Converses Of Napoleon S Theorem File Format PDF/Adobe Acrobat Quick View http://poncelet.math.nthu.edu.tw/disk5/js/geometry/napoleon/9.pdf
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
Extractions: About Saltire 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
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
Extractions: 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.
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
Extractions: 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. 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.
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
Extractions: 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.
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
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
Extractions: 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.
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
Extractions: 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.
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
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
Extractions: 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
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
Extractions: 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.
Extractions: If so we'd love to involve you in our research. 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. 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
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
Extractions: 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
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
