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 Geometry of the Sphere - John C. Polking, Rice University This set of Web pages formed the text for part of the Advanced Mathematics course in the High School Teachers Program at the 1996 IAS/Park City Mathematics Institute. Material covered includes basic information about spheres, proof and consequences of Girard's Theorem, and a proof of Euler's Formula. Teachers are encouraged to submit comments and/or lesson plans. more>> Neutral and Non-Euclidean Geometries - David C. Royster; University of North Carolina at Charlotte Course notes that include: Origins of geometry; spherical geometry; logic and the axiomatic method; proof; Euclid's mathematical system; incidence geometry; betweenness axioms; congruence theorems; axioms of continuity; neutral geometry; theorems of continuity; the work of Saccheri and Gauss; hyperbolic geometry; classification of parallels; the pseudosphere; hyperbolic trigonometry and hyperbolic analytic geometry; and more. more>>
All Sites - 30 items found, showing 1 to 30
 abraCAdaBRI - Yves Martin Liens et exercises pour le logiciel Cabri Géomètre: geéométries; affine plane; vectorielle plane; affine de l'espace; non euclidennes; logique (Alice); dossier coniques; pratique de Cabri. In French. ...more>> Circles and Spheres (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine An extensive annotated list of links to material on circles and spheres. ...more>> Clocks and Curvature (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center The total curvature of any surface topologically equivalent to the sphere is 4 pi. This can be seen very simply from the definition of the curvature of a region in terms of the angle of rotation when the surface is rolled around on the plane; the only ...more>> Coniques en coordonnées barycentriques - Jean Marie Laborde, AbraCAdaBRI Exemples des ellipses de Steiner; Théorème et Applications du théorème de Pascal; Théorème de Carnot par les coordonnées barycentriques. ...more>> Course Project Suggestions (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center An list of suggestions for projects in geometry, topology, symmetry, making geometric solids, calendars, spherical and hyperbolic trigonometry, puzzles, models, etc. Projects were to be exhibited at the Geometry Fair at the end of the course. ...more>> Curving Beyond Fermat - Ivars Peterson (MathTrek) "When Andrew Wiles of Princeton University proved Fermat's last theorem several years ago, he took advantage of recently discovered links between Pierre de Fermat's centuries-old conjecture concerning whole numbers and the theory of so-called elliptic ...more>> EggMath - Bradlow, Sullivan, Levy, UIUC A collection of modules (including many interactive applets) for K12 classrooms, based on the theme of eggs. Topics include: the shape of an egg (addressing symmetry and cross-section, surfaces of revolution, pin and string construction of ellipses, Cartesian ...more>> Elliptic Curves - Stéfane Fermigier A collection of links on research articles on elliptic curves and related topics (applications, modular forms, Fermat's Last Theorem). Algorithmic applications; Modular forms aspects; L-curves; High rank curves; Heights. Bibliographies. Some papers in ...more>> Elliptic Geometry Drawing Tools - Brad Findell Elliptic geometry calculations using the disk model. Includes scripts for: Finding the point antipodal to a given point; drawing the circle with given center through a given point; measuring the elliptic angle described by three points; measuring the ...more>> Fractals as Art - Melissa Binde, Swarthmore College "...fractals are an art form. The mathematics provides the form, but it is up to the individual creator (artist) to choose the boundaries, colors, and manner of presentation of each fractal." Three categories: "standard" fractal fare, reproducible with ...more>> Gaussian Curvature (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center What is the curvature inside the region on a sphere exterior to a tiny circle? On a polyhedron, what is the curvature inside a region containing a single vertex? two vertices? all but one vertex? all the vertices? ...more>> Geometric and Solid Modeling - Computer Science Dept., Univ. of North Carolina at Chapel Hill (UNC-CH) One area of focus for the UNC Research Group on Modeling, Physically-Based Simulation and Applications. The field of solid modeling deals with the design and representation of physical objects. The two major representation schemata used in solid modeling ...more>> Geometry On the Sphere (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center Great circles on the sphere are the analogs of straight lines in the plane. Such curves are often called geodesics. A spherical triangle is a region of the sphere bounded by three arcs of geodesics... Geometry on the surface of the sphere will come in ...