41. Converses Of Napoleon S Theorem File Format PDF/Adobe Acrobat Quick View http://poncelet.math.nthu.edu.tw/disk5/js/geometry/napoleon/9.pdf

42. Napoleon's Theorem Mathematical technology for industry and education. Napoleon's Theorem . Besides conquering most of Europe, Napoleon reportedly came up with this theorem http://www.saltire.com/applets/advanced_geometry/napoleon_executable/napoleon.ht

Saltire Home Geometry Applet Gallery Basic Triangles ... About Saltire Napoleon's Theorem Besides conquering most of Europe, Napoleon reportedly came up with this theorem: If you take any triangle ABC and draw equilateral triangles on each side, then join up the incenters of these triangles, the resulting triangle GHI is equilateral. See how to explore Napoleon's theorem using the Casio Classpad 300 Also see Napoleon's Theorem in our Geometry Formula Atlas If you are interested in this applet, you may like our Interactive Symbolic Geometry software Geometry Expressions

43. Napoleon's Theorem Napoleon s Triangle appears to be congruent to the original equilateral triangle ABC by the SSS postulate. Now, let s see what happens when our original http://jwilson.coe.uga.edu/EMT725/Class/Brooks/Napoleon/napoleon.html

Napoleon's Theorem by Kala Fischbein and Tammy Brooks Given any triangle, we can construct equilateral triangles on the sides of each leg. In these equilateral triangles, we can then find the centers: centroid, orthocenter, circumcenter, and incenter. Each of these centers is in the same location because the triangles are equilateral. After the centers have been located, we connect them thus forming Napoleon's Triangle. Construction of Napoleon's Triangle. Napoleon's Triangle is the grey triangle. Notice that it is also an equilateral triangle. Napoleon's Triangle appears to be congruent to the original equilateral triangle ABC by the SSS postulate. Now, let's see what happens when our original triangle is a right triangle. The green triangle, which is Napoleon's Triangle, is still an equilateral triangle. Let us explore when the original triangle is an isosceles triangle. Notice that the yellow triangle represents Napoleon's Triangle which remains an equilateral triangle. After exploring all of the special types of triangles, what happens when we have a scalene or general triangle? Again, notice that Napoleon's Triangle, the red triangle, is still equilateral no matter which type of triangle is used for the original triangle.

44. Napoleon's Theorem Napoleon's Theorem. This is a theorem attributed by legend to Napoleon Bonaparte. It is rather doubtful that the Emperor actually discovered this theorem, but it is true that http://www.math.washington.edu/~king/coursedir/m444a02/class/11-25-napoleon.html

Napoleon's Theorem This is a theorem attributed by legend to Napoleon Bonaparte.  It is rather doubtful that the Emperor actually discovered this theorem, but it is true that he was interested in mathematics.  He established such institutions as the Ecole Polytechnique with a view to training military engineers, but these institutions benefited mathematics greatly. French mathematicians made many important discoveries at the turn of the Eighteenth to the Nineteenth Century. Statement of Napoleon's Theorem For any triangle ABC, build equilateral triangles on the sides.  (More precisely, for a side such as AB, construct an equilateral triangle ABC', with C and C' on opposite sides of line AB; do the same for the other two sides.). Then if the centers of the equilateral triangles are X, Y, Z, the triangle XYZ is equilateral.

45. Essay 3 Napoleon's Theorem Napoleon s Theorem goes as follows Given any arbitrary triangle ABC http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Martin/essays/essay3.html

Essay 3: Napoleon's Triangle by Anita Hoskins and Crystal Martin Napoleon's Theorem goes as follows: Given any arbitrary triangle ABC, construct equilateral triangles on the exterior sides of triangle ABC. The segments connecting the centroids of the equilateral triangles form an equilateral triangle. Let's explore this theorem. Construct an equilateral triangle and see if Napoleon's triangle is equilateral. We can see from this construction, that when given an equilateral triangle, the resulting Napoleon triangle is also equilateral. Construct an isosceles triangle. Again, we see that with an isosceles triangle, Napoleon's triangle is still equilateral. Now, let's construct a right triangle. Still, even with a right triangle, Napoelon's triangle is equilateral. Now, we will prove that for any given triangle ABC, Napoleon's triangle is equilateral. We will use the following diagram: A represents vertex A and it's corresponding angle. a denotes the length of BC, c denotes the length of AB, and b denotes the length of AC. G, I, and H are the centroids of the equilateral triangles. x is the length of segment AG and y is the length of segment AI.

