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 Constructions with ruler and compass - Zef Damen A page that answers the question, What are ruler-and-compass constructions? With links to step-by-step drawings for constructions: bisecting a given angle; constructing: a line perpendicular to a given line that divides it into two equal parts; a line perpendicular to a given line passing through a given point on the line (or not on the line); the horizontal and vertical centerlines of a given circle; an equilateral triangle, given one side; an equilateral triangle inscribed in a given circle; a pentagon inscribed in a given circle; a hexagon, given one side, or inscribed in a given circle; a heptagon. more>> Geometric Constructions - Dave Rusin; The Mathematical Atlas An introduction to geometric constructions using a ruler and compass. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; selected topics; other web sites with this focus. more>> Geometric Construction with the Compass Alone - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny Information and exercises about geometric constructions: almost everything you can do with a ruler and a compass you can do with the compass alone. more>> Geometry Construction Reference - Paul Kunkel The basics of compass and straightedge construction, with notes about The Instruments and What is a construction? Construct the perpendicular bisector or the midpoint of a line segment; given a point on a line, construct a perpendicular line through the given point; given a point not on a line, construct a perpendicular line through the given point; construct the bisector of an angle; an angle congruent to a given angle; a line through a given point, parallel to a given line; an equilateral triangle or a 60-degree angle; divide a line segment into n congruent line segments; construct a line through a given point tangent to a given circle; construct the center point of a given circle; a circle through three given points; circumscribe a circle about a given triangle; inscribe a circle in a given triangle. more>> Impossible Constructions - Math Forum, Ask Dr. Math FAQ Problems from antiquity: trisecting an angle, squaring the circle, duplicating (or doubling) the cube. more>> The Many Ways to Construct a Triangle - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny In general, a triangle is defined by its three elements. SAS, ASA, and SSS provide three well-known examples but there are many more. Bogomolny provides a table of constructions (linked to constructions) and invites reader contributions. more>>
All Sites - 68 items found, showing 1 to 50
 A+ Compass - Art Stoner, Ed.D. A compass for use on whiteboards, with radius to 14+ inches. Uses a variety of markers and is safe for all surfaces. Easy to use and accurate. ...more>> Association of Teachers of Mathematics (ATM) A U.K.-based association that aims to support the teaching and learning of mathematics by encouraging increased understanding and enjoyment of mathematics. It addresses all those concerned with mathematics education in primary schools, secondary schools, ...more>> Before Pythagoras: The Culture of Old Babylonian Mathematics - New York University Institute for the Study of the Ancient World This archaeological exhibit explored the world of Old Babylonian mathematics through cuneiform tablets, and illustrates how the ancient civilization performed arithmetic on numbers based entirely on two symbols. Online highlights include images of a multiplication ...more>> Bob's Pages - Bob Allanson A collection of geometry applets. Generate and modify polyhedra, investigate the Mandelbrot and Julia sets, or experiment with Pappus's arbelos, the porisms of Poncelet and Steiner, and a logarithmic spiral. ...more>> Cabri en Physique - Yves Cortial Cabri en Physique propose près de 140 figures créées avec le logiciel de géométrie dynamique Cabri Géomètre dont une centaine d'animations en version CabriJava: d'illustrations de phénomènes ...more>> C.a.R. Geometry Program - Rene Grothmann A dynamic geometry program that simulates constructions with a ruler and compass (Compasses and Ruler). C.a.R. runs on Java as a local application, with Java Web Start, or as an applet in browsers. The free and open source program includes documentation ...more>> Center for Technology and Teacher Education - Curry School of Education, University of Virginia An interdisciplinary group that develops materials to prepare teachers to use technology to enhance and extend students' learning of mathematics. This site offers activities using graphing calculators, The Geometer's Sketchpad, Microsoft Excel, the ExploreMath.com ...more>> Collaborative Mathematics - Jason Ermer Videos for connecting "a worldwide community of mathematical problem solvers" and "cultivating a productive attitude toward challenging problems: one of creativity, resourcefulness, self-confidence, and perseverance." Two- and three-minute-long challenges ...more>> The Collapsing Compass - Godfried Toussaint There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most well-known results is the proof in 1672 due to Mohr that all constructions that can ...more>> College Math Prep for High School Students - C. J. Kentler and V. S. Manoranjan, Washington State University Self-scoring problems, new with every click, to gauge a student's preparedness for college level math: operations, solving for a variable, solving linear equations, word problems, solving absolute value equations, solving inequalities, distance between ...more>> The Complexity of Geometric Constructions - François Labelle Efficient constructions with straight-edge and collapsing compass (the geometric tools of Euclid). The question