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>> Maple Application Center - Waterloo Maple, Inc. Software you can order to explore, share, and publish math on the Internet. Interactive media for exploring and exchanging mathematical ideas, with content on a variety of subjects at the high school, university, and graduate level. (There are high school ...more>> Mathematics Graphics Gallery - Xah Lee A collection of mathematical images. Links to files on Xah Lee's sites that contain attractive mathematics graphics: Nested Inversion of Circles; Conic Sections; Epicycloid and Hypocycloids; Rose Curves; wallpaper designs; Transformation of the Plane; ...more>> Mathematics Meetings Feature Proof of Dodecahedral Conjecture by Undergraduate Sean McLaughlin (Math Chat) - Frank Morgan, MAA Online The Dodecahedral Conjecture says a very symmetric conjectured arrangement, based on the regular 12-faced dodecahedron, it is the optimal arrangement locally to pack unit balls around one fixed ball. This conjecture has now been proved, by Hales's undergraduate ...more>> Navworld - Joseph Portney A center for the art and science of navigation, providing navigational "cerebrations," famous historical accounts, interviews and biographies. See Earthshapes, different ideas of what the earth would look like if it were one of 12 different shapes (physical ...more>> Northwest to the Pole and Two-Headed Coins (Math Chat) - Frank Morgan; Christian Science Monitor Suppose you start at the earth's equator and travel continuously northwest until you reach the North Pole. What does your path look like? How long is your path? ...more>> On the Minimax Sphere Eversion - Rob Kusner, Mathematics and GANG, Univ. of Massachussetts at Amherst A brief paper describing the evolution of the animation of the minimax sphere eversion. Does not include the animation itself. ...more>> Photographic Polyhedron (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center As you stand in one place and look around, up, and down, there is a sphere's worth of directions you can look. One way to record what you see would be to construct a big sphere, with the image painted on the inside surface. To see the world as viewed ...more>> Randomness and Geometric Probability (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine An extensive annotated list of links to material on randomness and geometric probability: Buffon's needle; random domino tilings; random polygons, etc. ...more>> Science Museum Math Exhibit - The Geometry Center A museum exhibit on triangle tilings that contains sophisticated concepts such as tilings of the sphere and the relation between tilings and the Platonic and Archimedean solids: the sum of the angles of a planar triangle is always 180 degrees. Repeated ...more>> Spherical Geometry Demo - John M Sullivan, University of Illinois An applet demonstrating several features of spherical geometry, among them the parallel transport of tangent vectors, and the fact that the angles of triangles may not sum to 180 degrees. ...more>> Spirals (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine An extensive annotated list of links to material on spirals of all kinds. ...more>> Stereographic Projection (Geometry and the Imagination) - Conway, Doyle, Gilman, Thurston; The Geometry Center Let G be a sphere in Euclidean three space. We want to obtain a picture of the sphere on a flat piece of paper or a plane. Whenever one projects a higher dimensional object onto a lower dimensional object, some type of distortion must occur. There are ...more>> Surreal Films - Ivars Peterson - Science News Online Mathematicians have worked out a geometrically optimal transformation that minimizes the energy required to exchange a sphere's inside and outside surfaces. See Selected Images from The Optiverse, a video by John Sullivan, George Francis, and Stuart ...more>> Synergetics on the Web - Kirby Urner, 4D Solutions R. Buckminster Fuller's "explorations in the geometry of thinking" is detailed in two thick volumes, Synergetics and Synergetics 2. Synergetics thoroughly permeates the rest of Fuller's writings as well. The invention for which Fuller is most famous, ...more>> Triangles in Elliptic Geometry - Thomas Banchoff, The Geometry Center An examination of some properties of triangles in elliptic geometry, which for this purpose are equivalent to geometry on a hemisphere. The aim is to construct a quadrilateral with two right angles having area equal to that of a given spherical triangle. ...more>> Width, Diameter, and Geometric Inequalities (The Geometry Junkyard) - David Eppstein, Theory Group, ICS, UC Irvine An extensive annotated list of links to material on width, diameter, and geometric inequalities. ...more>>
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