61. Math Resources From Grau-Hall Scientific Napier Bones, Napoleon s theorem, Napoleon s theorem, a generalization,Napoleon s theorem by Plane Tesselation, Napoleon s theorem, complex variables, http://www.grauhall.com/math.htm

grauhall@grauhall.com 8524 Erinbrook Way Sacramento, CA 95826 Search this site! Type in one or more words in the white rectangle above, and then click on "Search." Powered by Atomz.com Teacher's Resources: Math - last updated on 06/20/03. To visit our new Shopping Cart area, click here e p i Click once on any underlined text to go to that site. (Last updated 05/25/03): The Abel Prise Arapahulian Rope Computer ... The Chinese Remainder Theorem - from Alexander Bogomolny at Cut-the-Knot Complexity Zoo Cornell Theory Center - Math Gateway ... Cryptography - downloadable copy Fields Medal Winners Combinational GameTheory - from David Eppstein Geometry - the online learning center Geometry Formulas and Facts Geometry Center Graphics Archives GeometryJunkyard - from David Eppstein Gliders in Life-Like Cellular Automata HAKMEM - a variety of results developed by the Artificial Intelligence Laboratory at M.I.T.under the aegis of A. R. P. A. Hilbert Functions and the Chinese Remainder Theorem Integer Sequences - an on-line encyclopedia KdV Institute - math links Lawrence Hall of Science - math and science education links Los Alamos National Laboratory - math e-print archive Loy: Jim Loy's Math Page MacTutor History of Math Virtual Math Lab - from KCOS TV Math Spans All Dimensions , from the Joint Policy Board for Mathematics MathJournals - from Math on the Web Mathematical Associationof America The Mathematical Atlas - a gateway to modern mathematics The Math Forum American Mathematical Society math pre-print server Elsevier math pre-print server

62. Mathematics Archives - Topics In Mathematics - Geometry KEYWORDS Napoleon theorem, Ceva s theorem, cevians, cevian triangle, Clawsonpoint, Euler line, Feuerbach theorem, Gergonne point, Kiepert hyperbola, http://archives.math.utk.edu/topics/geometry.html

Topics in Mathematics Geometry Alice Meets the 4th Dimension ADD. KEYWORDS: Four Dimensional Cube AMS's Materials Organized by Mathematical Subject Classification ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases AskERIC Lesson Plans - Geometry Border Pattern Gallery ADD. KEYWORDS: Symmetry Cabri Java Project ADD. KEYWORDS: Examples, Animations, 3D geometry, Loci, Conics, Hyperbolic Geometry SOURCE: TECHNOLOGY: Java applets ADD. KEYWORDS: Cabri Geometry resources Cercle d'Euler ADD. KEYWORDS: Euler Circles, Malfatti Circles, Poncelet Triangles, Morley Triangles, Podaires Triangles, Fermat Points, Feuerbach Points, Nagel Points, Gergonne Points Combinatorial Tiling Theory: Theorems - Algorithms - Visualization ADD. KEYWORDS: Two Dimensional Tilings, Three Dimensional Tilings, Face-Transitive Tilings, Periodic Delone Tilings, Orbifold Graphs, Classification of 3-Dimensional Tilings, Tiling Space by Platonic Solids, Enumeration of Polyhedral Crystal Structures The Computation of Certain Numbers Using a Ruler and Compass ADD. KEYWORDS:

63. Napoleon Napoleon s theorem Enlarge. Napoleon s theorem. In Britain he is remembered asa despot. During his lifetime, he was often caricatured as a tyrannical http://www.algebra.com/algebra/about/history/Napoleon.wikipedia

Napoleon Regular View Dictionary View (all words explained) Algebra Help my dictionary with pronunciation , wikipedia etc Napoleon I of France (Redirected from Napoleon "Napoleon" redirects here. For other uses, see Napoleon (disambiguation) Napoleon I of France, by Jacques-Louis David Napol©on Bonaparte 15 August 5 May ) was a general of the French Revolution , and the ruler of France as First Consul Premier Consul ) of the French Republic from 11 November to 18 May , then as Emperor of the French ( Empereur des Fran§ais ) and King of Italy under the name Napoleon I from 18 May to 6 April , and again briefly from 20 March to 22 June Napoleon is considered to have been a military genius, and is known for commanding many successful campaigns, together with some spectacular failures. Over the course of little more than a decade, he acquired control of most or all of the western and central mainland of Europe by conquest or alliance until his defeat at the Battle of the Nations near Leipzig in October , which led to his abdication several months later. He staged a comeback known as the Hundred Days les Cent Jours ), but was defeated decisively at the