46. Napoleon's Theorem@Everything2.com Proving this theorem was a class assignment. My proof may or may not be original (probably not). Theorem Let ABC be a triangle. Erect equilateral triangles A'BC, AB'C, ABC' http://www.everything2.com/title/Napoleon%27s theorem

47. Napoleon's Theorem Given any triangle, we can construct equilateral triangles on the sides of each leg. In these equilateral triangles, we can then find the centers centroid, orthocenter http://jwilson.coe.uga.edu/emt725/Class/Fischbein/napoleon.triangle/Napoleon/nap

Napoleon's Theorem by Kala Fischbein and Tammy Brooks Given any triangle, we can construct equilateral triangles on the sides of each leg. In these equilateral triangles, we can then find the centers: centroid, orthocenter, circumcenter, and incenter. Each of these centers is in the same location because the triangles are equilateral. After the centers have been located, we connect them thus forming Napoleon's Triangle. Construction of Napoleon's Triangle. Napoleon's Triangle is the grey triangle. Notice that it is also an equilateral triangle. Napoleon's Triangle appears to be congruent to the original equilateral triangle ABC by the SSS postulate. Now, let's see what happens when our original triangle is a right triangle. The green triangle, which is Napoleon's Triangle, is still an equilateral triangle. Let us explore when the original triangle is an isosceles triangle. Notice that the yellow triangle represents Napoleon's Triangle which remains an equilateral triangle. After exploring all of the special types of triangles, what happens when we have a scalene or general triangle? Again, notice that Napoleon's Triangle, the red triangle, is still equilateral no matter which type of triangle is used for the original triangle.

48. No. 2550: Napoleon’s Theorem There s even a famous result in trigonometry that bears his name — Napoleon s Theorem. But much of that fame comes from the question, “Did Napoleon actually http://uh.edu/engines/epi2550.htm

No. 2550 NAPOLEON’S THEOREM by Andrew Boyd Click here for audio of Episode 2550 machines that make our civilization run, and the people whose ingenuity created them. N A lot of fuel for the debate was provided by an off-hand comment of two twentieth century mathematicians. One was the famed geometer Donald Coxeter. In the textbook, Geometry Revisited , he and co-author Samuel Greitzer write, “… the possibility of Napoleon knowing enough geometry [to prove the result] is as questionable as the possibility that he knew enough English to compose the famous palindrome ABLE WAS I ERE I SAW ELBA.” Coxeter and Greitzer didn’t just challenge the claim that Napoleon was first. They didn’t think he was capable of solving it at all. It’s quite an insult coming from the English born Coxeter. certainly could have. Napoleon’s Theorem requires logical thinking but little more. Most proofs of it are understandable by a good high school student. What led Coxeter and Greitzer to disparage Napoleon’s abilities isn’t clear, though it may have been just a poor effort at humor. The palindrome ABLE WAS I ERE I SAW ELBA is fabled to have been uttered by Napoleon, who at one time was exiled to Elba. But was Napoleon the first to discover the result that bears his name? That’s not at all clear. Napoleon might never have actually discovered the steps in the proof. The result simply could have been named in his honor by someone seeking to curry favor.

