James Gregory: Verskil tussen weergawes

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[[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 is later deur [[Edmund Halley]] aangemoedig en aangeneem as die grondslag vir die eerste meting van die [[Astronomiese eenheid]].
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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]] 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.
 
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 θ between &minus;&pi;/4 and &pi;/4.
This formula was used by Madhava to calculate digits of [[pi|&pi;]] and later used in [[Europe]] for the same purpose, although more efficient formulas were later discovered.
 
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.
 
A crater on the moon is named for him, see [[Gregory (lunar crater)]]. The mathematician [[David Gregory]] was his nephew.
 
==References==
{{reflist}}
 
== See also ==
*[[Colin Maclaurin]]
*[[Telescope]]
*[[Kerala School#Possible_transmission_of_Keralese_mathematics_to_Europe|Possible transmission of Kerala mathematics to Europe]]
 
==External links==
{{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] at [http://mathdl.maa.org/convergence/1/ Convergence]
 
{{DEFAULTSORT:Gregory, James}}
 
[[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]]
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