64. Triangle Napoleon s theorem A triangle with three equilateral triangles. A purely geometricproof. It uses the Fermat point to prove Napoleon s theorem without http://www.algebra.com/algebra/homework/formulas/Triangle.wikipedia

Triangle Algebra Help Algebra Formulas -> Triangle ( Log On Ad: : algebra software that solves YOUR algebra homework problems with step-by-step help! Geometric and Other Formulas Problems, free tutors In Depth Triangle For alternative meanings, such as the musical instrument , see triangle (disambiguation) A triangle is one of the basic shapes of geometry : a two-dimensional figure with three vertices and three sides which are straight line segments Contents Types of triangles Basic facts Points, lines and circles associated with a triangle Computing the area of a triangle ... External links Types of triangles Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular , i.e. all its internal angles are equal—namely, 60°; it is a regular polygon In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles. In a scalene triangle all sides have different lengths. The internal angles in a scalene triangle are all different. Equilateral Isosceles Scalene Triangles can also be classified according to the size of their largest internal angle, described below using

65. Volume 5 Abstracts P. Pech The Harmonic Analysis of Polygons and Napoleon s theorem, 5 (2001) 013022 From this point of view Napoleon s theorem and its generalization, 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

66. Vol 43 Napoleon s theorem and Generalizations Through Linear Maps 433444 Abstract FullText PRJ Östergard, WD Weakley Classifying Optimal Ternary Codes of http://www.heldermann.de/BAG/bag43.htm

Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Volume 43 (2002) Number 1 Number 2 Number 1 forward to Number 2 B. Haas A Simple Counterexample to Kouchnirenko's Conjecture Abstract Full Text S. H. Hansen Picard Groups of Deligne-Lusztig Varieties with a View toward Higher Codimensions Abstract Full Text O. Mermoud, M. Steiner Configuration Spaces of Weighted Graphs in High Dimensional Euclidean Spaces Abstract Full Text T. Richter Lech Inequalities for Deformations of Singularities Defined by Power Products of Degree 2 Abstract Abstract-pdf Full Text J. Toelke To the Isotropic Generalization of Wallace Lines Abstract Full Text M. Bokler, K. Metsch On the Smallest Minimal Blocking Sets in Projective Space Generating the Whole Space Abstract Full Text C. Coleman, D. Easdown Decomposition of Rings under the Circle Operation Abstract Full Text E. Govaert, H. Van Maldeghem Distance-preserving Maps in Generalized Polygons. Part I: Maps on Flags Abstract Full Text R. Wisbauer, M. F. Yousif, Y. Zhou Ikeda-Nakayama Modules Abstract Full Text B. Weissbach, H. Martini

67. Triangle@Everything2.com Hero s formula for the area of a triangle Napoleon s theorem World s mostflexible programming language Pythagorean theorem http://www.everything2.com/index.pl?node=triangle

68. Center For Technology And Teacher Education: Content Areas: Mathematics Napoleon s theorem Explorations Draw a triangle. On the edges of the triangle,construct equilateral triangles. Find the centroids of the equilateral http://teacherlink.org/content/math/relatedlinks/sketchpad.html

English Mathematics Science Social Studies ... Related Links Geometry and the Geometer's Sketchpad Links 101 Project Ideas for The Geometer's Sketchpad This booklet from Key Curriculum Press is full of exciting project ideas for use in the classroom or at home. The projects are designed for users with varying degrees of Sketchpad experience and cover a wide range of subject areas (Art/Animation, Triangles, Real World Modeling, Calculus, Transformations and Tessellations, Trigonometry, Fractals, and many more). http://www.keypress.com/sketchpad/projideas/projideas.html Algebra and Calculus Sketches Allows the user to explore equations for lines, parabolas, and tangents using Geometer's Sketchpad. http://mathforum.org/sum95/ruth/sketches/algcalc.sketches.html Betweenness Theorem If point B lies between points A and C, the sum of the distances from A to B and from B to C will equal the distance from A to C. This site explores a geometric representation of this theorem. http://www.wpunj.edu/icip/itm/Lessonpl/sketch/coutts/coutts.html

69. SOME SELECTED PUBLICATIONS A generalized dual of Napoleon s theorem and some further extensions. Int. J.Math. Ed. Sci. Technol., 26(2), 233241, 1995. (Co-author J. Meyer, UOFS). 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).

