41. The Theorem Of Napoleon Please enable Java to see an interactive version of napoleon's theoremDrag any of the large red vertices of the inner triangle http://www.cinderella.de/junk/Napoleon.html

Please enable Java to see an interactive version of Napoleon's theorem Drag any of the large red vertices of the inner triangle to see Napoleon's theorem in action! If you erect an equilateral triangle on each side of a triangle, then the centroids of these triangles form again an equilateral triangle, no matter which triangle you started with in the beginning.

42. Maths Thesaurus Nanometre, Napier's bones, Napier's constant, Napoleon point, napoleon's theorem.Napoleon's triangles, Napoleon's point, Natural log, Natural logarithm, Natural number. http://thesaurus.maths.org/dictionary/map/indices/N

N (154 terms) n N n gon n-dimensional ... Numerology

43. Maths Thesaurus: Napoleon's Theorem Home napoleon's theorem If we take any triangle and draw equilateral triangleson each of its sides, then the incentres of these three new triangles form a http://thesaurus.maths.org/dictionary/map/word/2099

Napoleon's theorem If we take any triangle and draw equilateral triangles on each of its sides, then the incentres of these three new triangles form a triangle that is also equilateral. Find similar words More general: Defined earlier: Defined next: Theorem Napoleon's triangles First Napoleon point Second Napoleon Point Please enable Java for an interactive construction (with Cinderella). Created with Cinderella New search: Age: 19 Choose Language and Age Make a suggestion nrich@damtp.cam.ac.uk

44. Napoleon's Theorem napoleon's theorem. He also was interested in mathematics. His discovery, Napoleon'sTheorem, is a very interesting tesselation. It is basically this. http://www.geocities.com/SiliconValley/Monitor/8186/napoleon.html

NAPOLEON'S THEOREM Napoleon Bonaparte was a dictator and emperor of France during their height and power. He took over almost all of Europe and was a tactical leader. He also was interested in mathematics. His discovery, Napoleon's Theorem, is a very interesting tesselation. It is basically this. If you take any triangle ABC and draw equilateral triangles on the sides facing outwards then the incenters of the 3 equilateral triangles connected will form a equilateral triangle. Below is a diagram of this theorem. Later M.C. Escher discovered other things shown below and the theorem expanded to be a fairly complex tesselation. THE THEOREM MC ESCHER'S DISCOVERY to home page

45. Math Related To Car Engines, Littleton Highschool, On Geometry, Carburetors, Fue Finally, there is a napoleon's theorem which is a diagram made bythe French emperor. Go to napoleon's theorem for this section. http://www.geocities.com/SiliconValley/Monitor/8186/

MATH AND ENGINES Welcome to my page. My name is Daniel Huck and I am in 8th grade. I am in a geometry class at Littleton High School. I have a RC airplane so that is why I wrote this page. This page is about different engine air-fuel ratios on carburetors and fuel-injection that are related to math and has some animated diagrams and graphs. There is also some flexagon information and links. Finally, there is a Napoleon's Theorem which is a diagram made by the French emperor. I hope you find this page interesting and informative. I tried to make it very easy to understand with a lot of illustrations. Below is the description of my page. Napoleon's Theorem is an interesting design that involves triangles and incenter. My section has a design of one and tells more about this design. Go to Napoleon's Theorem for this section. I compare carburetors and fuel injection on cars and other vehicles. I also look into the air-fuel ratios of the 2. Included is many visuals and an animated throttle. Go to Carbs vs. Injection

46. June Lester - Mathematical Presentations University of Victoria, Canada, August 1993. A generalization of Napoleon'stheorem to ngons. A generalization of napoleon's theorem to n-gons. http://www.cecm.sfu.ca/~jalester/WebCV/presentations.html

