Napoleon's Theorem And The Fermat Point Napoleon s theorem and the Fermat Point. This page has a proof of Napoleon stheorem and also proofs of the main properties of the special ines and circles http://www.math.washington.edu/~king/coursedir/m444a03/notes/12-05-Napoleon-Ferm
Extractions: This page has a proof of Napoleon's theorem and also proofs of the main properties of the special ines and circles in this figure that all pass through the Fermat point. The proofs use several important tools that should be reviewed, if needed. See the References section at the end for places to look. The Napoleon figure is a triangle ABC with an equilateral triangle built on each side: BCA', CAB', ABC'. The centers of the equilateral triangles are X, Y, Z, respectively. For any triangle ABC, the triangle XYZ is an equilateral triangle. Proof: The rotation Y maps A to C. The rotation X maps C to B. So if we define S = X Y , then S(A) = X (Y (A)) = X (C) = B. But by the theory of composition of rotations (see Brown 2.4), S is a rotation by angle 240 degrees and the center D of S is constructed as the vertex of a triangle YXD, where angle X = 120/2 = 60 degrees and angle Y also = 60 degrees. Thus YXD is an equilateral triangle. But also Z (A) = B, since Z
The Geometer's Sketchpad® - JavaSketchpad: Napoleon's Theorem Napoleon s theorem. This JavaSketch is based on one of the activities in the Students explore Napoleon s theorem, which states that the triangle NPQ is http://www.keypress.com/sketchpad/javasketchpad/gallery/pages/napoleons_theorem.
Extractions: Getting Started Product Information How to Order Curriculum Modules ... gallery napoleons theorem This JavaSketch is based on one of the activities in the Sketchpad curriculum module Exploring Geometry . The first portion of the activity has students construct the figure below: an arbitrary triangle, with equilateral triangles on each side, and segments connecting the centers of the three equilateral triangles. The new segments form a third triangle, here triangle NPQ, which is the outer Napoleon triangle of triangle ABC. Drag the vertices of the original triangle ABC and observe the triangle formed by the centers of the equilateral triangles. Students explore Napoleon's Theorem, which states that the triangle NPQ is equilateral. Sorry, this page requires a Java-compatible web browser. Return to the JavaSketchpad Gallery Portions of the work on JavaSketchpad
Mudd Math Fun Facts: Napoleon's Theorem The Math Behind the Fact This theorem is credited to Napoleon, who was fond ofmathematics, though many doubt that he knew enough math to discover it! http://www.math.hmc.edu/funfacts/ffiles/10009.2.shtml
Extractions: Francis Edward Su From the Fun Fact files, here is a Fun Fact at the Easy level: Figure 1 Take any generic triangle, and construct equilateral triangles on each side whose side lengths are the same as the length of each side of the original triangle. Surprise: the centers of the equilateral triangles form an equilateral triangle! Presentation Suggestions:
Napoleon's Theorem Napoleon s theorem. by Kala Fischbein and Tammy Brooks Napoleon s Triangleappears to be congruent to the original equilateral triangle ABC by the SSS 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 Please Help,. david. Hi david,. The result is called Napoleon s theorem. There aredozens of elementary proofs; these can be found in Geometry books that 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
Napthm Napoleon s theorem is the name popularly given to a theorem which states that if The early history of Napoleon s theorem and the Fermat points F, http://www.pballew.net/napthm.html
Extractions: 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.