70. Sketchpad Sketches 1. Napoleon s theorem (named after the famous French Emperor) and severalgeneralizations. http//mzone.mweb.co.za/residents/profmd/napole.zip. http://mzone.mweb.co.za/residents/profmd/spzips.htm

Sketchpad 3 Sketches Michael de Villiers profmd@mweb.co.za http://mzone.mweb.co.za/residents/profmd/homepage.html IMPORTANT view and dynamically manipulate these Sketchpad 3 sketches, requires a copy of Sketchpad 3 or the demonstration copy of Sketchpad 3 , which can be downloaded for free from: http://mzone.mweb.co.za/residents/profmd/gsketchd.zip www.aladdinsys.com/expander or use WinZip from http://www.winzip.com/ - also available for free at many other sites). After unzipping, and Sketchpad or Sketchpad Demo For ordering a full version of Sketchpad in Southern Africa, consult: http://mzone.mweb.co.za/residents/profmd/homepage3.html Some of the sketches below can be used as investigations while others are intended as mere demonstrations. Note that the sketches have been prepared on a Macintosh Powerbook, hence the screen-size and outlay may differ a little for IBM compatibles and other Macintoshes. If you experience any downloading problems, please let me know. A. SOME SAMPLE SKETCHES FROM MY BOOK " Rethinking Proof with Sketchpad 3 ", Key Curriculum Press, USA.

71. Triangle - Enpsychlopedia A central theorem is the Pythagorean theorem stating that in any right triangle, Napoleon s theorem (http//agutie.homestead.com/files/Napoleon0.htm) A http://psychcentral.com/psypsych/Triangle

home resource directory disorders quizzes ... support forums Advertisement ( Triangle For alternate meanings, such as the musical instrument , see triangle (disambiguation) A triangle is one of the basic shapes of geometry : a two-dimensional figure with three vertices and three sides which are straight line segments Contents showTocToggle("show","hide") 1 Types of triangles 2 Basic facts 3 Points, lines and circles associated with a triangle 4 Computing the area of a triangle ... edit Types of triangles Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular , i.e. all its internal angles In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles. In a scalene triangle all sides have different lengths. The internal angles in a scalene triangle are all different. Equilateral Isosceles Scalene Triangles can also be classified according to the size of their largest internal angle, described below using degrees of arc.

72. Triangle -- Facts, Info, And Encyclopedia Article It uses the Fermat point to prove Napoleon s theorem without transformations byAntonio Gutierrez from Geometry Step by Step from the Land of the Incas http://www.absoluteastronomy.com/encyclopedia/t/tr/triangle.htm

Triangle [Categories: Polygons] For alternate meanings, such as (Click link for more info and facts about the musical instrument) the musical instrument , see (Click link for more info and facts about triangle (disambiguation)) triangle (disambiguation) A triangle is one of the basic shapes of (The pure mathematics of points and lines and curves and surfaces) geometry : a two-dimensional figure with three (Click link for more info and facts about vertices) vertices and three sides which are straight line segments. Types of triangles Triangles can be classified according to the relative lengths of their sides: In an equilateral triangle all sides are of equal length. An equilateral triangle is also equiangular , i.e. all its internal (The space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians) angle In an isosceles triangle two sides are of equal length. An isosceles triangle also has two equal internal angles. In a scalene triangle all sides have different lengths. The internal angles in a scalene triangle are all different. Equilateral Isosceles Scalene Triangles can also be classified according to the size of their largest internal angle, described below using

73. Andrew Glassner's Notebook Mirror reflections and billiard balls give way to mathematical constructs suchas Ptolemy s theorem, Napoleon s theorem and Fourier transformations. http://www.glassner.com/andrew/writing/books/notebook.htm

Andrew Glassner's Notebook In 1996 I started writing a regular column for the magazine IEEE Computer Graphics and Applications . I'm happy with my columns, but there are often things that need to get cut out for space reasons. Sometimes I realize some things could have been done better. And errors do make it into print. I've collected the first three years of columns, restored them to their original full-length form, expanded and revised each one, and fixed the errors, resulting in this book. The book now has a sequel, Andrew Glassner's Other Notebook The idea that graphics is fun is reflected in the book's subtitle, Recreational Computer Graphics . The cover is a notebook-style collage of some illustrations from different chapters, evoking the idea of a notebook. You can read notes on the original columns, plus the ones that haven't yet been collected

74. Professur Martini - Publikationen H. Martini, B. Weissbach Napoleon s theorem with weights in nspace. Martini,H. The theorem of Napoleon and related topics. http://www.mathematik.tu-chemnitz.de/prof/mart_pap.html

