ages from an amalgamation of two Celtic-speaking peoples, the Picts and Gaels, who founded the Kingdom of Scotland (or ''Alba'') in the 9th century. In the following two centuries, the Celtic-speaking Cumbrians of Strathclyde and the Germanic-speaking Angles of north Northumbria became part of Scotland. In the High Middle Ages, during the 12th-century Davidian Revolution, small numbers of Norman nobles migrated to the Lowlands. In the 13th century, the Norse-Gaels of the Western Isles became part of Scotland, followed by the Norse of the Northern Isles in the 15th century. In modern usage, "Scottish people" or "Scots" refers to anyone whose linguistic, cultural, family ancestral or genetic origins are from Scotland. The Latin word ''Scoti'' originally referred to the Gaels, but came to describe all inhabitants of Scotland. Cons ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
French Academy Of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefront of scientific developments in Europe in the 17th and 18th centuries, and is one of the earliest Academy of Sciences, Academies of Sciences. Currently headed by Patrick Flandrin (President of the Academy), it is one of the five Academies of the Institut de France. History The Academy of Sciences traces its origin to Colbert's plan to create a general academy. He chose a small group of scholars who met on 22 December 1666 in the King's library, near the present-day Bibliothèque nationale de France, Bibliothèque Nationals, and thereafter held twice-weekly working meetings there in the two rooms assigned to the group. The first 30 years of the Academy's existence were relatively informal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trisectrix Of Maclaurin
In algebraic geometry, the trisectrix of Maclaurin is a cubic plane curve notable for its trisectrix property, meaning it can be used to trisect an angle. It can be defined as locus of the point of intersection of two lines, each rotating at a uniform rate about separate points, so that the ratio of the rates of rotation is 1:3 and the lines initially coincide with the line between the two points. A generalization of this construction is called a sectrix of Maclaurin. The curve is named after Colin Maclaurin who investigated the curve in 1742. Equations Let two lines rotate about the points P = (0,0) and P_1 = (a, 0) so that when the line rotating about P has angle \theta with the ''x'' axis, the rotating about P_1 has angle 3\theta. Let Q be the point of intersection, then the angle formed by the lines at Q is 2\theta. By the law of sines, : = \! so the equation in polar coordinates is (up to translation and rotation) :r= a \frac = \frac = (4 \cos \theta - \sec \theta)\!. The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Braikenridge–Maclaurin Theorem
In geometry, the , named for 18th century British mathematicians William Braikenridge and Colin Maclaurin, is the converse to Pascal's theorem. It states that if the three intersection points of the three pairs of lines through opposite sides of a hexagon lie on a line ''L'', then the six vertices of the hexagon lie on a conic ''C''; the conic may be degenerate, as in Pappus's theorem. The Braikenridge–Maclaurin theorem may be applied in the Braikenridge–Maclaurin construction In Euclidean and projective geometry, just as two (distinct) points determine a line (a degree-1 plane curve), five points determine a conic (a degree-2 plane curve). There are additional subtleties for conics that do not exist for lines, and thu ..., which is a synthetic construction of the conic defined by five points, by varying the sixth point. Namely, Pascal's theorem states that given six points on a conic (the vertices of a hexagon), the lines defined by opposite sides intersect in three col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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