576:
561:
636:
621:
606:
591:
398:. Geometry in the 1700s was complex to the average learner. It was considered to be a dry subject. Clairaut saw this trend, and wrote the book in an attempt to make the subject more interesting for the average learner. He believed that instead of having students repeatedly work problems that they did not fully understand, it was imperative for them to make discoveries themselves in a form of active,
44:
446:
324:
256:, "with dining and with evenings, coupled with a lively taste for women, and seeking to make his pleasures into his day to day work, he lost rest, health, and finally life at the age of fifty-two." Though he led a fulfilling social life, he was very prominent in the advancement of learning in young mathematicians.
319:"It appears even Sir Isaac Newton was of the opinion, that it was necessary the Earth should be more dense toward the center, in order to be so much the flatter at the poles: and that it followed from this greater flatness, that gravity increased so much the more from the equator towards the Pole."
437:
and law of attraction into his solution, with minor edits to it. However, these equations only offered approximate measurement, and no exact calculations. Another issue still remained with the three body problem; how the Moon rotates on its apsides. Even Newton could account for only half of the
314:
Initially, Clairaut disagrees with Newton's theory on the shape of the Earth. In the article, he outlines several key problems that effectively disprove Newton's calculations, and provides some solutions to the complications. The issues addressed include calculating gravitational attraction, the
402:. He begins the book by comparing geometric shapes to measurements of land, as it was a subject that most anyone could relate to. He covers topics from lines, shapes, and even some three dimensional objects. Throughout the book, he continuously relates different concepts such as
787:
503:
direction of their ships, which was crucial not only in sailing to a location, but finding their way home as well. This held economic implications as well, because sailors were able to more easily find destinations of trade based on the longitudinal measures.
374:. Under the assumption that the Earth was composed of concentric ellipsoidal shells of uniform density, Clairaut's theorem could be applied to it, and allowed the ellipticity of the Earth to be calculated from surface measurements of gravity. This proved
228:â at the age of ten he began studying calculus. At the age of twelve he wrote a memoir on four geometrical curves and under his father's tutelage he made such rapid progress in the subject that in his thirteenth year he read before the
491:. It occurred to him to carry the approximation to the third order, and he thereupon found that the result was in accordance with the observations. This was followed in 1754 by some lunar tables, which he computed using a form of the
498:
The newfound solution to the problem of three bodies ended up meaning more than proving Newton's laws correct. The unravelling of the problem of three bodies also had practical importance. It allowed sailors to determine the
464:. Euler and d'Alembert were arguing against the use of Newtonian laws to solve the three body problem. Euler in particular believed that the inverse square law needed revision to accurately calculate the apsides of the Moon.
795:
244:, although he was below the legal age as he was only eighteen. He gave a path breaking formulae called the distance formulae which helps to find out the distance between any 2 points on the cartesian or XY plane.
456:
The question of the apsides was a heated debate topic in Europe. Along with
Clairaut, there were two other mathematicians who were racing to provide the first explanation for the three body problem;
467:
Despite the hectic competition to come up with the correct solution, Clairaut obtained an ingenious approximate solution of the problem of the three bodies. In 1750 he gained the prize of the
442:. This issue had puzzled astronomers. In fact, Clairaut had at first deemed the dilemma so inexplicable, that he was on the point of publishing a new hypothesis as to the law of attraction.
575:
338:
created much controversy, as he addressed the problems of Newton's theory, but provided few solutions to how to fix the calculations. After his return, he published his treatise
560:
220:
Clairaut was born in Paris, France, to Jean-Baptiste and
Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth. His father taught
104:
382:
showed that
Clairaut's result was true whatever the interior constitution or density of the Earth, provided the surface was a spheroid of equilibrium of small ellipticity.