A Generalization Of Napoleon's Theorem The famous Napoleon theorem is stated by Coxeter and Greitzer as follows This sounds even more surprising than the Napoleon s theorem itself. http://mathsforeurope.digibel.be/Napoleon2.html
Extractions: He was born on the island of Corsica and died in exile on the island of Saint-Hélène after being defeated in Waterloo. He attended school at Brienne in France where he was the top maths student. He took algebra, trigonometry and conics but his favorite was geometry. After graduation from Brienne, he was interviewed by Pierre Simon Laplace (1749-1827) for a position in the Paris Military School and was admitted by virtue of his mathematics ability. He completed the curriculum, which took others two or three years, in a single year and subsequently he was appointed to the maths section of the French National Institute. During the Egyptian military campaign of 1798-1799, Napoleon was accompanied by a group of educators, civil engineers, chemists, mineralogists and mathematicians, including Gaspard Monge (1746-1818) and Joseph Fourier (1768-1830). On his return from Egypt, Napoleon led a successful coup d'état and became head of France. As emperor, he instituted a number of juridical, economical and educational reforms and placed men such as
Extractions: TeX format There is a theorem, usually attributed to Napoleon, which states that if one takes any triangle in the Euclidean Plane, constructs equilateral triangles on each of its sides, and connects the midpoints of the three equilateral triangles, one will obtain an equilateral triangle. We consider an analogue of this problem in the hyperbolic plane. For download Keywords none Language English Category Primary: 37D40
Extractions: Institute of Geometry, Vienna University of Technology, Wiedner Hauptstr. 8-10/113, A-1040 Wien, Austria, e-mail: stachel@geometrie.tuwien.ac.at Abstract: Recently J. Fukuta and Z. Cerin showed how regular hexagons can be associated to any triangle, thus extending Napoleon's theorem. The aim of this paper is to prove that these results are closely related to linear maps. This reflects better the affine character of some constructions and gives also rise to a few new theorems. Keywords: Napoleon's theorem, triangle, regular hexagon, linear map Classification (MSC2000): Full text of the article: Previous Article Next Article Contents of this Number ELibM for the EMIS Electronic Edition
Extractions: email: pech@pf.jcu.cz Abstract: Plane closed polygons are harmonically analysed, i.e., they are expressed in the form of the sum of fundamental $k-$regular polygons. From this point of view Napoleon's theorem and its generalization, the so-called theorem of Petr, are studied. By means of Petr's theorem the fundamental polygons of an arbitrary polygon have been found geometrically. Keywords: finite Fourier series, polyon transformation Classification (MSC2000): Full text of the article will be available in end of 2002. Previous Article Next Article Contents of this Number ELibM for the EMIS Electronic Edition
Affine The outer vertices of the triangles define another regular ngon. Note that whenthe number of sides is equal to three this is Napoleon s theorem. http://www.angelfire.com/mn3/anisohedral/affine.html
Extractions: Search: Lycos Angelfire Free Games Share This Page Report Abuse Edit your Site ... Next This page uses JavaSketchpad , a World-Wide-Web component of The Geometer's Sketchpad Move the point M or either of the sliders at the top to vary the parameters. Note that the inside figure is a "flattened" or affine version the original n-gon. We construct triangles that are similar to the triangle at the center of the regular n-gon on the left. The outer vertices of the triangles define another regular n-gon. Note that when the number of sides is equal to three this is Napoleon's theorem. Sorry, this page requires a Java-compatible web browser. affine Return to applets. You can reach me by email.
Napoleon S Theorem Napoleon s theorem Draw three equilateral triangles using each side of the Napoleon s theorem states that the three centroids form the vertices of an http://www.math.psu.edu/dlittle/java/Geometry/Euclidean/napolean.html
DC MetaData For: Napoleon's Theorem With Weights In N-Space Abstract The famous theorem of Napoleon was recently extended to higher dimensions.With the help of weighted vertices of an nsimplex T in http://www.math.uni-magdeburg.de/preprints/shadows/98-20report.html
Teachers Notes-Bernhard Neumann suitable for a popular talk I found that somebody had called it Napoleon stheorem. Keywords. equilateral triangles geometry mathematics theorem http://www.science.org.au/scientists/notesbn.htm
Extractions: Interviews with Australian scientists Teachers notes Teachers notes to accompany an interview with mathematician, Professor Bernhard Neumann (1909-2002) You can either print out these notes or use them online. If using them online, use the links below to take you to the relevant sections. Professor Bernhard Neumann Introduction Professor Bernhard Neumann was interviewed in 1998 for the Interviews with Australian scientists series. By viewing the interviews in this series, or reading the transcripts and extracts, your students can begin to appreciate Australia's contribution to the growth of scientific knowledge. Information on how to order a copy of the video of Professor Neumann's interview is available at www.science.org.au/scientists , together with a full list of videotaped interviews, transcripts and teachers notes. The following summary of Neumann's career sets the context for the extract chosen for these teachers notes. The extract covers the geometrical ideas behind a talk that Neumann gave to general audiences. Use the focus questions that accompany the extract to promote discussion among your students. Summary of career Bernhard Neumann was born in Germany in 1909. He showed a precocious mathematical talent as a youngster, teaching himself calculus by the age of 12 and in Year 10 inventing three-dimensional analytical geometry. He earned a D Phil from Friedrich-Wilhelms Universität in Berlin in 1932, one of the youngest ever to receive this award in mathematics from Berlin.
