Topics in Mathematics Geometry

• Alice Meets the 4th Dimension
• AMS's Materials Organized by Mathematical Subject Classification
ADD. KEYWORDS: Electronic Journals, Preprints, Web Sites, Databases
• AskERIC Lesson Plans - Geometry
• Border Pattern Gallery
• Cabri Java Project
ADD. KEYWORDS: Examples, Animations, 3D geometry, Loci, Conics, Hyperbolic Geometry
SOURCE:
Cabri-géomètre
TECHNOLOGY: Java applets
• La Cabri-Thèque
• 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
• Connected Geometry
• Connecting Geometry
ADD. KEYWORDS: Course Materials, Communicating in Geometry, Symmetry & Transformations, Theorems in Geometry, Congruent Triangles, Triangle Properties, Right Triangles , Parallel Lines, Polygons, Similar Triangles, Circles, Perimeter & Area, Surface Areas & Volumes
SOURCE: Cathi Sanders, Eschool
TECHNOLOGY:
• Constructing Semi-Regular Tilings
SOURCE: Kevin J. Mitchell, Hobart and William Smith Colleges
• Convex Hulls
SOURCE: Alejo Hausner, Princeton University
TECHNOLOGY: Java applets
• Convex Uniform Polytopes in Four Dimensions
ADD. KEYWORDS: Schläfli symbols, Wythoff symbols, Archimedean polyhedra, Platonic polyhedra, Uniform polyhedron, Symmetry groups, Coxeter-Dynkin graphs
• CopyCat
ADD. KEYWORDS: Game, 3D, Graphs, Cube, Octahedron
• Curves for Computer Aided Geometric Design
SOURCE:
Jens Gravesen, Technical University of Denmark
TECHNOLOGY:
• The Discontinuous Groups of Rotation and Translation in the Plane
ADD. KEYWORDS: Tutorial, Derivation and Classification of Groups, Wallpaper Groups, Orbifolds, Crystallographic Notation, Bibliography
• Easymaths
ADD. KEYWORDS: Tutorials, Worksheets, Diagnostic tests
SOURCE: Mathematics Web Association
• An Electronic Primer on Geometric Constraint Solving
ADD. KEYWORDS: Molecular modeling, Computer-Aided Design, Tolerance Analysis, Geometric Theorem Proving, Bibliography
• Erich's Packing Center
• The Euclid Project
ADD. KEYWORDS: Chaos Theory, Euclid's Constructions, History, Ptolemy's Voyage, Golden Ratio
• EUROLOGO Web Server
• Flash Films
ADD. KEYWORDS: Polygons, Exploring Halves, Tangrams, Tiles
SOURCE: The Association of Teachers of Mathematics
TECHNOLOGY: Macromedia Flash
• Flatland - A Romance of Many Dimensions
• Forum Geometricorum
SOURCE: Department of Mathematical Sciences, Florida Atlantic University
TECHNOLOGY:
• From quasicrystals to Kleenex
ADD. KEYWORDS: Article, Tilings, Penrose, Quasicrystals
SOURCE: Alison Boyle, Plus magazine
• Front for the XXX Mathematics Archive - Metric Geometry
• Geombinatorics
ADD. KEYWORDS: Printed journal, Open problems of combinatorial and discrete geometry and related areas
• Geometer's Sketchpad Labs by Mike Riedy
ADD. KEYWORDS: Rotation & Translation Exploration, Cycloid, Area of a Parallelogram, Area of a Rectangle
• Geometric dissections on the web
SOURCE: Greg Frederickson, Purdue University
• Geometrie mit dem Computer (German)
ADD. KEYWORDS: Discussion Groups, Software, Notebooks
• Geometry
ADD. KEYWORDS: Collection of articles, Constructing the Heptadecagon, Parabola Through Four Points, Curvature, Intrinsic and Extrinsic, Sphere Packing In Curved Space, Min-Energy Configurations of Electrons On A Sphere, Distinct Point Sets With Same Distances, Isospectral Sets In One Dimension, Generating Functions for Point Set Distances, Curvature of Linear Interpolation, Gravity Sextant, Platonic Solids and Plato's Theory of Everything, etc.
