Thomas Simpson

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For other people named Thomas Simpson, see Thomas Simpson (disambiguation).

Thomas Simpson
Born20 August 1710
Sutton Cheney, Leicestershire
Died14 May 1761(1761-05-14) (aged 50)
Market Bosworth, Leicestershire
Known forSimpson's rule
Simpson–Weber triangle problem
Essays on several curious and useful subjects, in speculative and mix'd mathematicks, 1740

Thomas Simpson

definite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by Johannes Kepler, and in German it is called Keplersche Fassregel
, or roughly "Kepler's Barrel Rule".

Biography

Simpson was born in Sutton Cheney, Leicestershire. The son of a weaver,[1] Simpson taught himself mathematics. At the age of nineteen, he married a fifty-year old widow with two children.[2] As a youth, he became interested in astrology after seeing a solar eclipse. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife fled to Derby.[3] He moved with his wife and children to London at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night.[4]

From 1743, he taught mathematics at the Royal Military Academy, Woolwich. Simpson was a fellow of the Royal Society. In 1758, Simpson was elected a foreign member of the Royal Swedish Academy of Sciences.

He died in Market Bosworth, and was laid to rest in Sutton Cheney. A plaque inside the church commemorates him.

Early work

Simpson's treatise entitled The Nature and Laws of Chance and The Doctrine of Annuities and Reversions were based on the work of De Moivre and were attempts at making the same material more brief and understandable. Simpson stated this clearly in The Nature and Laws of Chance, referring to Abraham De Moivre's The Doctrine of Chances: "tho' it neither wants Matter nor Elegance to recommend it, yet the Price must, I am sensible, have put it out of the Power of many to purchase it". In both works, Simpson cited De Moivre's work and did not claim originality beyond the presentation of some more accurate data. While he and De Moivre initially got along, De Moivre eventually felt that his income was threatened by Simpson's work and in his second edition of Annuities upon Lives, wrote in the preface:[5]

"After the pains I have taken to perfect this Second Edition, it may happen, that a certain Person, whom I need not name, out of Compassion to the Public, will publish a Second Edition of his Book on the same Subject, which he will afford at a very moderate Price, not regarding whether he mutilates my Propositions, obscures what is clear, makes a Shew of new Rules, and works by mine; in short, confounds, in his usual way, every thing with a croud of useless Symbols; if this be the Case, I must forgive the indigent Author, and his disappointed Bookseller."

Work

Miscellaneous tracts, 1768

The method commonly called

James Gregory;[6]
still, the long popularity of Simpson's textbooks invites this association with his name, in that many readers would have learnt it from them.

In the context of disputes surrounding methods advanced by René Descartes, Pierre de Fermat proposed the challenge to find a point D such that the sum of the distances to three given points, A, B and C is least, a challenge popularised in Italy by Marin Mersenne in the early 1640s. Simpson treats the problem in the first part of Doctrine and Application of Fluxions (1750), on pp. 26–28, by the description of circular arcs at which the edges of the triangle ABC subtend an angle of pi/3; in the second part of the book, on pp. 505–506 he extends this geometrical method, in effect, to weighted sums of the distances. Several of Simpson's books contain selections of optimisation problems treated by simple geometrical considerations in similar manner, as (for Simpson) an illuminating counterpart to possible treatment by fluxional (calculus) methods.[7] But Simpson does not treat the problem in the essay on geometrical problems of maxima and minima appended to his textbook on Geometry of 1747, although it does appear in the considerably reworked edition of 1760. Comparative attention might, however, usefully be drawn to a paper in English from eighty years earlier as suggesting that the underlying ideas were already recognised then:

  • J. Collins A Solution, Given by Mr. John Collins of a Chorographical Probleme, Proposed by Richard Townley Esq. Who Doubtless Hath Solved the Same Otherwise, Philosophical Transactions of the Royal Society of London, 6 (1671), pp. 2093–2096.

Of further related interest are problems posed in the early 1750s by J. Orchard, in The British Palladium, and by T. Moss, in The Ladies' Diary; or Woman's Almanack (at that period not yet edited by Simpson).

Simpson-Weber triangle problem

This type of generalisation was later popularised by

Von Thünen's contributions, which go back to 1818, the Fermat point
problem can be seen as the very beginning of space economy.

In 1985,

Nobel Memorial Prize
in Economic Sciences in 2008.

Publications

See also

References

  1. ^ "Thomas Simpson". Holistic Numerical Methods Institute. Retrieved 8 April 2008.
  2. ^ Stigler, Stephen M. The History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
  3. ^ Simpson, Thomas (1710–1761) Archived 24 August 2004 at the Wayback Machine
  4. ^ Stigler, Stephen M. The History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
  5. ^ Stigler, Stephen M. The History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
  6. ^ Velleman, D. J. (2005). The Generalized Simpson's Rule. The American Mathematical Monthly, 112(4), 342–350.
  7. ^ Rogers, D. G. (2009). Decreasing Creases Archived 4 November 2013 at the Wayback Machine Mathematics Today, October, 167–170
  8. ^ Tellier, Luc-Normand, 1972, "The Weber Problem: Solution and Interpretation”, Geographical Analysis, vol. 4, no. 3, pp. 215–233.
  9. ^ Tellier, Luc-Normand, 1985, Économie spatiale: rationalité économique de l'espace habité, Chicoutimi, Gaëtan Morin éditeur, 280 pages.
  10. ^ Chen, Pey-Chun, Hansen, Pierre, Jaumard, Brigitte, and Hoang Tuy, 1992, "Weber's Problem with Attraction and Repulsion," Journal of Regional Science 32, 467–486.
  11. ^ Jalal, G., & Krarup, J. (2003). "Geometrical solution to the Fermat problem with arbitrary weights". Annals of Operations Research, 123, 67{104.
  12. ^ Ottaviano, Gianmarco and Jacques-François Thisse, 2005, "New Economic Geography: what about the N?”, Environment and Planning A 37, 1707–1725.

External links

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