From Israel@math.ubc.ca (Robert Israel) Subject Re NAPOLEON On The Napoleon s theorem I know about says the following (see Napoleon s theoremstates that the centers of the three outer Napoleon triangles form http://www.math.niu.edu/~rusin/known-math/00_incoming/napoleon
2005 Spring Meeting MD-DC-VA MAA Is it possible to prove Napoleon s theorem by tiling your bathroom floor?In this (very interactive!) afternoon session expect to be surprised. http://www.math.vt.edu/org/maa/spr05/
Extractions: How can meanderings through the floor plan of a house prove Brouwer's Fixed Point Theorem? How can gnomes playing deadly hat games help with the study of error-correcting codes? How can braiding one's hair lead to concepts in abstract algebra and invariant theory? How can playing with weird "triangular number arithmetic" lead to Euler's Theorem in graph theory, summation formulae, more invariant theory, and new questions in these classic studies? Why does the long division algorithm one learns in fifth grade work and what does it tell us about base one-and-a-half? How is this linked to the famous "3n+1" conjecture? Is it possible to prove Napoleon's theorem by tiling your bathroom floor?
The Educational Encyclopedia, Mathematics Carnot s theorem, bounded distance, barycentric coordinates, Pythagoreantheorem, Napoleon s theorem, Ford s touching circles, Euclid s Fifth postulate, http://users.pandora.be/educypedia/education/mathematics.htm
Extractions: Mathematics Algebra Complex numbers Formulas Fractals ... Fourier General overview Geometry Integrals and differentials Logarithms and exponentials Matrices and determinants ... Trigonometry General overview Aplusmath this web site is developed to help students improve their math skills interactively, algebra, addition, subtraction, multiplication, division, fractions, geometry for kids Ask Dr. Math Ask Dr. Math a question using the Dr. Math Web form, or browse the archive Calculus tutorial Karl's calculus tutorial, limits, continuity, derivatives, applications of derivatives, exponentials and logarithms, trig functions (sine, cosine, etc.), methods of integration Cut the knot! algebra, geometry, arithmetic, proofs, butterfly theorem, chaos, conic sections, Cantor function, Ceva's theorem, Fermat point, cycloids, Collage Theorem, Carnot's theorem, bounded distance, barycentric coordinates, Pythagorean theorem, Napoleon's theorem, Ford's touching circles, Euclid's Fifth postulate, Non-Euclidean Geometry, Projective Geometry, Moebius Strip, Ptolemy's theorem, Sierpinski gasket, space filling curves, iterated function systems, Heron's formula, Euler's formula, Hausdorff distance, isoperimetric theorem, isoperimetric inequality, Shoemaker's Knife, Van Obel theorem, Apollonius problem, Pythagoras, arbelos, fractals, fractal dimension, chaos, Morley, Napoleon, barycentric, nine point circle, 9-point, 8-point, Miquel's point, shapes of constant width, curves of constant width, Kiepert's, Barbier's
Nrich.maths.org::Mathematics Enrichment::Napoleon's Theorem (Dec 98) The Nrich Maths Project Cambridge, England. Mathematics resources for children,parents and teachers to enrich learning. Published on the 1st of each month. http://nrich.maths.org/public/viewer.php?obj_id=1944&part=index&refpage=monthind
