From: israel@math.ubc.ca (Robert Israel) Subject: Re: NAPOLEON on PBS TV; questions Date: 10 Nov 2000 00:17:28 GMT Newsgroups: sci.edu,soc.history,sci.math Summary: [missing] In article <3A0B1097.602D88DA@supaero.fr>, guillaume agostini wrote: >Napoleon was a rather good mathematician, even on nowadays's standards. >He made a couple a theorem, mainly in the geometry segment. The most >well-known (at least in France) is the Napoleon's theorem, which, if I >remember >well says that "pour tout triangle, l'aire de son cercle circonscrit est >egal a la >somme des aires des trois triangles inscrits des triangles equilatéraux >construits >sur ses côtès". This makes no sense to me. The "Napoleon's Theorem" I know about says the following (see http://cut-the-knot.com/ctk/Napolegon.html): --------------------- On the sides of a triangle construct equilateral triangles (outer or inner Napoleon triangles). Napoleon's theorem states that the centers of the three outer Napoleon triangles form another equilateral triangle. The statement also holds for the three inner triangles. --------------------- According to most sources, it's doubtful that Napoleon actually discovered this theorem. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 ============================================================================== From: holmburg@my-deja.com Subject: Re: NAPOLEON on PBS TV; questions Date: Sat, 11 Nov 2000 15:16:00 GMT Newsgroups: sci.edu,soc.history,sci.math In article <3A0D1D5E.3908471C@willinet.net>, arc_plutonium@hotmail.com wrote: In re: Napoleon and Mathematics If you end up doing that research, please consider sending something on it to the Napoleon Series (www.napoleonseries.org). According to Felix Markham's biography of Napoleon: "To his teachers Napoleon certainly appeared a model and promising pupil, especially in mathematics... The school inspector reported that Napoleon's aptitude for mathematics would make him suitable for the navy, but eventually it was decided that he should try for the artillery, where advancement by merit and mathematical skill was much more open..." A career in the artillery was in part technical and required a familiarity with ballistics, geometry, etc. Prior to the Revolution Napoleon undertook a study of the ballistics of mortars. After his return from Egypt Napoleon was invited to join the Institute de France, and was close friends with several mathematicians and scientists, including Fourier, Monge, Laplace, Chaptal and Berthollet. Fourier too distinguished himself in mathematics as a school boy, and was recommended for the artillery, but was not accepted due to his "low birth".In 1790 he became a teacher at the Benedictine college, Ecole Royale Militaire of Auxerre, where he had studied. In 1798 Fourier joined Napoleon's army in its invasion of Egypt as scientific adviser. Monge and Malus were also part of the expeditionary force. Fourier acted as an administrator as French type political institutions and administration was set up. In particular he helped establish educational facilities in Egypt and carried out archaeological explorations. While in Cairo Fourier helped found the Cairo Institute and was one of the twelve members of the mathematics division, the others included Monge, Malus and Napoleon Bonaparte. Fourier returned to France in 1801 with the remains of the expeditionary force and resumed his post as Professor of Analysis at the Ecole Polytechnique. Napoleon appointed him to be the Prefect of the Department of Isère. (After his return in 1801, Malus also held government posts in Antwerp, Strasbourg, and Paris.) Likewise Laplace received titles and high office as a result of his association with Bonaparte. However, Laplace was relieved of his duties as the Minister of the Interior after only six weeks, and Napoleon later commented that Laplace had "sought subtleties everywhere, had only doubtful ideas, and carried the spirit of the infinitely small into administration". The most famous exchange between these two men occurred after Laplace had given Napoleon a copy of his great work, the Mecanique Celeste. Napoleon looked it over, and remarked that in this massive volume about the universe there was not a single mention of God, its creator. Laplace replied "Sire, I had no need of that hypothesis". In fact, there is a story that, before he made himself ruler of the French, he engaged in a discussion with the great mathematicians Lagrange and Laplace until the latter told him, severely, "The last thing we want from you, general, is a lesson in geometry." Laplace became his chief military engineer. Regarding the idea that Napoleon might actually have discovered what is called "Napoleon's Theorem," Coxeter and Greitzer have said that: "The possibility of [Napoleon] knowing enough geometry for this feat is as questionable as the possibility of his knowing enough English to compose the famous palindrome, ABLE WAS I ERE I SAW ELBA. "The earliest definite appearance of this theorem is an 1825 article by Dr. W. Rutherford in "The Ladies Diary" See: http://www.seanet.com/~ksbrown/kmath270.htm http://cedar.evansville.edu/~ck6/bstud/napoleon.html Sent via Deja.com http://www.deja.com/ Before you buy.