of what can and cannot be constructed with this model of computation is basically answered by Galois Theory. This document deals with the minimum ...more>> The computation of certain numbers using the ruler and compass - Simon Plouffe, Journal of Integer Sequences A method for computing some numbers bit by bit using only the ruler and compass, in particular the construction for arctan(X)/Pi. This method is a spigot algorithm and can be applied to numbers that are constructible over the unit circle and the ellipse. ...more>> Curves - Igor Gerasimov This scientific animated screensaver draws the Archimedean spiral, cardioid, cycloid, cissoid of Diocles, folium of Descartes, deltoid, lituus, logarithmic spiral, nephroid, limacon of Pascal, semicubic parabola, strophoid, sinusoid, epicycloid, hypocycloid, ...more>> Dekov Software Educational software, a journal of computer-generated Euclidean geometry, and a computer-generated encyclopedia of Euclidean geometry. Current software titles include: Solving Triangles (step-by-step solutions to triangle problems in elementary geometry); ...more>> Designing Geometric Figures - Tim Fahey Geometric constructions: instructions for constructing a variety of geometric shapes and patterns. Symbols, basic constructions, basic shapes, and how to design patterns. ...more>> Doubling the Cube - MacTutor Math History Archives Linked essay covering the history of and some solutions to the classical problem in Greek mathematics of doubling or duplicating the cube, also called the Delian problem; and on proving the impossibility of constructing a solution using only ruler ...more>> Eskimo Pi - Keith Devlin (Devlin's Angle) "As everyone knows, in the last century, the State of Indiana passed a law legislating the value of pi to be 3. Well, perhaps it's a bit of an exaggeration to say that everyone knows it, but most people do. But that alone is very odd, since it is not ...more>> Euclid: The Game - Kasper Peulen Classic Euclidean constructions using GeoGebra JavaScript. ...more>> Explorations of a Problem with Two Squares - Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia Given a square of side s and segments drawn from each vertex to the midpoint of the second side, counting counter-clockwise, the segments intersect to form a new square. What is the ratio of the area of the shaded square to the area of the original square? ...more>> Fascinating Flat Facts about Phi - Ron Knott Phi and two-dimensional geometry - constructing the golden section: phi, Phi; Phi and the root-5 rectangle; the shape of a piece of paper; Phi and the pentagon triangles; Penrose tilings; a rectangle/triangle dissection problem; the Golden Spiral; trigonometry ...more>> Four Construction Problems - Cut the Knot!, Alexander Bogomolny Construct a triangle, given the three points in the plane that are the outer vertices of equilateral triangles constructed outward on the sides of the desired triangle. Construct a triangle, given the three points in the plane that are the centers of ...more>> Geom-e-Tree - John Miller Explore fractals with this tree-drawing app for iPod, iPhone, and iPad. Choose the number of branches, angle between branches, and the common ratio of the levels in the tree. See, in particular, the exercises and open questions on Geom-e-Tree for the ...more>> Geometric Arts - Ghee Beom "Quincy" Kim A site dedicated to geometry and visual perception: patterns, fractals, structures, rotations, spirographs, optical arts, knots, and more. Some constructions include the artist's reflections, instructions, and links to related sites and interactive applets. ...more>> Geometric Constructions - Arlen Strader; College of Education, Texas A&M University A 1997 Java applet that simulates compass-and-ruler constructions, with a lesson in its use. ...more>> Geometric Constructions - G.E. Martin; SUNY at Albany, Albany, NY A book that offers a comprehensive introduction to geometric constructions in the classical sense, combining purely mathematical, historical, and philosophical arguments and viewpoints. Contents include: Euclidean Constructions; The Ruler and Compass; ...more>> Geometry Assistant - ThinkQuest 1998 An applet/application for drawing dynamic geometry constructions: move any movable point and Geometry Assistant will automatically recalculate and redraw the whole construction. The site includes a place to add your unsolved geometry problem, and a Library ...more>> Geometry Constructions - Barry Sanders Constructions made using the Geometer's Sketchpad: Malfatti Circles (construct 3 circles internal to any triangle, each circle being externally tangent to the other two, and each touching adjacent sides of the triangle); Hart Circle (construct the circle ...more>> Geometry in Motion - Daniel Scher Direct interaction with geometric diagrams, courtesy of JavaSketchpad. The contents include a variety of curve-drawing devices (Intersecting Circles, Falling Ladder, Van Schooten's Parabola, and more); also other activities such as Constant Perimeter ...more>> Glossary - Interactive Mathematics Miscellany and Puzzles, Alexander Bogomolny A glossary of terms that also serves as an alphabetical index to Bogomolny's site. Each term is linked to an illustrated essay. ...more>> Hamilton's Math to Build On - Johnny & Margaret Hamilton Simple, straightforward explanations, drawings, questions and answers from the book Math to Build On by Johnny & Margaret Hamilton (copyright 1993). Excerpts offer pages on: Angles, Degrees, Variables & Constants; Squaring Numbers; Square Roots; ...more>> Helena A. Verrill - Department of Mathematics, Louisiana State University Notes, links, handouts, and other materials from the courses that Verrill