222:
91:
263:(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:
213:"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."
206:: "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
326:
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
331:
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
402:
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
327:
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
416:
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
221:
299:
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,
90:
138:, 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
723:
518:
267:
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,
255:
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
615:
Jalal, G., & Krarup, J. (2003). "Geometrical solution to the Fermat problem with arbitrary weights". Annals of
Operations Research, 123, 67{104.
244:; still, the long popularity of Simpson's textbooks invites this association with his name, in that many readers would have learnt it from them.
192:
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
542:
Stigler, Stephen M. The
History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
533:
Stigler, Stephen M. The
History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
506:
Stigler, Stephen M. The
History of Statistics: The Measurement of Uncertainty before 1900. The Belknap Press of Harvard University Press, 1986.
624:
Ottaviano, Gianmarco and
Jacques-François Thisse, 2005, "New Economic Geography: what about the N?”, Environment and Planning A 37, 1707–1725.
713:
241:
146:. 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
82:
653:
568:
593:
Tellier, Luc-Normand, 1985, Économie spatiale: rationalité économique de l'espace habité, Chicoutimi, Gaëtan Morin éditeur, 280 pages.
672:
432:
Miscellaneous tracts on some curious, and very interesting subjects in mechanics, physical-astronomy, and speculative mathematics
584:
Tellier, Luc-Normand, 1972, "The Weber
Problem: Solution and Interpretation”, Geographical Analysis, vol. 4, no. 3, pp. 215–233.
442:
Miscellaneous tracts on some curious and very interesting subjects in mechanics, physical-astronomy and speculative mathematics
728:
703:
466:
166:
515:
158:
636:
708:
20:
606:, and Hoang Tuy, 1992, "Weber's Problem with Attraction and Repulsion," Journal of Regional Science 32, 467–486.
718:
154:
at age twenty-five, where he supported his family by weaving during the day and teaching mathematics at night.
118:. The attribution, as often in mathematics, can be debated: this rule had been found 100 years earlier by
104:
333:
677:
430:
667:
440:
386:
370:
202:
123:
647:
485:
237:
565:
698:
693:
345:
8:
663:
461:
323:
300:
414:
337:
115:
176:, and was laid to rest in Sutton Cheney. A plaque inside the church commemorates him.
107:(20 August 1710 – 14 May 1761) was a British mathematician and inventor known for the
233:
197:
111:
78:
372:
Essays on several curious and useful subjects, in speculative and mix'd mathematicks
275:
Of further related interest are problems posed in the early 1750s by J. Orchard, in
248:
95:
Essays on several curious and useful subjects, in speculative and mix'd mathematicks
603:
252:
572:
522:
173:
119:
66:
552:
256:
48:
687:
328:
296:
162:
143:
135:
44:
312:
388:
Mathematical dissertations on a variety of physical and analytical subjects
341:
316:
308:
304:
292:
456:
640:
405:(Printed for the Author; Samuel Farrer; and John Turner, London, 1747)
646:
139:
259:
in the early 1640s. Simpson treats the problem in the first part of
303:
found the first direct (non iterative) numerical solution of the
151:
108:
147:
319:
problem can be seen as the very beginning of space economy.
247:
In the context of disputes surrounding methods advanced by
269:
Philosophical Transactions of the Royal Society of London
420:(two parts bound in one volume; J. Nourse, London, 1750)
657:. Vol. 25 (11th ed.). 1911. pp. 135–136.
165:. In 1758, Simpson was elected a foreign member of the
332:
attraction-repulsion problem is seen by Ottaviano and
291:
This type of generalisation was later popularised by
555:
The American Mathematical Monthly, 112(4), 342–350.
661:
286:
724:Members of the Royal Swedish Academy of Sciences
685:
637:Thomas Simpson and his Work on Maxima and Minima
315:'s contributions, which go back to 1818, the
240:(a student of Galileo) in 1639, and later by
283:(at that period not yet edited by Simpson).