June Lester - Mathematical Presentations Invited talks Conference talks Invited talks Conformal Spaces. Geometry Seminar, Department of Mathematics, University of Toronto, Canada, February 1979 Cone Preserving Mappings. Workshop in Geometry and Algebra, Technical University of Munich, W. Germany, February 1980 Characterizations of Lorentz Transformations. Geometry Colloquium, Mathematics Institute, University of Hannover, W. Germany, June 1980 Characterizations of Spacetime Transformations. Mathematics Colloquium. York University, Toronto, Canada, February 1983 Characterization Theorems on Metric Vector Spaces. Geometry Seminar, Department of Mathematics, University of Toronto, Canada, September 1985 Some Characterizations of Euclidean Motions. Mathematics Colloquium, University of Oldenburg, W. Germany, November 1985 Transformations Preserving Null Line Sections of a Domain. Mathematics Colloquium, University of Duisburg, W. Germany, November 1985 Mappings Preserving Null Line Sections of a Domain.

47. June Lester- Mathematical Publications 53 (1997) 4 35. A generalization of napoleon's theorem to n-gons. CR Math. Soc.Canada 16 (1994) 253 - 257. This work has spawned several other projects. http://www.cecm.sfu.ca/~jalester/WebCV/publications.html

June Lester - Mathematical publications Matric vector spaces Geometric characterization problems Spacetime geometry Complex triangle and polygon geometry ... Misscellaneous topics (Note: some of the papers listed below appear in more than one section. There are 39 distinct papers.) Metric vector spaces A metric vector space is a vector space which has a (usually indefinite) scalar product. I first became fascinated with these spaces as a beginning master's student. Geometrically interesting in their own right (as Euclidean n-space or Minkowski spacetime, for example), they are also invaluable as coordinate spaces: it's quite extraordinary just how many classical geometries can be coordinatized by n-tuples subject to some indefinite scalar product. And looking at these geometries through their coordinate spaces often makes obvious the isomorphisms between different models of the same geometry, or even between different geometries: the same coordinate space implies the same or related geometries. On Null-Cone Preserving Mappings.

48. Volume 5 Abstracts P. Pech The Harmonic Analysis of Polygons and napoleon's theorem, 5 (2001) 013022Plane closed polygons are harmonically analysed, ie, they are expressed in http://www.heldermann.de/JGG/jggabs05.htm

Journal for Geometry and Graphics Volume 5 (2001) Abstracts A. G. Horvath, I. Prok: Packing Congruent Bricks into a Cube, 5 (2001) 001012 Hence, fundamentally, this is a special packing problem: some bricks having fixed volume must be put into a container of given volume. From the combinatorial point of view, similar container problems were investigated by D. Jennings. The first author has found a possible universal arrangement, and someone else has found an additional one which has proved to be different under the symmetries of the cube. In the paper we introduce an algorithm for finding all the different universal arrangements. As a result we obtain 21 possibilities (listed in Section 4) by the corresponding computer program. Our method seems to be suitable for solving the analogous problem in higher dimensions. P. Pech: The Harmonic Analysis of Polygons and Napoleon's Theorem, 5 (2001) 013022 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. N. Ando, N. Yamahata, S. Masumi, M. Chatani: Shape Grammar and Form Properties of Architectural Figures, 5 (2001) 023034

49. CRC Concise Encyclopedia Of Mathematics On CD-ROM: N Inequality; Napierian Logarithm; Napkin Ring; Napoleon Points; Napoleon'sProblem; napoleon's theorem; Napoleon Triangles; Nappe; Narcissistic http://mathworld.pdox.net/math/n/n.htm

N N-Cluster n -Cube ... Nyquist Sampling Eric W. Weisstein

50. Alvy - Infinite Hexagon Theorem 2/17/03 See paper for full details, such as how this theorem is a generalizationof napoleon's theorem. An even prettier theorem. Sorry, this http://alvyray.com/Geometry/HexagonTheorm.htm

Every triangle has an infinite sequence of regular hexagons. Move any of the three red dots to change the gray triangle to any arbitrary triangle . This first theorem says there is an infinite sequence of regular hexagons intimately associated with each triangle, and centered on it (its centroid). Some of the hexagons you might think would be in the sequence aren't. Only those that are 2 n m times as large as the two smallest hexagons are in the sequence, for nonnegative integers n m . You can also move the green point along one edge of the triangle. This changes the parameterization of the hexagons. See paper for full details, such as how this theorem is a generalization of Napoleon's Theorem. An even prettier theorem. Sorry, this page requires a Java-compatible web browser. This page uses JavaSketchpad , a World-Wide-Web component of The Geometer's Sketchpad

51. Mathematica Information Center: Napoleon-Like Properties Of Spherical Triangles In elementary Euclidean geometry this result is known as napoleon's theorem.Consider the following generalization of this construction. http://library.wolfram.com/database/Articles/1610/

All Collections Articles Books Conference Proceedings Courseware Demos MathSource: Packages and Programs Technical Notes Title Napoleon-Like Properties of Spherical Triangles Author M. Treuden Journal / Anthology Proceedings of the 8th Annual ICTCM Year: Description Subject Teaching

52. STACHEL / Institut Fuer Geometrie Rend. Circ. Mat. Palermo, II. Ser., 70, 335351 (2002); napoleon's theoremand Generalizations Through Linear Maps. Beitr. Algebra Geom. http://www.geometrie.tuwien.ac.at/stachel/

Hellmuth STACHEL Mag. rer. nat., Univ. Graz, 1965 Dr. phil. in Mathematics, Univ. Graz, 1969 Habilitation in Geometry, TU Graz, 1971 Associate Professor for Geometry, TU Graz, 1976-1978 Professor for Geometry, Mining University Leoben, 1979-1980 Professor for Geometry, TU Wien, since 10/1980 Corresponding member, Austrian Academy of Sciences, since 1991 Editor in Chief of the ' Journal for Geometry and Graphics ', since 1997 Research Interests Classical Geometry and its Applications Descriptive Geometry and Computer Aided Design Kinematics Selected Recent Publications: Remarks on A. Hirsch's Paper concerning Villarceau Sections. J. Geometry Graphics Configuration Theorems on Bipartite Frameworks. Rend. Circ. Mat. Palermo, II. Ser., Napoleon's Theorem and Generalizations Through Linear Maps. Beitr. Algebra Geom. Preprint Remarks on Bricard's Flexible Octahedra of Type 3. Proc. 10th ICGG, Kiev (Ukraine), July 28 - Aug. 3, 2002: Vol. 1, 8-12 Ivory's Theorem in the Minkowski Plane. Math. Pannonica , 11-22 (2002) [Preprint Technical Report No. 85, Oct. 2001]

53. Geometria Translate this page Home. First Examples. Resp. Analysis. Exercises. JavaScript.napoleon's theorem. GeoScript-File GeoStyle-File. http://www.joensuu.fi/mathematics/DidMat/Ehmke/seminar-joensuu/napoleons_theorem

Home First Examples Resp. Analysis Exercises ... JavaScript Napoleon's Theorem GeoScript -File GeoStyle -File

54. SOME SELECTED PUBLICATIONS The Mathematical Gazette, 79(485), 374378, July 1995. 14. A generalized dualof napoleon's theorem and some further extensions. Int. J. Math. Ed. Sci. http://mzone.mweb.co.za/residents/profmd/publications.htm

SOME SELECTED PUBLICATIONS by Michael de Villiers Mathematical Articles International Journal for Mathematical Education in Science and Technology , 20(4), 585-603, August 1989. Imstusnews , 19, 15-16, November 1989. Spectrum , 28(2), 18-21, May 1990. Physics Teacher , 286-289, May 1991. Spectrum . International Journal for Mathematical Education in Science and Technology Mathematical Digest Imstusnews Spectrum International Journal for Mathematical Education in Science and Technology Australian Senior Mathematics Journal Pythagoras The Mathematical Gazette , 79(485), 374-378, July 1995. . Int. J. Math. Ed. Sci. Technol ., 26(2), 233-241, 1995. (Co-author: J. Meyer, UOFS). , 6(3), 169-171, Sept 1996. ). KZN AMESA Math Journal , Vol 3, No 1, 11-18. Mathematical Gazette , Nov. Mathematical Gazette , March 1999. Mathematics in School , March 1999, 18-21. Mathematics in College Mathematics Education Articles Mathematics Teacher , Vol.80, No.7, pp.528-532, October 1987. Pythagoras . 19, pp.27-30, April 1989. S.A. Tydskrif vir Opvoedkunde , 10(1), Feb 1990, 68-74 (co-author: E.C. Smith).

55. The Educational Encyclopedia, Mathematics Fermat point, cycloids, Collage Theorem, Carnot's theorem, bounded distance, barycentriccoordinates, Pythagorean theorem, napoleon's theorem, Ford's touching http://users.pandora.be/educypedia/education/mathematics.htm

Science Animals Biology Botany Bouw ... Resources Mathematics Algebra Arithmetric Complex numbers Formulas ... Fractals General overview Geometry Integrals and differentials Miscellaneous Statistics ... 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

56. CMB - Vol. 44, N3 Min Ho Lee and Hyo Chul Myung Hecke Operators on Jacobilike Forms, 282. AngelaMcKay An Analogue of napoleon's theorem in the Hyperbolic Plane, 292. http://journals.cms.math.ca/CMB/v44n3/index.en.html

CMB (2001) Vol 44 No 3 Algebraic Homology For Real Hyperelliptic and Real Projective Ruled Surfaces M. Cencelj and A. N. Dranishnikov Extension of Maps to Nilpotent Spaces Wai-Shun Cheung and Chi-Kwong Li Linear Operators Preserving Generalized Numerical Ranges and Radii on Certain Triangular Algebras of Matrices Min Ho Lee and Hyo Chul Myung Hecke Operators on Jacobi-like Forms Angela McKay An Analogue of Napoleon's Theorem in the Hyperbolic Plane A Proof of Casselman-Shahidi's Conjecture for Quasi-split Classical Groups Images of mod p ... Galois Representations Associated to Elliptic Curves Bertrand Schuman Une classe d'hamiltoniens polynomiaux isochrones P. J. Stacey Inductive Limit Toral Automorphisms of Irrational Rotation Algebras Luc Vinet and Alexei Zhedanov Spectral Transformations of the Laurent Biorthogonal Polynomials, II. Pastro Polynomials Wei Wang Positive Solution of a Subelliptic Nonlinear Equation on the Heisenberg Group Nik Weaver Hilbert Bimodules with Involution Anthony Weston On Locating Isometric l (n) Xi Zhang A Note on p -Harmonic 1-Forms on Complete Manifolds Canadian Mathematical Society

57. Der Satz Des Napoleon Translate this page Lester, JA, A generalization of napoleon's theorem to n-gons, CR Math. Rep. Acad. 8(1981), 458459 Wetzel, JE, Converses of napoleon's theorem, Amer. Math. http://www.wv.inf.tu-dresden.de/~pascal/verein/ikm97/napoleon.html

Gastvortrag: Der Satz des Napoleon F , der als Fermat-Torricelli-Punkt bekannt ist. Besitzt das Ausgangsdreieck ABC F derjenige Punkt P AP BP CP Lester, J. A., A generalization of Napoleon's theorem to n -gons, C. R. Math. Rep. Acad. Sci. Canada Martini, H., On the theorem of Napoleon and related topics, Math. Semesterber. Nelson, R.D., Napoleon revisited, Math. Gaz. Pickert, G., Bemerkungen zum Satz von Napoleon, Math. Semesterberichte Rigby, J.F., Napoleon revisited, J. Geom. Rigby, J. F., Napoleon, Escher, and tessellations, Math. Mag Scriba, Christoph J., Wie kommt "Napoleons Satz" zu seinem Namen? Hist. Math. Wetzel, J.E., Converses of Napoleon's theorem, Amer. Math. Monthly Back to my home page

