61. Napoleon Triangles Napoleon's Theorem. By Gooyeon Kim . Anecdote about Napoleon Bonaparte (17691821) Napoleon was known as an amateur mathematician. There is a historical anecdote about Napoleon http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Kim/emat6690/essay1/Napoleon's Th

Mathematics Education Department Napoleon's Theorem By Gooyeon Kim Anecdote about Napoleon Bonaparte (1769-1821) Napoleon was known as an amateur mathematician. There is a historical anecdote about Napoleon who was emperor of the French: It is known that Napoleon Bonaparte was a bit of a mathematician with a great interest in geometry. 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. What is Napoleon's Triangle? Given any triangle, construct equilateral triangles on each side and find the center of each equilateral triangle. The triangle formed by these three centers is Napoleon's Triangle Figure 1. GSP file Napoleon's Theorem: If equilateral triangles are erected externally on the sides of any triangle, then their centers form an equilateral triangle. Figure 2.

62. Napoleon S Theorem And Generalizations Through Linear Maps File Format Adobe PostScript View as HTML http://www.dmg.tuwien.ac.at/stachel/napol3f.ps.gz

63. YouTube - Napoleon's Theorem No matter what shape the green triangle has, the red triangle is always equilateral. For more information, films, and interactive material, see http//tinyurl.com/4wqal8 http://www.youtube.com/watch?v=pmUwPPcH8BQ

64. CategoryNapoleon S Theorem - Wikimedia Commons Mar 8, 2008 513pxNapoleon s theorem proof.png 513px-Napoleon s the 26370 bytes. Napoleon s theorem.svg 8228 bytes. Proof1826.svg 10104 bytes http://commons.wikimedia.org/wiki/Category:Napoleon's_theorem

65. File:513px-Napoleon& - Wikimedia Commons File513pxNapoleon s theorem proof.png. From Wikimedia Commons, the free http://commons.wikimedia.org/wiki/File:513px-Napoleon's_theorem_proof.png

From Wikimedia Commons, the free media repository Jump to: navigation search No file by this name exists. File usage on Commons There are no pages that link to this file. Retrieved from " http://commons.wikimedia.org/wiki/File:513px-Napoleon%26 Personal tools New features Log in / create account Namespaces File Discussion Variants Views Create Actions Search Navigation Main Page Welcome Community portal Village pump Participate Upload file Recent changes Latest files Random file ... Donate Toolbox What links here Special pages Printable version About Wikimedia Commons

66. Napoleons Theorem Article on Napoleons Theorem proving . Remarks The attribution to Napol on Bonaparte (17691821) is traditional, but dubious. http://myyn.org/m/article/napoleons-theorem/

67. The Harmonic Analysis Of Polygons And Napoleon S Theorem File Format PDF/Adobe Acrobat Quick View http://www.heldermann-verlag.de/jgg/jgg01_05/jgg0502.pdf

68. Nrich.maths.org :: Mathematics Enrichment :: Napoleon's Theorem Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR? http://nrich.maths.org/1944&part=note

Skip over navigation Search by Topic Tech Help Thesaurus ... Contact Us Be part of our research! Are you really good at maths? Are you the parent of someone who is really good at maths? Are you the teacher of someone who is really good at maths? If so we'd love to involve you in our research. Case studies Are you aged between 10 and 17? Read about Dr Yi Feng's research which involves talking to students over the next two years about their mathematical experiences in and out of school, and respond to the call for participants. AskNRICH Do you use the ASKNRICH site, or have you previously? Libby Jared's research involves looking at what goes on on the ASKNRICH site and why. To help with this research please respond to the ASKNRICH survey Read more about the research we are doing here This month: Napoleon's Theorem Problem Teachers' Notes Hint Solution Printable page Stage: 4 and 5 Challenge Level: Triangle $ABC$ has equilateral triangles drawn on its edges. Points $P$, $Q$ and $R$ are the centres of the equilateral triangles. You can change triangle $ABC$ below by dragging the vertices and observe what happens to triangle $PQR$. What can you prove about the triangle $PQR$?