19:For other people named Thomas Simpson, see
150:. He moved with his wife and children to
380:The Doctrine of Annuities and Reversions
340:that developed in the 1990s, and earned
220:
190:The Doctrine of Annuities and Reversions
157:From 1743, he taught mathematics at the
89:
673:MacTutor History of Mathematics Archive
686:
488:. Holistic Numerical Methods Institute
281:The Ladies' Diary; or Woman's Almanack
126:, or roughly "Kepler's Barrel Rule".
261:Doctrine and Application of Fluxions
714:18th-century English mathematicians
575:Mathematics Today, October, 167–170
13:
16:British mathematician and inventor
14:
740:
630:
409:Trigonometry, Plane and Spherical
167:Royal Swedish Academy of Sciences
602:Chen, Pey-Chun, Hansen, Pierre,
467:Simpson's rules (ship stability)
391:. London: Thomas Woodward. 1743.
159:Royal Military Academy, Woolwich
618:
609:
596:
553:The Generalized Simpson's Rule.
424:Select Exercises in Mathematics
351:
311:triangle problems. Long before
271:, 6 (1671), pp. 2093–2096.
21:Thomas Simpson (disambiguation)
587:
578:
558:
545:
536:
527:
509:
500:
478:
348:in Economic Sciences in 2008.
297:Simpson-Weber triangle problem
287:Simpson-Weber triangle problem
236:was known and used earlier by
161:. Simpson was a fellow of the
83:Simpson–Weber triangle problem
1:
472:
364:The Nature and Laws of Chance
194:The Nature and Laws of Chance
186:The Nature and Laws of Chance
179:
122:, and in German it is called
729:Fellows of the Royal Society
445:. London: John Nourse. 1768.
435:. London: John Nourse. 1757.
375:. London: John Nourse. 1740.
184:Simpson's treatise entitled
129:
7:
704:People from Market Bosworth
516:Simpson, Thomas (1710–1761)
450:
336:(2005) as a prelude to the
232:The method commonly called
10:
745:
18:
74:
55:
37:
30:
678:University of St Andrews
551:Velleman, D. J. (2005).
210:, wrote in the preface:
654:Encyclopædia Britannica
648:"Simpson, Thomas"
571:4 November 2013 at the
216:
203:The Doctrine of Chances
709:English mathematicians
564:Rogers, D. G. (2009).
521:24 August 2004 at the
338:New Economic Geography
229:
98:
719:Mathematical analysts
396:A Treatise of Algebra
279:, and by T. Moss, in
277:The British Palladium
238:Bonaventura Cavalieri
224:
93:
664:Robertson, Edmund F.
358:Treatise of Fluxions
346:Nobel Memorial Prize
226:Miscellaneous tracts
208:Annuities upon Lives
134:Simpson was born in
124:Keplersche Fassregel
662:O'Connor, John J.;
462:Series multisection
324:Luc-Normand Tellier
301:Luc-Normand Tellier
566:Decreasing Creases
230:
116:definite integrals
99:
604:Jaumard, Brigitte
198:Abraham De Moivre
88:
87:
736:
680:
668:"Thomas Simpson"
658:
650:
625:
622:
616:
613:
607:
600:
594:
591:
585:
582:
576:
562:
556:
549:
543:
540:
534:
531:
525:
513:
507:
504:
498:
497:
495:
493:
486:"Thomas Simpson"
482:
446:
436:
392:
376:
253:Pierre de Fermat
69:, Leicestershire
62:
28:
27:
744:
743:
739:
738:
737:
735:
734:
733:
684:
683:
645:
633:
628:
623:
619:
614:
610:
601:
597:
592:
588:
583:
579:
573:Wayback Machine
563:
559:
550:
546:
541:
537:
532:
528:
523:Wayback Machine
514:
510:
505:
501:
491:
489:
484:
483:
479:
475:
453:
439:
429:
385:
369:
354:
289:
219:
196:, referring to
182:
174:Market Bosworth
142:after seeing a
132:
120:Johannes Kepler
114:to approximate
81:
70:
67:Market Bosworth
64:
60:
51:
42:
33:
24:
17:
12:
11:
5:
742:
732:
731:
726:
721:
716:
711:
706:
701:
696:
682:
681:
659:
643:
632:
631:External links
629:
627:
626:
617:
608:
595:
586:
577:
557:
544:
535:
526:
508:
499:
476:
474:
471:
470:
469:
464:
459:
452:
449:
448:
447:
437:
427:
421:
412:
406:
399:
393:
383:
377:
367:
361:
353:
350:
295:in 1909. The
288:
285:
273:
272:
257:Marin Mersenne
249:René Descartes
234:Simpson's Rule
218:
215:
181:
178:
131:
128:
112:Simpson's rule
102:Thomas Simpson
86:
85:
79:Simpson's rule
76:
75:Known for
72:
71:
65:
63:(aged 50)
57:
53:
52:
49:Leicestershire
43:
41:20 August 1710
39:
35:
34:
32:Thomas Simpson
31:
15:
9:
6:
4:
3:
2:
741:
730:
727:
725:
722:
720:
717:
715:
712:
710:
707:
705:
702:
700:
697:
695:
692:
691:
689:
679:
675:
674:
669:
665:
660:
656:
655:
649:
644:
642:
638:
635:
634:
621:
612:
605:
599:
590:
581:
574:
570:
567:
561:
554:
548:
539:
530:
524:
520:
517:
512:
503:
487:
481:
477:
468:
465:
463:
460:
458:
455:
454:
444:
443:
438:
434:
433:
428:
425:
422:
419:
418:
413:
410:
407:
404:
400:
397:
394:
390:
389:
384:
381:
378:
374:
373:
368:
365:
362:
359:
356:
355:
349:
347:
343:
339:
335:
330:
329:space economy
325:
320:
318:
314:
310:
306:
302:
298:
294:
284:
282:
278:
270:
266:
265:
264:
262:
258:
254:
250:
245:
243:
242:James Gregory
239:
235:
227:
223:
214:
211:
209:
205:
204:
199:
195:
191:
187:
177:
175:
170:
168:
164:
163:Royal Society
160:
155:
153:
149:
145:
144:solar eclipse
141:
137:
136:Sutton Cheney
127:
125:
121:
117:
113:
110:
106:
103:
96:
92:
84:
80:
77:
73:
68:
58:
54:
50:
46:
45:Sutton Cheney
40:
36:
29:
26:
22:
671:
652:
620:
611:
598:
589:
580:
560:
547:
538:
529:
511:
502:
490:. Retrieved
480:
441:
431:
423:
417:Mathematicks
415:
408:
401:
395:
387:
379:
371:
363:
357:
352:Publications
342:Paul Krugman
321:
317:Fermat point
307:and Simpson-
293:Alfred Weber
290:
280:
276:
274:
268:
260:
246:
231:
225:
212:
207:
201:
193:
189:
185:
183:
171:
156:
133:
101:
100:
94:
61:(1761-05-14)
25:
699:1761 deaths
694:1710 births
641:Convergence
457:Probability
172:He died in
59:14 May 1761
688:Categories
473:References
313:Von ThĂĽnen
180:Early work
322:In 1985,
140:astrology
130:Biography
109:eponymous
569:Archived
519:Archived
451:See also
492:8 April
426:(1752)
411:(1748)
398:(1745)
382:(1742)
366:(1740)
360:(1737)
334:Thisse
305:Fermat
228:, 1768
152:London
97:, 1740
309:Weber
148:Derby
494:2008
217:Work
188:and
56:Died
38:Born
639:at
200:'s
105:FRS
690::
676:,
670:,
666:,
651:.
344:a
251:,
169:.
47:,
496:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