• Geometry
• Geometry and the Imagination
ADD. KEYWORDS: Course Materials, Bicycle tracks, Polyhedra, Knots, Surfaces, Mobius Band, Geometry on the sphere, Curvature of surfaces, Gaussian curvature, Symmetry and orbifolds, symmetry groups and orbifolds, Hyperbolic Geometry, Stereographic Projection
• The Geometry Applet
ADD. KEYWORDS: Euclid's Elements, history, interactive pages
• Geometry Bibliography, articles from Mathematics Teacher
• Geometry in Hawaiian History and Culture
• Geometry in Motion
ADD. KEYWORDS: Intersecting Circles, The Falling Ladder, The Sliding Triangle, The Bent Straw, The Folded Circle, Van Schooten's Ellipse, Congruent Triangles, Concentric Circles, The Taut String, Van Schooten's Parabola, The Expanding Circle, The Hanging String, The Taut String, Part 2, Van Schooten's Hyperbola, Congruent Triangles, Part 2, Pantograph of Sylvester, The Limacon
SOURCE: Daniel Scher
• The Geometry Junkyard
• Geometry Learning Project
ADD. KEYWORDS: Curriculum Materials, NCTM Standards
• Geometry Learning Units - Elementary School
• Geometry Learning Units - Middle School
ADD. KEYWORDS: Lesson Plans, Symmetry and Reflection
• Geometry Learning Units - High School
• The Geometry of the Sphere
ADD. KEYWORDS: Tutorial, Lunes, Area on the sphere, Spherical triangles, Girard's Theorem, Similarity, Euler's formula
SOURCE: John C. Polking, Rice University
TECHNOLOGY: Java applets
• The Geometry of War, 1500-1750
ADD. KEYWORDS: Museum exhibition, Gunnery, Rangefinding and Surveying, and Fortification, Troop Formations and the Telescope, Bibliography
• Geometry Online
ADD. KEYWORDS: History of Geometry, Hidden Polygons, Isosceles Triangle Puzzler, Circles and Pythagorus, The Golden Ratio, Experiment with Volume, School-Bus Geometry
• Geometry Through Art
• Geometry Tutorials
ADD. KEYWORDS: Ptolemy's inequality, Euler's theorem
• Geometry Web Page
ADD. KEYWORDS: Lesson Plans, Tangrams, Golden Ratio, Geoboard, Polygons, Symmetry, Constructions, Polyominoes and Polyiamonds, Star Polygons, Special Points in Polygons, Polygon Tessellations, Kaleidoscope Tessellations, Escher Tessellations, Space Cubes, Polyhedra, Symmetry in Space, Topological Considerations
• GEONET - Dynamische Geometrie-Software
• Golenor's Geometry Gala!
SOURCE: Matt Golenor and Center for Technology and Teacher Education, University of Virginia
TECHNOLOGY: Windows Media Player and Geometer's Sketchpad
• Go Geometry from the Land of the Incas
ADD. KEYWORDS: Theorems, Problems, Quiz, Puzzle, Triangle, Quadrilateral, Circle, Square, Solid Geometry, Dynamic Geometry, Archimedes, Incas, Machu Picchu, Nazca lines, Art, Van Gogh, Escher
• GoMath Tutorials
• Gomath.com - Geometry
ADD. KEYWORDS: Triangle, Parallelogram, Trapezoid, Rectangle, Square, Rhombus, Regular N-gon, Sphere, Cube, Cuboid, Pyramid, Rectangular Wedge, Circle, Sector of Circle, Segment of Circle, Annulus/Circular Ring, Sector of Circular Ring, Ellipse, Frustum of a Pyramid, Cone, Frustum of a Cone, Right Circular Cylinder, Right Circular Cylinder with Oblique Face
SOURCE: Cubic Science, Inc
TECHNOLOGY: Server side programs
• GridWorld
• Harcourt Animated Math Glossary
• Hyperbolic Geometry
ADD. KEYWORDS: Tessellations of the Unit Disk, Mathematica, Fuchsian Groups
• Hyperbolic Geometry using Cabri
ADD. KEYWORDS: Cabri geometry, Circumscribed Circle, Isometries of H2, Tessellation of H2 using regular triangles.
• Hyperbolic Geometry with The Geometer's Sketchpad
ADD. KEYWORDS: Constructs a hyperbolic line through two given points, Measures a hyperbolic angle specified by three points, Measures hyperbolic distance between two points, Midpoint, Drops a perpendicular segment from a given point to a given line, Draws a hyperbolic circle given the center and a point on the circle.
SOURCE: Robert J. Frank, Seton Hill College
• Hyperbolische Geometrie (in German)
• Hyperspace Structures
• Interactive Mathematics Miscellany and Puzzles Geometry Page
ADD. KEYWORDS: Geometric Probability, Carnot's Theorem, Ceva's Theorem, Conic Sections, Euclid's Fifth Postulate, Fermat's Point and Generalizations, Ford's touching circles, Isoperimetric Theorem and Inequality, Fractals, Napoleon's Theorem, Ptolemy's Theorem, Regular polyhedra and Euler's Theorem, Steiner's Theorem, Three Circles and Common Tangents
• An Introduction to the Works of Euclid With an Emphasis on the Elements
• Investigations in Teaching Geometry
ADD. KEYWORDS: CD-ROM, Iintegrated media case
SOURCE: Elizabeth Goldman, Vanderbilt University et al.