Professur Geometrie Publikationen Navigator Math-Net Seite TUC Forschung Professuren ... Geometrie Publikationen Fak.f.Math. TUC Professur Geometrie : Prof. Dr. Horst Martini - Publikationen Boltyanski, V. / Martini, H.: Kupitz, Y. / Martini, H.: From intersectors to successors, Graphs and Combinatorics 17 (2001), 99-111, ISSN 0911-0911 Martini, H. / Swanepoel, K. / Weiss, G.: The geometry of Minkowski spaces - a survey, Part I, Expositiones Mathematicae 19 (2001), 97-142, ISSN 0723-0869 Makai, E. / Martini, H. / Odor, T.: On an integro-differential transform on the sphere, Studia Sci. Math. Hungar. 38 (2001), 299-312, ISSN 0081-6906 Boltyanski, V. / Martini, H.: Median and center hyperplanes in Minkowski spaces - a unified approach, Discrete Mathematics 241 (2001), 407-426, ISSN 0012- 365X Kupitz, Y. / Martini, H.: Geometric graphs and curves of constant width, Congressus Numerantium 152 (2001), 149-158, ISSN 0384-9864 Martini, H.:

75. Jahresbericht 1999 - Publikationen Martini, H./ Weissbach, B. Napoleon s theorem with weights in nspace.Geometriae Dedicata 74 (1999), 213-223. Martini, H./ Wenzel, W. On lattices, http://www.mathematik.tu-chemnitz.de/report/99_papr.html

F M ATHEMATIK T ECHNISCHE U C HEMNITZ Homepage Math-Net Guide Forschung Jahresberichte Jahresbericht Forschung 1999 - Publikationen Professuren a Campo, F. W.: 2-best solutions under distance constraints the model and exemplary results for matroids. Advances in Applied Mathematics 22 (1999), 155-185. k-best solutions under distance constraints in valuated r-matroids. Advances in Applied Mathematics 22 (1999), 381-412. Apel, T.: Anisotropic finite elements: Local estimates and applications. Erschienen in der Reihe "Advances in Numerical Mathematics", Teubner, Stuttgart, 1999. Apel, T.: Interpolation of non-smooth functions on anisotropic finite element meshes. Math. Modeling Numer. Anal. 33(1999), 11491185 Basor, E. L./ Ehrhardt, T.: On a class of Toeplitz + Hankel operators. New York J. Math. 5 (1999), 1-16. Benner, P. / Byers, R. / Mehrmann, V. / Xu, H.: Numerical Solution of Linear-Quadratic Control Problems for Descriptor Systems, Proceedings of the IEEE conference on Computer Aided Control Systems Design, Hawaii, August 1999, (CD Rom). Benner, P. / Byers, R. / Mehrmann, V. / Xu, H.:

76. MTE 410 - Winter 2005 Napoleon s theorem with a proof indicated, form a circle, Eyeball theorem, threecircles whose tangents intersect in three point that lie on a straight line http://personalwebs.oakland.edu/~liptak/mte410.html

MTE 410, Elementary School Mathematics and the Computer , 4 credits - Winter 2005 Syllabus Projects Final exam Homework assignments ... Detailed syllabus. Place and Time : Mon, Wed at 3:30-5:17 pm in SEB 384. Office hours : Mon, Wed 1:00-2:00 pm, or by appointment (SEB 347). During office hours I let everyone who showed up into my office and discuss questions in a round-robin manner. If you would like a one-to-one meeting, e-mail me to set up an appointment. Textbook : There will be two books required for this course: Punished By Rewards: The Trouble with Gold Stars, Incentive Plans, A's, Praise, and Other Bribes , by Alfie Kohn, ISBN: 0618001816. The Schools Our Children Deserve: Moving Beyond Traditional Classrooms and "Tougher Standards" , by Alfie Kohn, ISBN: 0618083456. Software Terrapin LOGO . This software is on all computers in the Kresge library computer labs (rooms 129A and 129B). However, I recommend that you purchase a copy for your own computer. If you wish to do so, Terrapin LOGO may be purchased at http://www.terrapinlogo.com/

77. Gov's Web Napoleon s theorem 6. Properties of Parallelograms 7. Exterior Angles in a Polygon8. Star Polygons 9. Chords in a Circle 10. Triangle Area Problem http://www.northern.edu/haighw/gov.html

