James Gregory (mathematician)

See also: James Gregory, Gregory

James Gregory (November 1638 - October 1675) was a Mathématicien and a Scottish Astronome . He was born with Drumoak close to Aberdeen and died in Edinburgh. He was professor at the University of St Andrews and the university of Edinburgh.

In 1660, it publishes Optica Promota , in which it describes a model of Télescope which bears its name today. This telescope drew the attention of several scientists: Robert Hooke, the physicist of Oxford which built it finally, Sir Robert Moray, founding member of the Royal Society and Isaac Newton, which worked on a similar project. This type of telescope is hardly any more used, because it is more powerful for the usual uses.

Raise in Bologna of Stefano degli Angeli, it brings back of Italy the first developments in series, and the métodes resulting from the work of Cavalieri. Gregory, admiror enthusiastic of Newton, maintains with him a friendly correspondence, and it incorporates its ideas in its own teaching, ideas discussed and revolutionists at the time.

In 1667, it publishes Vera Circuli and Hyperbolae Quadratura , in which it shows that the surfaces of the circle and the hyperbole are given by the sum of infinite series.

This work contains a remarkable geometrical proposal which says that the report/ratio of the surfaces of an arbitrary sector of the disc and corresponding sector of the registered regular polygon or ex-registered voter cannot be expressed with a finished number of terms. He deduced from it that the Quadrature of the circle is impossible, but its argument is insufficient. This book contains also the oldest publication of the expansion of the functions sine, cosine, arcsinus and arccosinus in Taylor series. It was reprinted in 1668 with an appendix Geometriae Pars on calculation solid volumes of of revolution.

In 1671 or earlier perhaps, it shows the formula

$\ theta = \ tan \ theta - (1/3) \ tan^3 \ theta + (1/5) \ tan^5 \ theta - \ ldots$ ,

true for θ between - π/4 and π/4. This formula will be used later to calculate the figures of π.

See too

Internal bond

Mathematical in Europe at the XVIIe century

External bond

more on the telescope of Gregory: http://www.astrosurf.com/astroptics/

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