1145:
742:
303:
shape. They sought to prove if Newton's theory and calculations were correct or not. Before the expedition team returned to Paris, Clairaut sent his calculations to the
309:
334:
This conclusion suggests not only that the Earth is of an oblate ellipsoid shape, but it is flattened more at the poles and is wider at the centre. His article in
171:
476:
252:
Clairaut was unmarried, and known for leading an active social life. His growing popularity in society hindered his scientific work: "He was focused," says
1140:
851:"An Inquiry concerning the Figure of Such Planets as Revolve about an Axis, Supposing the Density Continually to Vary, from the Centre towards the Surface"
1155:
635:
620:
605:
590:
1096:
315:
rotation of an ellipsoid on its axis, and the difference in density of an ellipsoid on its axes. At the end of his letter, Clairaut writes that:
707:
Other dates have been proposed, such as 7 May, which Judson Knight and the Royal
Society report. Here is a discussion and argument for 13 May.
1150:
1023:
527:, taking accurate measurements of the planet's size and distance from the Earth. This was the first precise reckoning of the planet's size.
414:
to geometry. Some of the theories and learning methods outlined in the book are still used by teachers today, in geometry and other topics.
1060:
987:
1047:
1135:
689:
379:
184:
769:
260:
433:, Clairaut was able to solve the problem using four differential equations. He was also able to incorporate Newton's
1052:
1015:
979:
492:
468:
461:
241:
1107:
232:
an account of the properties of four curves which he had discovered. When only sixteen he finished a treatise on
1101:
229:
165:. He was a prominent Newtonian whose work helped to establish the validity of the principles and results that
280:
660:
655:
204:
200:
112:
108:
818:
674:
399:
358:. This hydrostatic model of the shape of the Earth was founded on a paper by the Scottish mathematician
665:
343:
100:
1031:
1130:
1125:
942:
684:
480:
426:, or how the Earth, Moon, and Sun are attracted to one another. With the use of the recently founded
1087:
180:
1091:
872:
547:
434:
423:
192:
188:
116:
537:
1056:
1019:
983:
971:
950:
862:
284:
359:
153:
291:. The goal of the excursion was to geometrically calculate the shape of the Earth, which
946:
891:
363:
1008:
679:
487:
is strictly
Newtonian in character. This contains the explanation of the motion of the
457:
367:
253:
1119:
1003:
791:
304:
225:
520:
375:
292:
288:
166:
162:
411:
221:
196:
133:
17:
710:
43:
427:
233:
158:
519:
as affected by the perturbation of the planets, particularly on the path of
500:
407:
371:
351:
300:
867:
850:
183:. In that context, Clairaut worked out a mathematical result now known as "
825:. School of Mathematics and Statistics, University of St Andrews, Scotland
583:"ThĂ©orie de la Figure de la Terre, tirĂ©e des Principes de lâHydrostatique"
568:"ThĂ©orie de la Figure de la Terre, tirĂ©e des Principes de lâHydrostatique"
307:. The writing was later published by the society in the 1736â37 volume of
483:
successfully computed the date of the 1759 return of Halley's comet. The
430:
395:
370:
would, under the mutual attraction of its particles, take the form of an
176:
549:
Théorie de la figure de la terre, tirée des principes de l'hydrostatique
539:
Theorie de la figure de la terre, tirée des principes de l'hydrostatique
328:
Théorie de la Figure de la Terre, tirée des
Principes de lâHydrostatique
445:
403:
378:'s theory that the shape of the Earth was an oblate ellipsoid. In 1849
355:
347:
323:
955:
930:
876:
287:, which was undertaken for the purpose of estimating a degree of the
240:, which, on its publication in 1731, procured his admission into the
524:
516:
508:
488:
444:
439:
322:
175:
of 1687. Clairaut was one of the key figures in the expedition to
422:
One of the most controversial issues of the 18th century was the
907:
Smith, David (1921). "Review of ĂlĂ©ments de GĂ©omĂ©trie. 2 vols".
512:
27:
French mathematician, astronomer, and geophysicist (1713â1765)
1066:
1080:
342:(1743). In this work he promulgated the theorem, known as
191:, being the first to obtain a satisfactory result for the
157:; 13 May 1713 â 17 May 1765) was a French mathematician,
768:
Taner Kiral, Jonathan
Murdock and Colin B. P. McKinney.
788:"Fellow Details: Clairaut; Alexis Claude (1713 - 1765)"
354:
with the compression and the centrifugal force at the
817:
O'Connor and, J. J.; E. F. Robertson (October 1998).