• Isoptikon
ADD. KEYWORDS: Geometrically defined cubic curves (isoptics)
SOURCE: Paris Pamfilos, University of Crete
TECHNOLOGY: Macintosh and Microsoft Windows program
• Japanese Temple Geometry
• Japanese Temple Geometry Problem
• Java Applets in Mathematics (in French)
• Java Applets on Mathematics
ADD. KEYWORDS: Sum of Angles in a Triangle, Thales' Circle, Special Lines and Circles in a Triangle, Center of Mass in a Triangle, Cyclic Quadrilateral, Pythagorean Theorem, Platonic Solids, Spherical Triangle
• JAVA Gallery of Geometric Algorithms
ADD. KEYWORDS: Delaunary Triangulation, Edge Matching, Point Filter
• Java Geometry Explorer
ADD. KEYWORDS: Art, Cardioid, Nephroid, Ranunculoid, Chords
• JAVA KALI
ADD. KEYWORDS: Wallpaper groups, Frieze and Rosette Groups
• Jim Plank's Origami Page
ADD. KEYWORDS: Dodecahedrons, Tetrahedrons, Octrahedrons, Snub Cube, Icosahedron, Polyhedrons, Rhombicuboctahedron, Modular Origami.
ADD. KEYWORDS: Articles, Geometer's Sketchpad, Capturing Area and A Solution, Orthotravels, Tangents Problem, Explorations with Heron's Formula, Witch of Agnesi, GLaD Construction, Ratio Result for Triangles, Partitioning a Line Segment
• The Kepler Conjecture
ADD. KEYWORDS: Sphere packings, Articles, Software, Mathematica
• Klein Bottle
• Kwanzaa Math: The Mkeka
• Lobachevskian Geometry with Interactive Drawing-Pad
ADD. KEYWORDS: non-Euclidean geometry, Poincaré model, Lobachevskian Plane
SOURCE: Kerry E. Grant, Southern Connecticut State University
TECHNOLOGY: Java applets
• Manipula Math with JAVA
• Map Projection Overview
SOURCE: Peter H. Dana from University of Colorado at Boulder
• Math Forum K-12 Geometry
ADD. KEYWORDS: Classroom materials, software, newsgroups
• Math Forum - College Level Geometry
ADD. KEYWORDS: Classroom materials, software, newsgroups
• Math Forum - Advanced Geometry
• Math Jeopardy
ADD. KEYWORDS: Competition, Problem Solving, Estimation, Geometry, Patterns
SOURCE: Dan Ashlock, Iowa State University
• Math Quilts
ADD. KEYWORDS: Tessellations, Perspective and Fractals
• Math.com - Geometry
ADD. KEYWORDS: Geometry Building Blocks, Geometry words, Coordinate geometry, Pairs of lines, Classifying angles, Angles and intersecting lines, Circles, Polygons, Triangles, Quadrilaterals, Area of polygons and circles, Congruent figures, Similar figures, Squares and square roots, The Pythagorean Theorem and right triangle facts, Three-dimensional Figures, Prisms, Pyramids, Cylinders, cones, and spheres
SOURCE: Math.com
TECHNOLOGY: Javascript
• A Mathematical Approach to Slicing Doughnuts
• Mathematical Cartography
SOURCE: Hans Havlicek from the Technische Universität Wien
• Mathematical Laboratory
ADD. KEYWORDS: Pantographs, Symmetry to an axis, Symmetry to a point, Traslation, Rotation (Pantograph of Sylvester), Glide reflection, Homothety (Pantograph of Scheiner), Similariy (Pantograph of Sylvester), Affinity, Inversor of Peaucellier, Prospettograph of Lambert, Product of two central simmetries, Product of two reflections in intersecting lines
SOURCE: University Museum of Natural History and Scientific Instruments
• Mathematics of Cartography
SOURCE: Cynthia Lanius from Rice University
• Mathématikos - Géométrie [in French]
ADD. KEYWORDS: Geometric transformations, Regular polygons, Pappus' Theorem, Nine point circle, ...
SOURCE: Jean-Paul Quelen, professeur de mathématiques au lycée Jean Monnet - Strasbourg
TECHNOLOGY: Java Applets
• Mathworld - Geometry
ADD. KEYWORDS: Definitions, List of Theorem
• Museo Universitario di Storia Naturale e della Strumentazione Scientifica - Mathematical Laboratory
ADD. KEYWORDS: Mathematical Drawing Machines, Pantographs, Curvegraphs
• National Library of Virtual Manipulatives for Interactive Mathematics - Geometry
ADD. KEYWORDS: Circular Geoboard, Cob Web Plot, Golden Rectangle, Iterative Fractals, Mandelbrot and Julia Sets, Koch Triangle, Platonic Duals, Platonic Solids, Polygon Fractals, Geoboard, Slicing Solids, Tesselations, