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Lyn 1: [[Image:James_Gregory.jpeg\|thumb\|175px\|right\|James Gregory]] '''James Gregory''' (November [[1638]] – Oktober [[1675]]), was 'n [[Skotland\|Skotse]] [[wiskundige]] en [[sterrekundige]]. Hy is in [[Drumoak]], [[Aberdeenshire (unitêr)\|Aberdeenshire]] gebore en het in [[Edinburgh]] gesterf. Hy was opeenvolgend professor by die [[Universiteit van Sint Andrews]] en die [[Universiteit van Edinburgh]]. In [[1663]] het Gregory ''Optica Promota'' gepubliseer waarin hy die kompakte weerkaatsende teleskoop, wat as die [[Gregory-teleskoop]] bekendstaan, beskryf. Sy optikastelsel word ook in radioteleskope soos die Arecibo, wat oor 'n "Gregory-koepel" beskik gebruik.<ref>{{cite web \|url=http://www.pbs.org/safarchive/3_ask/archive/qna/3291_cordes.html \|title=Jim Cordes Big Dish \|accessdate=2007-11-22}}</ref> Die teleskoop ontwerp het die aandag verskeie mense in wetenskapkringe: die Oxfordse [[fisikus]] [[Robert Hooke]], Sir [[Robert Moray]], stigterslid van die [[Royal Society]] en[[Isaac Newton]], wat aan 'n soortgelyke projek gewerk het. Die Gregory-teleskoop was die eerste praktiese spieëlteleskoop en het vir 'n eeu en 'n half die standaard waarnemingsinstrument gebly. In die ''Optica Promota'' het hy ook 'n metode beskryf waarin die Oorgang van Venus gebruik word om die afstand van die Aarde na die [[Son]] te meet. Die ~~metdode~~metode is later deur [[Edmund Halley]] aangemoedig en aangeneem as die grondslag vir die eerste meting van die [[Astronomiese eenheid]]. Gregory, wat 'n entoeasitiese ondersteuner van Newton was, het later vriendskaplike korrespondensie met hom gevoer en sy idees in sy eie dosering opgeneem; idees wat om daardie stadium omsterde en as heel revolusionêr gesien is. ~~<!--~~ Later, Gregory, who was an enthusiastic supporter of Newton, carried on much friendly correspondence with him and incorporated his ideas into his own teaching, ideas which at that time were controversial and considered quite revolutionary. In [[1667]] het hy ''Vera Circuli et Hyperbolae Quadratura'' gepubliseer waarin hy aangetoon het hoe die oppervlak van die [[sirkel]] en [[hiperbool]] in die vorm van oneindige konvergente reekse verkry kan word. Hierdie werk bevat 'n merkwaardige meetkundige stelling wat beweer dat die verhouding van die oppervlak van enige arbitrêre sektor van 'n sirkel tot dié van die omringde reguliere poligone nie uitdrukbaar is in 'n eindige aantal terme nie. Hy het gevolglik die afleiding gemaak dat die [[kwadratuur van die sirkel]] onmoontlik is. Dit is deur [[Jean-Étienne Montucla\|Montucla]] aanvaar, maar dit is nie afdoende nie, aangesien dit denkbaar is dat een of ander besondere sektor gekwadreer sou kon word, en dat hierdie besondere sektor die hele sirkel mog wees. Nogtans was Gregory effektief onder die eerste om te spekuleer oor die bestan van wat nou [[transendentale getal]]le genoem word. Verder kan beide die eerste bewys van die fundamentele teorema van [[analise]] en die ontdekking van die [[Taylor-reeks]] beide aan hom toegeskryf word. Die boek bevat ook reeks-uitbreidings van [[sinus\|sin]](x), [[cosinus\|cos]](x), boogsin(x) en boogcos(x). (Die vroegste formulering van die uitbreidings is gemaak deur Madhava in [[Indië]] in die [[14de eeu]]). Dit is in [[1668]] herdruk met 'n aanhangsel, ''Geometriae Pars'', waarin Gregory verduidelik hoe die volumes van [[omwentelingsligaam]] bepaal kon word. In [[1667]] he issued his ''Vera Circuli et Hyperbolae Quadratura'', in which he showed how the areas of the [[circle]] and [[hyperbola]] could be obtained in the form of [[Infinite series\|infinite convergent series]]. This work contains a remarkable geometrical proposition to the effect that the [[ratio]] of the area of any arbitrary sector of a circle to that of the inscribed or circumscribed [[regular polygon]]s is not expressible by a finite number of terms. Hence he inferred that the [[quadrature of the circle]] was impossible; this was accepted by [[Jean-Étienne Montucla\|Montucla]], but it is not conclusive, for it is conceivable that some particular sector might be squared, and this particular sector might be the whole circle. Nevertheless Gregory was effectively among the first