Extractions: 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
The Educational Encyclopedia, Mathematics Fermat point, cycloids, Collage theorem, Carnot s theorem, bounded distance, barycentric coordinates, Pythagorean theorem, Napoleon s theorem, Ford s touching http://users.telenet.be/educypedia/education/mathematics.htm
Extractions: Science Animals Biology Botany Bouw ... Resources Mathematics Algebra 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
Triangle Menelaus theorem, MidArc Points, Mittenpunkt, Mollweide s Formulas, Morley Centers, Morley s theorem, Nagel Point, Napoleon s theorem, Napoleon Triangles http://164.8.13.169/Enciklopedija/math/math/t/t285.htm
Extractions: A triangle is a 3-sided Polygon sometimes (but not very commonly) called the Trigon . All triangles are convex. An Acute Triangle is a triangle whose three angles are all Acute . A triangle with all sides equal is called Equilateral . A triangle with two sides equal is called Isosceles . A triangle having an Obtuse Angle is called an Obtuse Triangle . A triangle with a Right Angle is called Right . A triangle with all sides a different length is called Scalene Let stand for a triangle side and for an angle, and let a set of s and s be concatenated such that adjacent letters correspond to adjacent sides and angles in a triangle. Triangles are uniquely determined by specifying three sides ( SSS Theorem ), two angles and a side ( AAS Theorem ), or two sides with an adjacent angle ( SAS Theorem ). In each of these cases, the unknown three quantities (there are three sides and three angles total) can be uniquely determined. Other combinations of sides and angles do not uniquely determine a triangle: three angles specify a triangle only modulo a scale size ( AAA Theorem ), and one angle and two sides not containing it may specify one, two, or no triangles (
Alvy - Infinite Hexagon Theorem 5/3/03 See paper for full details, such as how this theorem is a generalization of Napoleon s theorem. An even prettier theorem. Sorry, this 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
June Lester - Mathematical Presentations University of Victoria, Canada, August 1993. A generalization of Napoleon s theorem to ngons. A generalization of Napoleon s theorem to n-gons. http://www.cecm.sfu.ca/~jalester/WebCV/presentations.html
Extractions: 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.
Aphorisms Page 1 Hence Napoleon s theorem, as manifested on the American Literary Scene; the less your stature the more ferocious you become. They http://a.robotheart.org/aphorisms_one.html
Extractions: She is like seeing les demoiselles d'avignon for the first time. It's impossible to be more strange, or more beautiful because of it. Darkness drives exploration. The explorer doesn't love what is there, but what might be. Exploration is the same as education; both are processes of defining one's ignorance. What you really learn is how little you know; the explorer is another student, who learning how big and dark that newfound country really is as he becomes more and more intimate with some small stretch of forest. Like un-carved slabs of stone, new countries, loves, and work depend on the imagination. Finished works, like settled lands and knowing love, starve the imagination, and imagination brings love with it when it goes. We love not people but possibilities, not what you are but everything you could represent Often, what you represent is everything, but what you are. The ability to dispense with reality is the imagination's greatest power; that's what allows it to accomplish what it does
SOME SELECTED PUBLICATIONS The Mathematical Gazette, 79(485), 374378, July 1995. 14. A generalized dual of Napoleon s theorem and some further extensions. Int. J. Math. Ed. Sci. http://mzone.mweb.co.za/residents/profmd/publications.htm
Sketchpad Sketches 1. Napoleon s theorem (named after the famous French Emperor) and several generalizations. 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.
