Thomas Simpson
FRS (20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the
eponymous
An eponym is a person, a place, or a thing after whom or which someone or something is, or is believed to be, named. The adjectives which are derived from the word eponym include ''eponymous'' and ''eponymic''.
Usage of the word
The term ''epon ...
Simpson's rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761).
The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads
\int_a^b f(x) \, ...
to approximate definite integrals. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by
Johannes Kepler
Johannes Kepler (; ; 27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws ...
, and in German it is called
Keplersche Fassregel.
Biography
Simpson was born in
Sutton Cheney
Sutton Cheney ( ) is a village and civil parish in the borough of Hinckley and Bosworth in the county of Leicestershire, England, near the county border with Warwickshire.OS Explorer Map 232 : Nuneaton & Tamworth: (1:25 000) : In addition to the ...
, Leicestershire. The son of a weaver, Simpson taught himself mathematics. At the age of nineteen, he married a fifty-year old widow with two children. As a youth, he became interested in
astrology
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
after seeing a
solar eclipse
A solar eclipse occurs when the Moon passes between Earth and the Sun, thereby obscuring the view of the Sun from a small part of the Earth, totally or partially. Such an alignment occurs during an eclipse season, approximately every six mon ...
. He also dabbled in divination and caused fits in a girl after 'raising a devil' from her. After this incident, he and his wife had to flee to
Derby
Derby ( ) is a city and unitary authority area in Derbyshire, England. It lies on the banks of the River Derwent in the south of Derbyshire, which is in the East Midlands Region. It was traditionally the county town of Derbyshire. Derby g ...
. 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.
From 1743, he taught mathematics at the
Royal Military Academy, Woolwich
The Royal Military Academy (RMA) at Woolwich, in south-east London, was a British Army military academy for the training of commissioned officers of the Royal Artillery and Royal Engineers. It later also trained officers of the Royal Corps of S ...
. Simpson was a fellow of the
Royal Society
The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
. In 1758, Simpson was elected a foreign member of the
Royal Swedish Academy of Sciences
The Royal Swedish Academy of Sciences ( sv, Kungliga Vetenskapsakademien) is one of the royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for prom ...
.
He died in Market Bosworth, and was laid to rest in
Sutton Cheney
Sutton Cheney ( ) is a village and civil parish in the borough of Hinckley and Bosworth in the county of Leicestershire, England, near the county border with Warwickshire.OS Explorer Map 232 : Nuneaton & Tamworth: (1:25 000) : In addition to the ...
. 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 De Moivre's 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:
"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
The method commonly called
Simpson's Rule
In numerical integration, Simpson's rules are several approximations for definite integrals, named after Thomas Simpson (1710–1761).
The most basic of these rules, called Simpson's 1/3 rule, or just Simpson's rule, reads
\int_a^b f(x) \, ...
was known and used earlier by
Bonaventura Cavalieri
Bonaventura Francesco Cavalieri ( la, Bonaventura Cavalerius; 1598 – 30 November 1647) was an Italian mathematician and a Jesuate. He is known for his work on the problems of optics and motion, work on indivisibles, the precursors of in ...
(a student of Galileo) in 1639, and later by
James Gregory; 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
René Descartes ( or ; ; Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Ma ...
,
Pierre de Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he ...
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
Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for ...
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. 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
Alfred Weber
Alfred Weber (; 30 July 1868 – 2 May 1958) was a German economist, geographer, sociologist and theoretician of culture whose work was influential in the development of modern economic geography.
Life
Alfred Weber, younger brother of the ...
in 1909. The
Simpson-Weber triangle problem consists in locating a point D with respect to three points A, B, and C in such a way that the sum of the transportation costs between D and each of the three other points is minimised. In 1971,
Luc-Normand Tellier
Luc-Normand Tellier (born October 10, 1944) is a Professor Emeritus in spatial economics of the University of Quebec at Montreal.
Education and teaching
After teaching for two years (1964–1966) at the Collège Saint-André of Kigali, Rwanda, ...
found the first direct (non iterative) numerical solution of the
Fermat
Pierre de Fermat (; between 31 October and 6 December 1607 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is ...
and Simpson-
Weber
Weber (, or ; German: ) is a surname of German origin, derived from the noun meaning " weaver". In some cases, following migration to English-speaking countries, it has been anglicised to the English surname 'Webber' or even 'Weaver'.
Notable pe ...
triangle problems. Long before
Von Thünen's contributions, which go back to 1818, the
Fermat point
In Euclidean geometry, the Fermat point of a triangle, also called the Torricelli point or Fermat–Torricelli point, is a point such that the sum of the three distances from each of the three vertices of the triangle to the point is the smallest ...
problem can be seen as the very beginning of space economy.
In 1985,
Luc-Normand Tellier
Luc-Normand Tellier (born October 10, 1944) is a Professor Emeritus in spatial economics of the University of Quebec at Montreal.
Education and teaching
After teaching for two years (1964–1966) at the Collège Saint-André of Kigali, Rwanda, ...
formulated an all-new problem called the “attraction-repulsion problem”, which constitutes a generalisation of both the Fermat and Simpson-Weber problems. In its simplest version, the attraction-repulsion problem consists in locating a point D with respect to three points A1, A2 and R in such a way that the attractive forces exerted by points A1 and A2, and the repulsive force exerted by point R cancel each other out. In the same book, Tellier solved that problem for the first time in the triangle case, and he reinterpreted the
space economy theory, especially, the theory of land rent, in the light of the concepts of attractive and repulsive forces stemming from the attraction-repulsion problem. That problem was later further analysed by mathematicians like Chen, Hansen, Jaumard and Tuy (1992), and Jalal and Krarup (2003). The attraction-repulsion problem is seen by Ottaviano and
Thisse (2005)
[Ottaviano, Gianmarco and Jacques-François Thisse, 2005, "New Economic Geography: what about the N?”, Environment and Planning A 37, 1707–1725.] as a prelude to the
New Economic Geography that developed in the 1990s, and earned
Paul Krugman
Paul Robin Krugman ( ; born February 28, 1953) is an American economist, who is Distinguished Professor of Economics at the Graduate Center of the City University of New York, and a columnist for ''The New York Times''. In 2008, Krugman was t ...
a
Nobel Memorial Prize
The Nobel Memorial Prize in Economic Sciences, officially the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel ( sv, Sveriges riksbanks pris i ekonomisk vetenskap till Alfred Nobels minne), is an economics award administered ...
in Economic Sciences in 2008.
Publications
* ''Treatise of Fluxions'' (1737)
* ''The Nature and Laws of Chance'' (1740)
*
* ''The Doctrine of Annuities and Reversions'' (1742)
*
* ''A Treatise of Algebra'' (1745)
* ''Elements of Plane Geometry. To which are added, An Essay on the Maxima and Minima of Geometrical Quantities, And a brief Treatise of regular Solids; Also, the Mensuration of both Superficies and Solids, together with the Construction of a large Variety of Geometrical Problems '' (Printed for the Author; Samuel Farrer; and John Turner, London, 1747) [The book is described as being ''Designed for the Use of Schools'' and the main body of text is Simpson's reworking of the early books of The Elements of Euclid. Simpson is designated ''Professor of Geometry in the Royal Academy at Woolwich''.]
* ''Trigonometry, Plane and Spherical'' (1748)
''Doctrine and Application of Fluxions. Containing (besides what is common on the subject) a Number of New Improvements on the Theory. And the Solution of a Variety of New, and very Interesting, Problems in different Branches of the Mathematicks''(two parts bound in one volume; J. Nourse, London, 1750)
* ''Select Exercises in Mathematics'' (1752)
*
*
See also
*
Probability
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...
*
Series multisection
*
Simpson's rules (ship stability)
Simpson's rules are a set of rules used in ship stability and naval architecture, to calculate the areas and volumes of irregular figures. This is an application of Simpson's rule for finding the values of an integral, here interpreted as the ...
References
External links
Thomas Simpson and his Work on Maxima and Minimaa
Convergence*
*
{{DEFAULTSORT:Simpson, Thomas
1710 births
1761 deaths
People from Market Bosworth
English mathematicians
18th-century English mathematicians
Mathematical analysts
Members of the Royal Swedish Academy of Sciences
Fellows of the Royal Society