58. ENC: Curriculum Resources: The Geometer's Sketchpad (ENC-017728, Full Record) Trigonometric ratios Reflections in the coordinate plane Reflections across intersectinglines Modeling a ladder problem napoleon's theorem Morley's Theorem A http://www.enc.org/resources/records/full/0,1240,017728,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Advanced Search ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. ENC#: ENC-017728 Edition: Windows version 3.0 (release 3.10). Publisher: Key Curriculum Press, Inc Date: Ordering Information Grades: 7 8 9 10 11 12 Post-secondary Abstract: Sample activities, which cover art, explorations, demonstrations, and constructions, are included. For example, the activity in art discusses vanishing points and gives step-by-step directions for drawing a box with two-point perspective. One investigation explores exterior angles in a polygon. The investigation starts with summing the exterior angles of a pentagon. Parts of the pentagon are moved to see if the sum changes. The students are expected to make a conjecture concerning the sum of the exterior angles of any polygon and investigate the conjecture by constructing and manipulating other polygons. Blackline masters and teaching notes are provided for these activities. (Author/JAR). Reviews and Awards: Satterfield, Melanie. (2001). Review of

59. Publications 1986) 636639. On napoleon's theorem, Ellipse, 1 (Summer 1993) 8. “AlgebraicDiet Plan,” Centroid, 22 (Spring 1995) 30. Gaskets http://www.apsu.edu/HOEHNl/publications.htm

Publications: Mathematics Magazine "Solution to Problem #648," 40 (Sept. 1967) 228. "Averages on the Move," 58 (May 1985) 151-156. Co-authored with Ivan Niven. "Summations Involving Computer-Related Functions,"62 (June 1989) 191-196. Co-authored with Jim Ridenhour. "Solutions of x^n + y^n = z^(n+1) ," 62 (Dec. 1989) 342. "A New Proof of the Double Butterfly Theorem," 63 (Oct. 1990) 256-257. "A Menelaus-Type Theorem for the Pentagram," 66 (Apr. 1993) 121-123. "Mathematical Quickie #866," 70 (June 1997) 224 & 229. "Mathematical Quickie #869," 70 (Oct. 1997) 299 & 307. "Problem Proposal #1574," 72 (June 1999) 236. "Problem Proposal #1635," 74 (Dec. 2001) 403. "Extriangles and Excevians," 74 (Dec. 2001) 384 - 388. "Problem Proposal #," (to appear). College Mathematics Journal "Problem Proposal #114," 9 (Mar. 1978) 95. "A Geometrical Interpretation of the Weighted Mean," 15 (Mar. 1984) 135-139. "Solution to Problem #227," 15 (Mar. 1984) 165-166.

60. Glossary Music (and transformations). N. Click on the letter to obtain informationon napoleon's theorem; Network; Why there is no Nobel Prize in Mathematics; http://westview.tdsb.on.ca/Mathematics/glossary.html

This page will be under constant revision so please use the reload button on your browser to refresh the page. Last revised October 23, 2002 Glossary of Mathematics Student Questions - Possible Answers A Source of Ideas for Mathematics Teachers Click on the appropriate letter A B C D ... Z Good Reference Sites http://www.mathacademy.com/platonic_realms/encyclop/encymain.html Interesting Math Words Illustrated Math Dictionary (Harcourt) Math Glossary (Harcourt) ... A Click on the letter to obtain information on: Absolute Value Acre Common Acronyms Acute Triangle What is Algebra? Algorithm Altitude Analytic Geometry Area of an Ellipse Area of a Triangle ASCII B Click on the letter to obtain information on: Numbers in Other (than 10) Bases Binomial Bourbaki Box-and-Whiskers Plot Brackets Buckyballs C Click on the letter to obtain information on: Calculus Cardinal Numbers Catalan's conjecture Catenary Centroid Chord Circumcentre Complex Numbers Conjecture vs Proof Conics - terminology Important Constants Law of Cosines Game of Craps Visual Dictionary of Special Plane Curves D Decimals Deductive Reasoning Degree Persi Diaconis Division Symbol Discrete Mathematics Divisibility Rules Dot Product E Click on the letter to obtain information on: e Famous Equations and Inequalities M.C. Escher

Page 3     41-60 of 90    Back | 1  | 2  | 3  | 4  | 5  | Next 20