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Radians
The radian (SI symbol rad) is the SI unit for measuring angles, and is the standard unit of angular measure used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it subtends; one radian is just under 57.3 degrees (expansion at  A072097). The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and the radian is now considered an SI derived unit.[1] Separately, the SI unit of solid angle measurement is the steradian. The radian is most commonly represented by the symbol rad.[2] An alternative symbol is c, the superscript letter c (for "circular measure"), the letter r, or a superscript R,[3] but these symbols are infrequently used as it can be easily mistaken for a degree symbol (°) or a radius (r)
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Rad (unit)
The rad is a deprecated unit of absorbed radiation dose, defined as 1 rad = 0.01 Gy = 0.01 J/kg.[1] It was originally defined in CGS units in 1953 as the dose causing 100 ergs of energy to be absorbed by one gram of matter. It has been replaced by the gray (Gy) in SI derived units but is still used in the United States, though "strongly discouraged" in the chapter 5.2 of style guide for U.S. National Institute of Standards and Technology authors.[2] A related unit, the roentgen, is used to quantify the radiation exposure
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Belfast
Belfast
Belfast
(/ˈbɛlfɑːst, -fæst/; from Irish: Béal Feirste), meaning "rivermouth of the sandbanks"[11] is the capital and largest city of Northern Ireland, and the second largest on the island of Ireland.[12] On the River Lagan, it had a population of 333,871 in 2015.[1] By the early 1800s the former town was home to a major port. Belfast played a key role in the Industrial Revolution
Industrial Revolution
in the 19th century, becoming the biggest linen producer in the world, earning it the nickname "Linenopolis". By the time it was granted city status in 1888, it was a major centre of the Irish linen as well as tobacco-processing, rope-making and shipbuilding industries. Harland and Wolff, which built the RMS Titanic, was the world's biggest and most productive shipyard.[13] It later also sustained a major aerospace and missiles industry
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°
؋ ​₳ ​ ฿ ​₿ ​ ₵ ​¢ ​₡ ​₢ ​ $ ​₫ ​₯ ​֏ ​ ₠ ​€ ​ ƒ ​₣ ​ ₲ ​ ₴ ​ ₭ ​ ₺ ​₾ ​ ₼ ​ℳ ​₥ ​ ₦ ​ ₧ ​₱ ​₰ ​£ ​ 元 圆 圓 ​﷼ ​៛ ​₽ ​₹ ₨ ​ ₪ ​ ৳ ​₸ ​₮ ​ ₩ ​ ¥ 円Uncommon typographyasterism ⁂fleuron, hedera ❧index, fist ☞interrobang ‽irony punctuation ⸮lozenge ◊tie ⁀RelatedDiacritics Logic symbolsWhitespace charactersIn other scriptsChinese Hebrew Japanese Korean Category Portal Bookv t eThe degree symbol (°) is a typographical symbol that is used, among other things, to represent degrees of arc (e.g
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Circumference
In geometry, the circumference (from Latin circumferentia, meaning "carrying around") of a circle is the (linear) distance around it.[1] That is, the circumference would be the length of the circle if it were opened up and straightened out to a line segment. Since a circle is the edge (boundary) of a disk, circumference is a special case of perimeter.[2] The perimeter is the length around any closed figure and is the term used for most figures excepting the circle and some circular-like figures such as ellipses
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Arc Length
Determining the length of an irregular arc segment is also called rectification of a curve. Historically, many methods were used for specific curves
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Roger Cotes
Roger Cotes FRS (10 July 1682 – 5 June 1716) was an English mathematician, known for working closely with Isaac Newton
Isaac Newton
by proofreading the second edition of his famous book, the Principia, before publication. He also invented the quadrature formulas known as Newton–Cotes formulas
Newton–Cotes formulas
and first introduced what is known today as Euler's formula.[5] He was the first Plumian Professor at Cambridge University from 1707 until his death.Contents1 Early life 2 Astronomy 3 The Principia 4 Mathematics 5 Death and assessment 6 See also 7 References 8 Sources 9 External linksEarly life[edit] Cotes was born in Burbage, Leicestershire. His parents were Robert, the rector of Burbage, and his wife, Grace, née Farmer. Roger had an elder brother, Anthony (born 1681), and a younger sister, Susanna (born 1683), both of whom died young
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Al-Kashi
Ghiyāth al-Dīn Jamshīd Masʿūd al-Kāshī (or al-Kāshānī)[1] (Persian: غیاث الدین جمشید کاشانی‎ Ghiyās-ud-dīn Jamshīd Kāshānī) (c. 1380 Kashan, Iran – 22 June 1429 Samarkand, Transoxania) was a Persian astronomer and mathematician.[2][3] Much of al-Kāshī's work was not brought to Europe, and much, even the extant work, remains unpublished in any form.[4]Contents1 Biography 2 Astronomy2.1 Khaqani Zij 2.2 Astronomical Treatise on the size and distance of heavenly bodies 2.3 Treatise on Astronomical Observational Instruments2.3.1 Plate of Conjunctions 2.3.2 Planetary computer3 Mathematics3.1 Law of cosines 3.2 The Treatise of Chord and Sine 3.3 The Key to Arithmetic3.3.1 Computation of 2π 3.3.2 Decimal fractions 3.3.3 Khayyam's triangle4 Biographical film 5 Notes 6 See also 7 References 8 External linksBiography[edit] Al-Kashi was one of the best mathematicians in the history of Iran