NAPOLEON BONAPARTE The famous Napoleon theorem is stated by Coxeter and Greitzer as follows If equilateral triangles are erected externally on the sides of any triangle, their http://faculty.evansville.edu/ck6/bstud/napoleon.html
Extractions: Emperor of the French The famous Napoleon Theorem is stated by Coxeter and Greitzer as follows: If equilateral triangles are erected externally on the sides of any triangle, their centers form an equilateral triangle. They continue with a historical anecdote: It is known that Napoleon Bonaparte was a bit of a mathematician with a great interest in geometry. In fact, there is a story that, before he made himself ruler of the French, he engaged in a discussion with the great mathematicians Lagrange and Laplace until the latter told him, severely, "The last thing we want from you, general, is a lesson in geometry." Laplace became his chief military engineer. Coxeter and Greitzer then remark that Napoleon probably did not know enough geometry to discover Napoleon's Theorem, just as he probably did not know enough English to compose the palindrome often attributed to him: Able was I ere I saw Elba. The portrait is by Anne-Louis Girodet-Trioson (1767-1824). I thank the MAA for permission to quote from H. S. M. Coxeter and S. L. Greitzer
Extractions: Angle between two Simson lines Theorem by Antonio Gutierrez Angle Trisection by Bob Hesse Geometry Forum Articles Thomas B anchoff's Project List Build a Rainbow (Gallery of Interactive geometry) ... Cabri II Conic Macros By Jim King, U. of Washington. Cartesio 3.03e is an educational computer graphics program for advanced high school and beginning university students. Circles of Light: The Mathematics of Rainbows (Gallery of Interactive Geometry) Center for Geometry Analysis Numerics and Graphics (GANG) Computational Geometry Resources Carleton Computer Science Graduate Society Conic Sections (Visual Dictionary of Special Plane Curves) - Xah Lee Connected Geometry Education Development Center, Inc. Dave's Math Tables Deep Secrets - The Great Pyramid, The Golden Ratio and The Royal Cubit by L. Cooper Demonstration of the Archimedes' solution to the Trisection problem Dynamic Geometry Home Page Development Center, Inc. in Newton. Elliptic curves Elliptic Geometry Drawing Tools Bill Findell: Disk EMAT 4600/6600 Problem Solving in Mathematics by Jim Wilson Erich's Packing Center by Erich Friedman Euclid's Elements, Introduction
I LOVE These pages contain several examples of a quincunx, and simple explanations of these concepts. Central Limit theorem Applet R. Todd Ogden; Dept. http://www.mccallie.org/myates/5lessonplansonline.htm
Extractions: Lessons linked to specific occupations encourage students to see where applied courses can take them in the real, working world. Over a thousand years ago, artisans in the Islamic world began to develop a system for constructing intricate geometric art based on radially symmetric starlike figures. This site has an applet that lets you create your own, plus descriptions of the various patterns. Visual Geometry Pages are an online geometry book. It is a book illustrating problems from differential geometry and mathematical visualization using applets, images, animations, and Java software. For some really really terrific eye candy on the most complex shapes imaginable: i-Math Investigations are ready-to-use, online, interactive, multimedia math investigations. Complete i-Maths include student investigations, teacher notes, answers, and related professional development activities. (Not every i-Math is currently complete, but they are all ready to be used. To get an idea of what a complete i-Math looks like, see Shedding Light on the Subject: Function Models of Light Decay Interactive Tools for Mathematics Investigations
CONTRIBUTED PRESENTATIONS SCHEDULE Gary Richter, Southwestern University. SESSION II, 253 Maguire 230 245 A Square Version of Napoleon s theorem; Bo Green, Abilene Christian University; http://orgs.tamu-commerce.edu/maa/papers98.html
INVESTIGATING HISTORICAL PROBLEMS centers of the circles. Figure 5 Napoleon s theorem. Other questions or extensions of this construction could be · What happens if http://www.ma.iup.edu/MAA/proceedings/vol1/enderson/enderson.htm
Extractions: Mary C. Enderson Indiana University of Pennsylvania, Mathematics Department 233 Stright Hall, Indiana, PA 15705 Investigating Historical Problems Using Geometer's Sketchpad Mary C. Enderson Naturally, history has a place in the mathematics classroom that should not be overlooked. What many mathematicians fail to recognize is the enhancement of historical investigations by use of technology. Geometer's Sketchpad , a dynamic and interactive piece of software, provides a work environment that allows one to create, test, validate, and manipulate objects. It has the power and flexibility to allow students to examine an infinite number of situations, instead of one singular static case, which is invaluable in attempts to make mathematical conjectures and generalizations. The purpose of this paper is not to shed new light on tasks or problems related to history of math, but to share "golden" opportunities where use of Geometer's Sketchpad (GSP) enhances the investigation of many famous geometric problems. The scope of situations to investigate with this software are unlimited. Users quickly see how technology often generates many additional questions or tasks for students to explore, as well as enabling them to visualize the connections among various mathematics topics.