Governor Janklow's Faculty Awards for Teaching with Technology Report on Activities and Accomplishments William Haigh Professor of Mathematics Northern State University Major Activities Visitation of Aberdeen Area Workplaces Workshops Attended Selection of Software Development of Class Activities ... Course Changes Aberdeen Area Workplaces Visited A total of eight Aberdeen area workplaces (Table 1) were visited to observe the computer technology used and, where appropriate, incorporated into university mathematics classes (Table 2) . The computer technology used at these worksites included: (1) spreadsheets; (2) programming in various languages; (3) statistical analysis packages; (4) Internet; (5) software to solve systems of differential equations; (6) topographic map packages; and (7) graphing packages. Table 1. Aberdeen Area Workplaces Visited Horton Vehicle Components Inc. Northwestern Public Service Student Loan Finance Corporation Dalager Engineering K.O. Lee Company Hub City Inc. National Weather Service Table 2. Classroom Activities Developed

78. SHOTO SUGAKU A proof of Napoleon s theorem by complex numbers, Kiichiro Tanaka. On a solutionand generalization of Shigeki s question, Kiichiro Tanaka http://www.asahi-net.or.jp/~nj7h-ktr/e_mokuji02-03.html

Journal of elementary mathematics„ŸSHOTOH SUGAKU„Ÿ VOL.43@January 2002 Preface @How we can make our students not to lose interest in Arithmetic and Mathematics Saburo Tamura Articles in memory of Prof. Sadaharu Nakazawa @Memories of Prof Sadaharu Nakazawa Yoshiharu Yasuda Articles @On subgroups of the additive relation with or without infinity Kentaro Murata Lectures @Traditional Japanese Mathematics (Wasan) Part VI HinotoYonemitsu @A study of a group(5) @The dodecahedral group Yasuo Matsuda Research @Squares of the directed polygon Hiroshi Asami @On a novel way to factor quadratic polynomials Masataka Kaname @From finity to infinity (6) Mitsuhiro Kotani @On the Tarner lines and Seimiya lines(13) Toshiyuki Kinoshita @On some generalizations of a limit of a sequence Mitsuru Kumano @Basic problems on the combination Akira Sawanobori @On the repeatin decimal and Artin's primitive root conjecture Minoru Shimobayashiyama @On some generalizations of Lerch's theorem Mitsuaki Takabayashi @On the equation 5 y Mitsuaki Takabayashi On the calculation of the length of the bisection of the angle by the bounded method Toshitaka Toyonari @On some limit values of some simple sequences Masakazu Nihei @An introduction of some classical entrance examination formathematics Juichi Harada @Li Shanlan's Summation Formula Yasuo Fujii @Binary expansions of and „ŸA simple@method@by@paperfolding Hiromi Honda @Proofs Without Words Taichi Maekawa @Calculation of The volume of some solids Yasuo Matsuda @Problems From Prof. Willie Yong(Singapore) part1

79. Australian Mathematics Trust One notable example of the latter is the DouglasNeumann theorem, an extensionof Napoleon s theorem discovered independently by Bernhard and the Fields http://www.amt.canberra.edu.au/bhnobit.html

VALE BERNHARD NEUMANN 1909-2002 Emeritus Professor Bernhard Hermann Neumann, who provided the greatest inspirational influence in mathematics in Australia over a 40-year period, died in Canberra on 21 October 2002 not long after happily celebrating his 93rd birthday. He first visited Australia for three months in 1959, during sabbatical leave, and fell in love with the country. So when, late in 1960, he was invited to found a Department of Mathematics in the research-focussed Australian National University, he was receptive to the idea. Within days of his permanent arrival on 2 October 1962, he also became involved in activities supporting the teaching of mathematics in schools. Bernhard had a great influence in the founding and administration of the Australian Mathematics Trust. He became a mentor and source of inspiration to Peter O’Halloran (1931-1994) who, while on the staff of the Canberra College of Advanced Education (later the University of Canberra) during the period of the early 1970s to the early 1990s, is acknowledged as the Founder of the Trust. Peter gained great strength from Bernhard’s encouragement, not only while Bernhard held his position as head of mathematics in the Institute of Advanced Studies at the Australian National University, but also after Bernhard’s retirement. Bernhard took an active personal part in the Trust’s activities. He was the Inaugural Chairman of the Australian Mathematical Olympiad Committee, a position he held from 1980 to 1986. He was also the representative of the Canberra Mathematical Association (a sponsor of the Australian Mathematics Competition (AMC) for the Westpac Awards) on first the AMC Governing Board, and then on the Advisory Committee of the Trust. He was an active member of the Advisory Committee until his death.

80. Alvy - Infinite Hexagon Theorem See paper for full details, such as how this theorem is a generalization ofNapoleon s theorem. An even prettier theorem. 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

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