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James Thomson (engineer)
Prof James Thomson FRS FRSE
FRSE
LLD (16 February 1822 – 8 May 1892) was an engineer and physicist whose reputation is substantial though it is overshadowed by that of his younger brother William Thomson (Lord Kelvin).Contents1 Biography 2 Legacy 3 Publications 4 References 5 External linksBiography[edit] Born in Belfast, much of his youth was spent in Glasgow. His father James was professor of mathematics at the University of Glasgow
Glasgow
from 1832 onward and his younger brother William was to become Baron Kelvin. James attended Glasgow
Glasgow
University from a young age and graduated (1839) with high honors in his late teens. After graduation, he served brief apprenticeships with practical engineers in several domains; and then gave a considerable amount of his time to theoretical and mathematical engineering studies, often in collaboration with his brother, during his twenties in Glasgow
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Lord Kelvin
William Thomson, 1st Baron Kelvin, OM, GCVO, PC, FRS, FRSE
FRSE
(26 June 1824 – 17 December 1907) was a Scots-Irish[1][2] mathematical physicist and engineer who was born in Belfast
Belfast
in 1824. At the University of Glasgow
Glasgow
he did important work in the mathematical analysis of electricity and formulation of the first and second laws of thermodynamics, and did much to unify the emerging discipline of physics in its modern form. He worked closely with mathematics professor Hugh Blackburn
Hugh Blackburn
in his work. He also had a career as an electric telegraph engineer and inventor, which propelled him into the public eye and ensured his wealth, fame and honour. For his work on the transatlantic telegraph project he was knighted in 1866 by Queen Victoria, becoming Sir William Thomson
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Queen's University Belfast
Queen's University
Queen's University
Belfast
Belfast
(informally Queen's or QUB) is a public research university in Belfast, Northern Ireland.[note 1] The university was chartered in 1845, and opened in 1849 as "Queen's College, Belfast". The university forms the focal point of the Queen's Quarter
Queen's Quarter
area of the city, one of Belfast's six cultural districts
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Thomas Muir (mathematician)
Sir Thomas Muir FRS[1] FRSE
FRSE
CMG LLD (25 August 1844 – 21 March 1934) was a Scottish mathematician, remembered as an authority on determinants.[2][3][4]Contents1 Life 2 Family 3 Publications by Sir Thomas Muir 4 References 5 External linksLife[edit] He was born in Stonebyres in South Lanarkshire, and brought up in the small town of Biggar. He was educated at Wishaw
Wishaw
Public School. At the University of Glasgow
University of Glasgow
he changed his studies from classics to mathematics after advice from the future Lord Kelvin. After graduating he held positions at the University of St Andrews
University of St Andrews
and the University of Glasgow. From 1874 to 1892 he taught at Glasgow High School. In 1882 he published Treatise on the theory of determinants; then in 1890 he published a History of determinants
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Θ
Theta
Theta
(UK: /ˈθiːtə/, US: /ˈθeɪtə/; uppercase Θ or ϴ, lowercase θ (which resembles digit 0 with horizontal line) or ϑ; Ancient Greek: θῆτα thē̂ta [tʰɛ̂ːta]; Modern: θήτα thī́ta [ˈθita]) is the eighth letter of the Greek alphabet, derived from the Phoenician letter Teth
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University Of St Andrews
University
University
of St Andrews                                 St Mary's College                                       School of Medicine                                 St Leonard's College                              &
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Regular Polygon
Regular polygonsEdges and vertices nSchläfli symbol n Coxeter–Dynkin diagramSymmetry group Dn, order 2nDual polygon Self-dualArea (with side length, s) A = 1 4 n s 2 cot ⁡ ( π n ) displaystyle A= tfrac 1 4 ns^ 2 cot left( frac pi n right) Internal angle ( n − 2 ) × 180 ∘ n displaystyle (n-2)times frac 180^ circ n Internal angle
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Calculus
Calculus
Calculus
(from Latin
Latin
calculus, literally 'small pebble', used for counting and calculations, as on an abacus)[1] is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. It has two major branches, differential calculus (concerning rates of change and slopes of curves),[2] and integral calculus (concerning accumulation of quantities and the areas under and between curves).[3] These two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Wilhelm Leibniz
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