Everything about James Gregory Astronomer And Mathematician totally explained
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James Gregory (November
1638 – October
1675), was a
Scottish mathematician and
astronomer.
He was born at
Drumoak,
Aberdeenshire, and died at
Edinburgh. He was successively
professor at the
University of St Andrews and the
University of Edinburgh.
In
1663 he published his
Optica Promota, in which the compact
reflecting telescope known by his name, the
Gregorian telescope, is described. His system of Gregorian optics is also used in
radio telescopes such as
Arecibo, which features a "Gregorian dome".
The telescope design attracted the attention of several people in the scientific establishment:
Robert Hooke, the Oxford physicist who eventually built the telescope, Sir
Robert Moray,
polymath and founding member of the
Royal Society and
Isaac Newton, who was at work on a similar project of his own.
The Gregorian telescope was the first practical reflecting telescope and remained the standard observing instrument for a century and a half. However, the Gregorian telescope design is rarely used today, as other types of reflecting telescopes are known to be more efficient for standard applications.
In the
Optica Promota he also described the method for using the transit of Venus to measure the distance of the Earth from the Sun, which was later advocated by
Edmund Halley and adopted as the basis of the first effective measurement of the
Astronomical Unit.
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 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 polygons isn't expressible by a finite number of terms. Hence he inferred that the
quadrature of the circle was impossible; this was accepted by
Montucla, but it isn't conclusive, for it's 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
sin(x),
cos(x), arcsin(x) and arccos(x). (The earliest enunciations of these expansions were made by
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 mathematician Madhava of Sangamagrama had originally discovered, the
arctangent series
»
for θ between −π/4 and π/4.
This formula was used by Madhava to calculate digits of
π and later used in
Europe for the same purpose, although more efficient formulas were later discovered.
James Gregory discovered 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 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.
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