972:"The First Anticipated Return: Halley's Comet 1758"
129:
96:
88:
72:
53:
34:
1010:Fourier analysis on finite groups and applications
1007:
507:Clairaut subsequently wrote various papers on the
105:Clairaut's theorem on equality of mixed partials
366:fluid set in rotation about a line through its
179:that helped to confirm Newton's theory for the
1110:A Short Account of the History of Mathematics
1081:Chronologie de la vie de Clairaut (1713â1765)
715:Chronologie de la vie de Clairaut (1713-1765)
8:
643:"Théorie de la Lune & Tables de la Lune"
628:"Théorie de la Lune & Tables de la Lune"
613:"Théorie de la Lune & Tables de la Lune"
598:"Théorie de la Lune & Tables de la Lune"
523:. He also used applied mathematics to study
238:Recherches sur les courbes a double courbure
931:"The 18th century battle over lunar motion"
450:Théorie de la Lune & Tables de la Lune,
890:Clairaut, Alexis Claude (1 January 1881).
394:. The book outlines the basic concepts of
42:
31:
1146:Members of the French Academy of Sciences
954:
866:
745:. In Schlager, Neil; Lauer, Josh (eds.).
552:(in French). Paris: Louis Courcier. 1808.
542:(in French). Paris: Laurent Durand. 1743.
747:Science and Its Times, Vol. 4: 1700-1799
1097:MacTutor History of Mathematics Archive
823:MacTutor History of Mathematics Archive
711:"13 mai 1713(1): Naissance de Clairaut"
700:
556:
350:at points on the surface of a rotating
893:Elements of geometry, tr. by J. Kaines
390:In 1741, Clairaut wrote a book called
929:Bodenmann, Siegfried (January 2010).
849:Claude, Alexis; Colson, John (1737).
187:". He also tackled the gravitational
152:
7:
924:
922:
920:
918:
844:
842:
840:
770:"The Four Curves of Alexis Clairaut"
736:
734:
732:
709:Courcelle, Olivier (17 March 2007).
283:, he took part in the expedition to
1141:18th-century French mathematicians
1070:, Vol. 60, 1992, pp. 549â554.
25:
362:, which had shown that a mass of
270:Mathematical and scientific works
634:
619:
604:
589:
574:
559:
475:; the team made up of Clairaut,
340:Théorie de la figure de la terre
266:Clairaut died in Paris in 1765.
1156:18th-century French astronomers
690:Symmetry of second derivatives
263:of London on 27 October 1737.
1:
1151:Fellows of the Royal Society
418:Focus on astronomical motion
1068:American Journal of Physics
261:Fellow of the Royal Society
1172:
1053:Princeton University Press
1016:Cambridge University Press
980:Princeton University Press
970:Grier, David Alan (2005).
855:Philosophical Transactions
493:discrete Fourier transform
336:Philosophical Transactions
310:Philosophical Transactions
1048:When Computers Were Human
976:When Computers Were Human
242:Royal Academy of Sciences
199:he is also credited with
154:[alÉksiklodklÉÊo]
139:
122:
41:
1102:University of St Andrews
743:"Alexis Claude Clairaut"
410:, and other branches of
216:Childhood and early life
195:of the Moon's orbit. In
909:The Mathematics Teacher
741:Knight, Judson (2000).
515:, and on the motion of
462:Jean le Rond d'Alembert
424:problem of three bodies
305:Royal Society of London
281:Pierre Louis Maupertuis
279:In 1736, together with
248:Personal life and death
868:10.1098/rstl.1737.0045
453:
331:
321:
295:theorised in his book
275:The shape of the Earth
146:Alexis Claude Clairaut
48:Alexis Claude Clairaut
36:Alexis Claude Clairaut
1136:Scientists from Paris
675:Differential geometry
469:St Petersburg Academy
448:
400:experiential learning
392:ĂlĂ©ments de GĂ©omĂ©trie
346:, which connects the
326:
317:
1088:Robertson, Edmund F.
685:Intermolecular force
481:Nicole Reine Lepaute
169:had outlined in the
1086:O'Connor, John J.;
1045:Grier, David Alan,
947:2010PhT....63a..27B
661:Clairaut's relation
656:Clairaut's equation
205:Clairaut's relation
201:Clairaut's equation
181:figure of the Earth
113:Clairaut's relation
109:Clairaut's equation
982:. pp. 11â25.