to speculate about the existence of what are now termed [[transcendental numbers]]. In addition the first proof of the [[fundamental theorem of calculus]] and the discovery of the [[Taylor series]] can both be attributed to him. In [[1671]], of moontlik vroeër, het hy die teorema wat die [[14de eeu]]se Indiese wiskundige [[Madhava van Sangamagrama]] orosponklik ontdek het, die [[boogtangens]]-reeks The book also contains series expansions of [[sine\|sin]](x), [[cosine\|cos]](x), arcsin(x) and arccos(x). (The earliest enunciations of these expansions were made by [[Madhava of Sangamagrama\|Madhava]] in [[India]] in the [[14th century]]). It was reprinted in [[1668]] with an appendix, ''Geometriae Pars'', in which Gregory explained how the volumes of [[solids of revolution]] could be determined. In [[1671]], or perhaps earlier, he rediscovered the theorem that 14th century [[Indian mathematics\|Indian mathematician]] [[Madhava of Sangamagrama]] had originally discovered, the [[arctangent]] series :<math>\theta = \tan \theta - (1/3) \tan^3 \theta + (1/5) \tan^5 \theta - \cdots,\,</math> ~~for~~vir θ ~~between~~tussen −π/4 ~~and~~en π/4. ~~This formula was used by Madhava to calculate digits of [[pi\|π]] and later used in [[Europe]] for the same purpose, although more efficient formulas were later discovered.~~ Hierdie formule is eers deur Madhava en later in [[Europa]] gebruik om diesyfers van [[pi\|π]] uit te werk. James Gregory discovered [[diffraction]] and the [[Diffraction grating]] by passing [[sunlight]] through a bird [[feather]] and observing the diffraction pattern produced. In particular he observed the splitting of sunlight into its component colours - this occurred a year after Newton had done the same with a [[prism (optics)\|prism]] and the phenomenon was still highly controversial. James Gregory het [[diffraksie]] en die Diffraksietralie ontdek deur [[sonlig]] deur 'n voël se veer te laat skyn en die diffraksiepartroon wat geproduseer word te bestudeer. Hy het in besonder die verdeling van sonlig in die komponentkleur waargeneem - dit het gebeur 'n jaar nadat Newton dieselfde met 'n prisma gedoen het en die verskynsel steeds uiters omstrede was. ~~A crater on the moon is named for him, see [[Gregory (lunar crater)]]. The mathematician [[David Gregory]] was his nephew.~~ 'n Maankrater, [[Gregory (maankrater)]] is na hom vernoem. Die wiskundige [[David Gregory]] was sy kleinneef. ~~==References==~~ ~~{{reflist}}~~ == ~~See also~~ Verwysings== {{Verwysings}} [[Colin Maclaurin]] [[Telescope]] [[Kerala School#Possible_transmission_of_Keralese_mathematics_to_Europe\|Possible transmission of Kerala mathematics to Europe]] ==~~External~~Eksterne ~~links~~skakels== {{commons\|James Gregory\|James Gregory (astronomer and mathematician)}} {{MacTutor Biography\|id=Gregory\|title=James Gregory}} * [http://www.maths.tcd.ie/pub/HistMath/People/Gregory/RouseBall/RB_JGregory.html Trinity College Dublin History of Mathematics] *[http://mathdl.maa.org/convergence/1/?pa=content&sa=viewDocument&nodeId=388&bodyId=343 James Gregory's Euclidean Proof of the Fundemental Theorem of Calculus] atby [http://mathdl.maa.org/convergence/1/ Convergence] [[Kategorie:1638 geboortes]] ~~{{DEFAULTSORT:Gregory, James}}~~ [[Kategorie:1675 sterftes]] [[Kategorie:17de eeuse wiskundiges]] [[Kategorie:Skotse sterrekunde]] [[Kategorie:Skotse uitvinders]] [[Kategorie:Skotse wiskundiges]] ~~[[Category:1638 births]]~~ ~~[[Category:1675 deaths]]~~ ~~[[Category:People from Aberdeenshire]]~~ ~~[[Category:17th century mathematicians]]~~ ~~[[Category:Scottish astronomers]]~~ ~~[[Category:Scottish inventors]]~~ ~~[[Category:Scottish mathematicians]]~~ ~~[[Category:Alumni of the University of St Andrews]]~~ ~~[[Category:Academics of the University of St Andrews]]~~ ~~[[Category:Academics of the University of Edinburgh]]~~ ~~[[Category:Scientific instrument makers]]~~ ~~-->~~ [[bn:জেম্‌স গ্রেগরি (জ্যোতির্বিজ্ঞানী)]] [[bg:Джеймс Грегъри]] [[de:James Gregory (Mathematiker)]] [[en:James Gregory (astronomer and mathematician)]] [[fr:James Gregory (mathématicien)]] [[it:James Gregory]] Line 62 ⟶ 48: [[fi:James Gregory]] [[sv:James Gregory]] {{Wiskundige-saadjie}}

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