teaches, such as Solving Discrete Problems, Calculus, Elliptic Curves, and Modular Forms. She also provides a Java applet for a wallpaper drawing program and step-by-step illustrations ...more>> Interactive Mathematics Miscellany and Puzzles - Alexander Bogomolny "The peculiar beauty of Mathematics lies in deduction, in the dependency of one fact upon another. The less expected a dependency is, the simpler the facts on which the deduction is based - the more beautiful is the result." This award-winning site offers ...more>> Inversion Geometry - Paul Kunkel The elementary concepts are explained, with a quick reference for other lessons that employ inversion geometry. ...more>> James P. Dildine - James P. Dildine Interactive math lessons for exploring parabolas, triangle areas, Pythagorean triples, triangle angle sums (powered by a Cabri Java applet), cancer and mathematics (image analysis, and determining the area and perimeter of non-regular figures), systems ...more>> Mathematical Problems - Torsten Sillke Some in German, most in English. Topics include graph theory, number theory, combinatorics (enumerations), geometry, algorithms and complexity, recreational mathematics, tiling and packing, dissections, probability, algebra, analysis. Also links to "Math-News" ...more>> Mathematiksoftware S I und SII (vorwiegend Shareware) - Monika Schwarze Eine Zusammenstellung nützlicher Mathematikprogramme aus dem Shareware-Markt zur Aufarbeitung von Lernrückständen, Wiederholung und Stärkung der Sicherheit mathematischer Rechenroutinen. Vor allen die Programme für die SII dienen der Überprüfung gemachter ...more>> mathlab.com - Mehrdad Simkani A Java applet of unmarked straightedge and collapsible compass tools to virtually draw the lines and circles fundamental to Euclidean geometry. The help page explains how to use the Euclid applet, and contains descriptions for constructing found in propositions ...more>> MathResources247.com - Ampac Enterprises, LLC Educational math toys, games, activities, and teaching supplies such as MathSafari, Hot Dots, Math Ad Libs, overheads, geoboards, algebra tiles, balances, and play money (realistic looking coins). ...more>> Maths Outdoors - Juliet Robertson Blog posts from an education consultant "passionate about getting children outside." Posts on learning math outside with a kinesthetic emphasis, which date back to September, 2008, have included "Leaf Logic," "Investigating Right Angles with Sticks," ...more>> A Mechanism for Drawing Archimides Spiral - Liang Chen A mechanism that can be used to draw Archimides Spiral, one of a group of curves that can be used for trisecting angles. The author's paper is available for downloading in postscript format. ...more>> Mechanisms by Tchebyshev - Mathematical Etudes Foundation Archival photographs, reproductions, and computer animations of Tchebyshev's machines: plantigrade machine; mechanism for transforming rotation into translational motion; paddling mechanism; wheelchair; paradoxical mechanism; mechanism for transforming ...more>> A Nameless Number - Len Smiley Triangle-free polygon dissections are a variant of the dissection questions of Catalan, Schroeder, and others: In a convex (n+2)-gon with n+2 labeled nodes, what is a(n), the number of ways of drawing non-intersecting diagonals so that no triangles are ...more>> On the Square - Paul Kunkel Given four arbitrary, unique points, A, B, C, and D, construct one line through each point such that the four lines form a square. ...more>> Orthocenter - Paul Kunkel What is significant about the orthocenter of a triangle? Why does it even have a name? This investigation was prepared for a geometry teachers' workshop. It includes a lesson handout in Word format and was written for use in a computer lab with the Geometer's ...more>> Panagiotis Stefanides Geometry presented at national conferences in Greece. Contents include: Quantization of Circle Duality; Logos Pyr Chronos; 'Buena Fortuna' (artwork); Geometric Mean Ratio (T) by Ruler and Compass; Quadrature Master Theorem; Corollary (Circle Circumference ...more>> Peanut Software for Windows - Rick Parris Abstracts and links for downloading free mathematics software: Wingeom (high-precision geometric constructions); Winplot (general-purpose plotting utility); Winstats (scatter plots, curve fitting, histograms, statistical data, and standard theoretical ...more>> Plane Geometry Web Pages - David Jaffe Materials from a geometry course originally taught to future middle and high school teachers. Using definitions, theorems, proofs, and examples, the site introduces mappings; isometries and similarities; angles and trigonometry; congruence and similarity; ...more>> Platonic Solids - Buckley; Metropolitan School District of Pike Township, Indianapolis, IN A demonstration of the construction of the five Platonic Solids from Book 13 of Euclid's Elements. Contents include: Prop 13 - pyramid; Prop 14 - octahedron; Prop 15 - cube; Prop 16 - icosahedron; Prop 17- dodecahedron; and a Glossary Of Terms. ...more>> Polygons Made To Order (SMILE) - Loretta Malone, Washington High School A lesson designed to teach students to construct a regular polygon inscribed in a circle by using isosceles triangles with vertex angles at the center of the circle and legs as radii; determine the values of the angles; and discover that as the number ...more>> PUERTRA - Javier Sánchez González The software package PUERTRA implemented a theoretical study of formal properties of Islamic geometrical art. PUERTRA modeled the Islamic rectilinear interlaced lattices found extensively in wood work (artesonado ceilings, mosque minbars, doors and windows, ...more>>
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