Untitled Document 4 David Gale, Mathematical entertainments, The Mathematical Intelligencer 18 (1996), 3134. 5 John E. Wetzel, Converses of Napoleon s theorem, Am. Math. http://matematica.uni-bocconi.it/betti/note.htm
Publications 1986) 636639. 3. On Napoleon s theorem, Ellipse, 1 (Summer 1993) 8. 4. Algebraic Diet Plan, Centroid, 22 (Spring 1995) 30. http://www.apsu.edu/HOEHNl/publications.htm
Extractions: Dalsi vzdelavani ucitelu ... doc. RNDr. Pavel Pech, CSc. Kvalifikacni prace: Integrabilita skoro tecnych struktur. Diplomova prace, MFF UK Praha, 1974, 25 stran. O nerovnostech prostorovych krivek a prostorovych n-uhelniku. Kandidatska disertacni prace, MFF UK Praha, 1991, 73 stran. Vztahy mezi nerovnostmi v n-uhelnicich. Habilitacni prace, PF JU C. Budejovice, 1994, 101 stran. Vysokoskolska skripta a ucebni texty: Priprava k prijimacim zkouskam z matematiky. Pedagogicka fakulta C. Budejovice, 1986, 33 stran. Analyticka geometrie linearnich utvaru. PF JU C. Budejovice, 1994, 158 stran, (spoluautor J. Strobl). Kuzelosecky. Ucebni text, Pedagogicka fakulta C. Budejovice, 2002, 98 stran. Puvodni vedecka sdeleni: Inequality between sides and diagonals of a space n-gon and its integral analog. Cas. pro pest. mat. 115 (1990), 343-350. Petrova veta. Sbornik 11. seminare odborne skupiny pro geometrii a pocitacovou grafiku. Bedrichov, JCMF, 1991, 6-12. A sharpening of a discrete analog of Wirtinger's and isoperimetric inequalities.
Project W derived quadrilateral; Napoleon s theorem; Circle through three points; 4 special points of a triangle; The shape of birds eggs; Triangle http://www.pasd.wednet.edu/school/hs/Teachers/Buck/Team.htm
Extractions: Number Sense, Measurement, Geometry Algebra and Probability/Statistics check out http://www.chipola.edu/instruct/math/cleveland/Calculus%20III/Classroom%20Demos.htm GIZMOS Others: Geometry: Cabri Java Applets - Jen-chung Chuan Angles on a chord Angles on a chord and center Similar triangles ... The shape of birds' eggs Triangle calculation 3 sides Triangle calculation 2 sides and the included angle Triangle calculation 2 sides and the non-included angle Triangle calculation 2 angles and the included side Similar triangles Perpendicular bisectors of a right triangle Pythagorean triples ... derived quantities calculator which gives the lengths of altitude and median along with the radii of the incircle and circumcircle icosohedron tangent circles One Circle, Two Points
Extractions: Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Classroom Calendar Digital Dozen ENC Focus ... 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. Grades:
SHOTO SUGAKU Trocoid as an object for 3dimensional graphics of a herix, Kiichiro Tanaka. A proof of Napoleon s theorem by complex numbers, 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
Der Satz Des Napoleon 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