749:. pp. 247â248
666:Clairaut's theorem
485:Théorie de la lune
473:Théorie de la lune
454:
435:inverse-square law
344:Clairaut's theorem
332:
230:Académie française
193:apsidal precession
189:three-body problem
185:Clairaut's theorem
117:Apsidal precession
101:Clairaut's theorem
1092:"Alexis Clairaut"
1025:978-0-521-45718-7
956:10.1063/1.3293410
819:"Alexis Clairaut"
259:He was elected a
143:
142:
124:Scientific career
16:(Redirected from
1163:
1108:W.W. Rouse Ball
1104:
1034:
1029:
1013:
1000:
994:
993:
967:
961:
960:
958:
926:
913:
912:
904:
898:
897:
887:
881:
880:
870:
846:
835:
834:
832:
830:
814:
808:
807:
805:
803:
794:. Archived from
784:
778:
777:
774:MAA publications
765:
759:
758:
756:
754:
738:
727:
726:
724:
722:
705:
638:
623:
608:
593:
581:Introduction to
578:
563:
553:
543:
376:Sir Isaac Newton
293:Sir Isaac Newton
167:Sir Isaac Newton
156:
151:
79:
63:
61:
46:
32:
21:
18:Alexis Clairault
1171:
1170:
1166:
1165:
1164:
1162:
1161:
1160:
1116:
1115:
1085:
1077:
1042:
1037:
1026:
1002:
1001:
997:
990:
969:
968:
964:
928:
927:
916:
906:
905:
901:
889:
888:
884:
848:
847:
838:
828:
826:
816:
815:
811:
801:
799:
798:on 23 July 2019
786:
785:
781:
767:
766:
762:
752:
750:
740:
739:
730:
720:
718:
708:
706:
702:
698:
652:
645:
639:
630:
624:
615:
609:
600:
594:
585:
579:
570:
564:
546:
536:
533:
420:
388:
360:Colin Maclaurin
277:
272:
250:
234:Tortuous Curves
224:. Alexis was a
218:
213:
149:
115:
111:
107:
103:
84:
81:
77:
68:
65:
59:
57:
49:
37:
28:
23:
22:
15:
12:
11:
5:
1169:
1167:
1159:
1158:
1153:
1148:
1143:
1138:
1133:
1128:
1118:
1117:
1114:
1113:
1105:
1083:
1076:
1075:External links
1073:
1072:
1071:
1064:
1041:
1038:
1036:
1035:
1024:
1004:Terras, Audrey
995:
988:
962:
914:
899:
882:
836:
809:
779:
760:
728:
699:
697:
694:
693:
692:
687:
682:
680:Human computer
677:
672:
670:
668:
663:
658:
651:
648:
647:
646:
641:First page of
640:
633:
631:
626:Dedication to
625:
618:
616:
611:Dedication to
610:
603:
601:
595:
588:
586:
580:
573:
571:
565:
558:
555:
554:
544:
532:
529:
521:Halley's comet
477:JĂ©rome Lalande
471:for his essay
458:Leonhard Euler
438:motion of the
419:
416:
387:
384:
368:centre of mass
276:
273:
271:
268:
249:
246:
217:
214:
212:
209:
141:
140:
137:
136:
131:
127:
126:
120:
119:
98:
97:Known for
94:
93:
90:
86:
85:
82:
80:(aged 52)
74:
70:
69:
66:
55:
51:
50:
47:
39:
38:
35:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
1168:
1157:
1154:
1152:
1149:
1147:
1144:
1142:
1139:
1137:
1134:
1132:
1129:
1127:
1124:
1123:
1121:
1112:
1111:
1106:
1103:
1099:
1098:
1093:
1089:
1084:
1082:
1079:
1078:
1074:
1069:
1065:
1062:
1061:0-691-09157-9
1058:
1054:
1050:
1049:
1044:
1043:
1039:
1033:
1027:
1021:
1017:
1012:
1011:
1005:
999:
996:
991:
989:0-691-09157-9
985:
981:
978:. Princeton:
977:
973:
966:
963:
957:
952:
948:
944:
940:
936:
935:Physics Today
932:
925:
923:
921:
919:
915:
910:
903:
900:
895:
894:
886:
883:
878:
874:
869:
864:
860:
856:
852:
845:
843:
841:
837:
824:
820:
813:
810:
797:
793:
792:Royal Society
789:
783:
780:
775:
771:
764:
761:
748:
744:
737:
735:
733:
729:
716:
712:
704:
701:
695:
691:
688:
686:
683:
681:
678:
676:
673:
671:
669:
667:
664:
662:
659:
657:
654:
653:
649:
644:
637:
632:
629:
622:
617:
614:
607:
602:
599:
596:1765 copy of
592:
587:
584:
577:
572:
569:
566:1743 copy of
562:
557:
551:
550:
545:
541:
540:
535:
534:
530:
528:
526:
522:
518:
514:
510:
505:
502:
496:
494:
490:
486:
482:
478:
474:
470:
465:
463:
459:
451:
447:
443:
441:
436:
432:
429:
425:
417:
415:
413:
409:
405:
401:
397:
393:
385:
383:
381:
380:George Stokes
377:
373:
369:
365:
361:
357:
353:
349:
345:
341:
337:
329:
325:
320:
316:
313:
311:
306:
302:
298:
294:
290:
286:
282:
274:
269:
267:
264:
262:
257:
255:
247:
245:
243:
239:
235:
231:
227:
223:
215:
210:
208:
206:
202:
198:
194:
190:
186:
182:
178:
174:
173:
168:
164:
160:
155:
147:
138:
135:
132:
128:
125:
121:
118:
114:
110:
106:
102:
99:
95:
91:
87:
83:Paris, France
75:
71:
67:Paris, France
56:
52:
45:
40:
33:
30:
19:
1109:
1095:
1067:
1046:
1009:
998:
975:
965:
941:(1): 27â32.
938:
934:
908:
902:
892:
885:
858:
854:
827:. Retrieved
822:
812:
800:. Retrieved
796:the original
782:
773:
763:
751:. Retrieved
746:
719:. Retrieved
714:
703:
642:
627:
612:
597:
582:
567:
548:
538:
531:Publications
506:
501:longitudinal
497:
484:
472:
466:
455:
449:
421:
391:
389:
339:
335:
333:
327:
318:
308:
296:
289:meridian arc
278:
265:
258:
251:
237:
219:
170:
163:geophysicist
145:
144:
123:
78:(1765-05-17)
29:
1131:1765 deaths
1126:1713 births
861:: 277â306.
717:(in French)
412:mathematics
364:homogeneous
222:mathematics
197:mathematics
134:Mathematics
89:Nationality
76:17 May 1765
64:13 May 1713
1120:Categories
1040:References
428:Leibnizian
159:astronomer
60:1713-05-13
408:astrology
372:ellipsoid
352:ellipsoid
301:ellipsoid
297:Principia
211:Biography
172:Principia
1055:, 2005.
1006:(1999).
829:12 March
802:26 April
753:26 April
721:26 April
650:See also
431:calculus
396:geometry
386:Geometry
943:Bibcode
511:of the
440:apsides
404:physics
356:equator
348:gravity
299:was an
285:Lapland
226:prodigy
177:Lapland
150:French:
1059:
1022:
986:
877:103921
875:
517:comets
330:, 1743
254:Bossut
161:, and
130:Fields
92:French
1032:p. 30
873:JSTOR
696:Notes
525:Venus
509:orbit
489:apsis
1057:ISBN
1020:ISBN
984:ISBN
831:2009
804:2018
755:2018
723:2018
513:Moon
479:and
460:and
452:1765
203:and
73:Died
54:Born
951:doi
863:doi
1122::
1100:,
1094:,
1090:,
1051:,
1030:,
1018:.
1014:.
974:.
949:.
939:63
937:.
933:.
917:^
871:.
859:40
857:.
853:.
839:^
821:.
790:.
772:.
731:^
713:.
495:.
406:,
236:,
207:.
1063:.
1028:.
992:.
959:.
953::
945::
911:.
896:.
879:.
865::
833:.
806:.
776:.
757:.
725:.
312:.
148:(
62:)
58:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