49. Napoleon's Theorem Napoleon s Theorem. Napoleon=proc() local A,B,C ItIsEquilateral( CET(A,B) , CET(B,C) , CET(C,A) ) end Previous Definitions Theorems Next. http://www.math.rutgers.edu/~zeilberg/PG/Napoleon.html

Napoleon's Theorem ItIsEquilateral CET (A,B) , CET (B,C) , CET (C,A) ): end: Previous Definitions Theorems Next

50. Principles Of Nature: Napoleon's Theorem 121—135) is known as Napoleon s Theorem. Apparently Napoleon Bonaparte had a strong interest in geometry and this theory has been attributed to him. http://www.principlesofnature.net/references/Napoleons_theorem_in_geometry.htm

Principles of Nature: towards a new visual language Appendix 2 Excerpt from (W Roberts, 2003) reformatted for web presentation. Napoleon's Theorem . Apparently Napoleon Bonaparte had a strong interest in geometry and this theory has been attributed to him. If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle. Similarly, if equilateral triangles are erected internally (or centripetally) around the sides of any triangle as in Figure A-2.2, their centres also form an equilateral triangle known as the inner Napoleon triangle We do not prove it here, but the difference in area between the outer and inner Napoleon triangles around any triangle is equal to the area of the original triangle in question If we combine the Napoleon Theorem with the new relative unit of area the etu ), we see a most interesting relation, p representing the difference in areas of the outer and inner napoleon triangles expressed in etu. An etu is the area of an equilateral triangle of unitary side length back to top Introduction ... is flawed as a method of proof

51. A Proof Of Napoleon S Theorem File Format PDF/Adobe Acrobat Quick View http://www.wbabin.net/math/alhajabed.pdf

52. Casio ClassPad 300 Explorations -- Napoleon’s Theorem 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 http://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

53. 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 http://nrich.maths.org/1944

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 $PQR$?

54. Napoleon's Theorem. Plane Geometry. Elearning. Napoleon s Theorem, Equilateral Triangles. Plane Geometry, Index. Elearning. http://gogeometry.com/geometry/napoleon_index_theorem_problem.html

55. Napoleon's Theorem — The Gateway To 21st Century Skills This is a step by step proof of Napoleon's Theorem. Napoleon's Theorem GEM Element Element Value title Napoleon's Theorem description http://www.thegateway.org/browse/713

56. Geometry Classes, Problem 248. Napoleon's Theorem III. Area Inner And Outer Napo Napoleon s Theorem III. Area Inner and outer Napoleon triangles. Math http://www.gogeometry.com/problem/p248_napoleon_theorem_iii_area_inner_outer.htm

Problem 248. Napoleon's Theorem III. Area Inner and outer Napoleon triangles The figure shows a triangle ABC of area S. If A B C is the outer Napoleon triangle of area S and A B C is the inner Napoleon triangle of area S , prove that S = S - S See also: Problem 247 Problem 246 Equilateral Triangle Home ... Post a comment

57. MacCool S Proof Of Napoleon S Theorem A Sequel To The MacCool/West File Format PDF/Adobe Acrobat Quick View http://www.maths.tcd.ie/pub/ims/bull59/M5903.pdf

58. Napoleon's Theorem The result is called Napoleon s theorem. There are dozens of elementary proofs; these can be found in Geometry books that cover geometry beyond the basic http://mathcentral.uregina.ca/QQ/database/QQ.09.03/david5.html

Quandaries and Queries David Calculus, 12th grade HOw do i prove this : FOr any triangle, if you make 3 equillateral triangles using the sides of the the original triangle, the central points of the 3 tringles another triangle that is equillateral. Please Help, david Hi david, The result is called Napoleon's theorem. There are dozens of elementary proofs; these can be found in Geometry books that cover geometry beyond the basic theorems of Euclid. For example Coxeter's Geometry Revisited, or his Introduction to Geometry. You can also look on the Cut the Knot Web Site. Chris and Penny Go to Math Central

59. YouTube - Napoleon's Theorem http//demonstrations.wolfram.com/Nap The Wolfram Demonstrations Project contains thousands of free interactive visualizations, with new entries added daily. Construct http://www.youtube.com/watch?v=7OQYXyhZ9mA

60. Napoleon S Theorem, Shakespeare S Theorem, And Desargues S Theorem File Format PDF/Adobe Acrobat Quick View http://www.vacadsci.org/vjsArchives/v44/44-3/44-269.pdf

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