69. ON NAPOLEON S THEOREM IN THE ISOTROPIC PLANE Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/D05X411566432777.pdf

70. Funny Interesting Facts | Weird |Science Yoga Bizarre|: Napoleon's Theorem Interesting facts,facts,Interesting,facts about pairs strong, Germany,Australia,franc, Austria,health, Mexico,Italy,Canada, strange,weird,weird facts India mumbai, Pakistan http://cool-interesting-facts.blogspot.com/2008/03/napoleons-theorem.html

skip to main skip to sidebar Interesting facts,facts,Interesting,facts about pairs strong, Germany,Australia,franc, Austria,health, Mexico,Italy,Canada, strange,weird,weird facts India mumbai, Pakistan, Brazil, William Shakespeare, china, japan, cricket, facts weird,most weird,most,true facts,facts true,a few words,few words, sports, science facts about animals dogs, cats, horse, politics facts, Egypt facts, strange, useless,all arts bizarre yoga facts Enter your search terms Submit search form Advertisement Sunday, March 2, 2008 Napoleon's Theorem Napoleon's theorem states that if we construct equilateral triangles on the sides of any triangle (all outward or all inward), the centers of those equilateral triangles themselves form an equilateral triangle, as illustrated below. This is said to be one of the most-often rediscovered results in mathematics. The earliest definite appearance of this theorem is an 1825 article by Dr. W. Rutherford in "The Ladies Diary". Although Rutherford was probably not the first discoverer, there seems to be no direct evidence supporting any connection with Napoleon Bonaparte, although we know that he did well in mathematics as a school boy. According to Markham's biography, 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...

71. Casio ClassPad 300 Explorations -- Napoleon�s Theorem Napoleon s theorem offers a tour de force for constraint geometry. The theorem states that for any arbitrary triangle, if you construct an equilateral http://www.classpad.org/explorations/napoleon/napoleon.html

Home ClassPad News Overview Online Store ... Saltire Family of Websites Napoleon�s Theorem with the Casio ClassPad Napoleon�s theorem offers a tour de force for constraint geometry. The theorem states that for any arbitrary triangle, if you construct an equilateral triangle on each edge, and join the centers of the incircles of these triangles, then the resulting triangle is equilateral. The theorem is named for, and supposedly discovered by, Napoleon Bonaparte, himself no stranger to tours de force. Take a triangle and draw a triangle on each of its sides We can make the subtended triangles equilateral simply by specifying congruence constraints. Start by making AC congruent to AF and AC congruent to FC� (Congruence is the second option on the Measurement Selection drop down button when two segments are selected.) We can follow the same procedure for the other two triangles: We have created the required equilateral triangles. Now for the incircles. We sketch the circles then set tangency constraints - three for each. Now let�s join the centers of these circles. Shading the resulting triangle makes it stand out from the cat�s cradle of lines and circles. If you�re not convinced that it is indeed equilateral - and why should you be, Napoleon was more famous for geopolitics than geometry - inspect its side lengths

72. Napoleon S Theorem And Generalizations Through Linear Maps File Format PDF/Adobe Acrobat Quick View http://www.emis.de/journals/BAG/vol.43/no.2/b43h2sta.pdf

73. JSTOR: An Error Occurred Setting Your User Cookie Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.jstor.org/stable/2324901

Skip to main content Login Help Contact Us Trusted archives for scholarship Search Basic Advanced Citation Locator ... Profile An Error Occurred Setting Your User Cookie The JSTOR site requires that your browser allows JSTOR ( http://www.jstor.org ) to set and modify cookies. JSTOR uses cookies to maintain information that will enable access to the archive and improve the response time and performance of the system. Any personal information, other than what is voluntarily submitted, is not extracted in this process, and we do not use cookies to identify what other websites or pages you have visited. JSTOR is part of ITHAKA, a not-for-profit organization helping the academic community use digital technologies to preserve the scholarly record and to advance research and teaching in sustainable ways. Terms and Conditions Accessibility

74. CiteSeerX � Napoleon S Theorem And Generalizations Through Linear Maps by H Stachel Related articles http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.1345

75. Napthm Napoleon s Theorem is the name popularly given to a theorem which states that if equilateral triangles are constructed on the three legs of any triangle, http://www.pballew.net/napthm.html

Napoleon's Thm and the Napoleon Points Napoleon's Theorem is the name popularly given to a theorem which states that if equilateral triangles are constructed on the three legs of any triangle, the centers of the three new triangles will also form an equilateral triangle. In the figure the original triangle is labeled A, B, C, and the centers of the three equilateral triangles are A', B', C'. If the segments from A to A', B to B', and C to C' are drawn they always intersect in a single point, called the First Napoleon Point. If the three equilateral triangles are drawn interior to the original triangle, the centers will still form an equilateral triangle, but the segments connecting the centers with the opposite vertices of the original triangle meet in a (usually) different point, called the 2nd Napoleon Point. Although it is known that Napoleon had a keen interest in geometry, math historians seem unable to find evidence he really discovered the theorem. Here is a letter on the subject from Antreas P. Hatzipolakis, a real living Greek mathematician, to the Geometry Forum. The early history of Napoleon's theorem and the Fermat points F, F' (which are also called isogonic centers of ABC) is summarized in Mackey [21], who traces the fact that LMN and L'M'N' are equilateral to 1825 to one Dr. W. Rutherford [27] and remarks that the result is probably older.

76. DC MetaData For: Napoleon's Theorem With Weights In N-Space by H Martini 1998 - Cited by 9 - Related articles http://www.math.uni-magdeburg.de/preprints/shadows/98-20report.html

Napoleon's Theorem with Weights in n-Space by Preprint series: 98-20, Preprints MSC 51N10 Affine analytic geometry 51N20 Euclidean analytic geometry Abstract The famous theorem of Napoleon was recently extended to higher dimensions. With the help of weighted vertices of an n-simplex T in E n , n >= 2, we present a weighted version of this generalized theorem, leading to a natural configuration of (n-1)-speres corresponding with T by an almost arbitrarily chosen point. Besides the Euclidean point of view, also affine aspects of the theorem become clear, and in addition a critical discussion on the role of the Fermat-Tooicelli point in this framework is given. Keywords: Napoleon's Theorem, Torricelli's configuration Upload: Update: The author(s) agree, that this abstract may be stored as full text and distributed as such by abstracting services.

77. Napoleon’s Theorem | Futility Closet Jul 7, 2010 This discovery is traditionally credited to Napoleon, but there s no evidence supporting that contention. Indeed, this theorem is said to be http://www.futilitycloset.com/2010/07/07/napoleons-theorem/

Skip to content Skip to search - Accesskey = s Futility Closet Posted in by Greg Ross on July 7th, 2010 Construct equilateral triangles on the sides of any triangle, and their centers will form an equilateral triangle. See A Better Nature (Image: Wikimedia Commons Leave a comment ... Name (required) Mail (will not be published) (required) Website An idler's miscellany of compendious amusements Random Item Subscribe by RSS Subscribe by Email Info About Futility Closet Contact/Submissions Search Categories Art Crime Death Entertainment ... Uncategorized Archives October 2010 September 2010 August 2010 July 2010 ... January 2005 Meta Log in RSS Back to top The Journalist template by Lucian Marin - Built for WordPress

78. YouTube - Napoleon's Theorem Oct 7, 2008 No matter what shape the green triangle has, the red triangle is always equilateral. For more information, films, and interactive material, http://il.youtube.com/watch?v=pmUwPPcH8BQ

79. Scientific Commons Napoleon S Theorem And Generalizations Through by H Stachel 2007 - Related articles http://en.scientificcommons.org/42893200

���r�6����d"���LcYb�g�M�N���i���$W"�` P��Y�m��n �"�e˱��3�' ���]� ��d���@Al�@�%~�9�R�64S,J4����� <��h � �P:�j����F�2 <Y�c"-ꛩ�Ӌ�D�s�v_��a"Ғi���iȡ6�g�����Z��� �1q�*�����

80. Go Geometry: Problem 248. Napoleon's Theorem III. Area Inner And Outer Napoleon Feb 9, 2009 Inner Napoleon Triangle Napoleon s Theorem III. Area Inner and outer Napoleon triangles. See complete Problem 248 at http://gogeometry.blogspot.com/2009/02/problem-248-napoleons-theorem-iii-area.ht

Page 4     61-80 of 86    Back | 1  | 2  | 3  | 4  | 5  | Next 20