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
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
Extractions: 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
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
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
Extractions: Geometric and Other Formulas Problems, free tutors In Depth 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 Triangles can be classified according to the relative lengths of their sides: Equilateral Isosceles Scalene Triangles can also be classified according to the size of their largest internal angle, described below using
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
Extractions: 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.
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
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
Extractions: 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).
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
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
Extractions: 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.
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
Extractions: home resource directory disorders quizzes ... support forums Advertisement ( 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 Triangles can be classified according to the relative lengths of their sides: Equilateral Isosceles Scalene Triangles can also be classified according to the size of their largest internal angle, described below using degrees of arc.
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
Extractions: 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. Triangles can be classified according to the relative lengths of their sides:
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
Extractions: 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
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
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
Extractions: 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.:
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
Extractions: 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: 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/
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
Extractions: 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.
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
Extractions: 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 A 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
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
Extractions: 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 OHalloran (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 Bernhards 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 Bernhards retirement. Bernhard took an active personal part in the Trusts 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.
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
Extractions: 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
