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Colin Maclaurin
Colin Maclaurin (; gd, Cailean MacLabhruinn; February 1698 – 14 June 1746) was a Scottish Scottish usually refers to something of, from, or related to Scotland, including: *Scottish Gaelic, a Celtic Goidelic language of the Indo-European language family native to Scotland *Scottish English *Scottish national identity, the Scottish iden ... mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ... who made important contributions to geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ... and algebra Algebra (from ar, الجبر, lit=reunion of broken parts ...
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David Erskine, 11th Earl Of Buchan
David Steuart Erskine, 11th Earl of Buchan (12 June 174219 April 1829), styled Lord Cardross between 1747 and 1767, was a Scotland, Scottish antiquarian, founder of the Society of Antiquaries of Scotland in 1780, and patron of the arts and sciences. Background and education Erskine was the second but eldest surviving son of Henry Erskine, 10th Earl of Buchan, by Agnes, daughter of Sir James Steuart, 7th Baronet. He was the brother of Henry Erskine (lawyer), Henry Erskine and Thomas Erskine, 1st Baron Erskine, Lord Erskine. He studied at St. Andrews University (1755–59) Edinburgh University, Edinburgh University (1760-62) and University of Glasgow, Glasgow University (1762–63). He studied under Adam Smith, and Joseph Black. He married, on 15 October 1771, his second cousin Margaret Fraser (d. 12 May 1819), the great-granddaughter of David Erskine, 9th Earl of Buchan. They had no children. Career His active criticism helped to effect a change in the method of electing Scottish ...
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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 number, 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 inequality (mathematics), inequalities: :S_1 \geq \sqrt \geq \sqrt[3] \geq \cdots \geq \sqrt[n] with equality if and only if all the ''a''''i'' are equal. For ''n'' = 2, this gives the usual ...
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Glendaruel
Glendaruel is a glen in the Cowal peninsula in Argyll and Bute, Scotland. The main settlement in Glendaruel (Scottish Gaelic, Gaelic: ''Gleann Dà Ruadhail'') 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. Th ...
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Orthography
An orthography is a set of conventions for writing Writing is a medium of human communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an apparent answer to the painful divisions between self and other, private and public, and inner tho ... a language A language is a structured system of communication Communication (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the ..., including norms of spelling Spelling is a set of conventions that regulate the way of using s (writing system) to represent a language in its . In other words, spelling is the rendering of speech sound (phoneme) into writing (grapheme). Spelling is one of the elements of , ..., hyphen The hyphen is a punctuation mark used to join word In linguistics, a word of a spoken language can be defined as the smallest ...
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Taylor Series
In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., the Taylor series of a function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ... is an infinite sum In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ... of terms that are expressed in terms of the function's derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as number ...
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Algebra
Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the broad areas of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ..., together with number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of devoted primarily to the study of the s and . German mathematician (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen ..., geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ... and analysis Analysis is the process of breaking a compl ...
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Geometry
Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic Arithmetic (from the Ancient Greek, Greek wikt:en:ἀριθμός#Ancient Greek, ἀριθμός ''arithmos'', 'number' and wikt:en:τική#Ancient Greek, τική wikt:en:τέχνη#Ancient Greek, έχνη ''tiké échne', 'art' or 'cra ..., one of the oldest branches of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal .... It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a geometer A geometer is a mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancie ...
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Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and their changes (cal ... in their work, typically to solve mathematical problem A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), ...s. Mathematicians are concerned with number A number is a mathematical object A mathematical object is an abstract concept arising in mathematics. In the usual language of mathematics, an ''object'' is anything that has been (or could be) formally defined, and with which one may do deduct ...s, data Data (; ) are individual facts A fact is s ...
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Scottish People
The Scots ( sco, Scots Fowk; gd, Albannaich) are a nation and ethnic group native to Scotland. Historically, they emerged in the Scotland in the Early Middle Ages, early Middle Ages from an amalgamation of two Celtic languages, Celtic-speaking peoples, the Picts and Gaels, who founded the Kingdom of Scotland (or ''Kingdom of Alba, Alba'') in the 9th century. In the following two centuries, the Celtic-speaking Hen Ogledd, Cumbrians of Kingdom of Strathclyde, Strathclyde and the Germanic-speaking Anglo-Saxons, Angles of north Northumbria became part of Scotland. In the Scotland in the High Middle Ages, High Middle Ages, during the 12th-century Davidian Revolution, small numbers of Normans, Norman nobles migrated to the Lowlands. In the 13th century, the Norse-Gaels of the Kingdom of the Isles, 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, c ...
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French Academy Of Sciences
The French Academy of Sciences (French: ''Académie des sciences'') is a learned society A learned society (; also known as a learned academy, scholarly society, or academic association) is an organization that exists to promote an discipline (academia), academic discipline, profession, or a group of related disciplines such as the ..., founded in 1666 by Louis XIV Louis XIV (Louis Dieudonné; 5 September 16381 September 1715), also known as Louis the Great () or the Sun King (), was King of France from 14 May 1643 until his death in 1715. His reign of 72 years and 110 days is the List of longest-reigning mo ... at the suggestion of Jean-Baptiste Colbert Jean-Baptiste Colbert (; 29 August 1619 – 6 September 1683) was a French statesman who served as First Minister of State from 1661 until his death in 1683 under the rule of King Louis XIV. His lasting impact on the organisation of the country's ..., to encourage and protect the spirit of French scientific research ...
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Trisectrix Of Maclaurin
In 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 curve is th ...
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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, which is a synthetic geometry, 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 collinear points. This can be reversed to construct the possible locations for a sixth point, given five existing ones. References

Theorems about polygons Conic sections {{elementary-geometry-stub ...
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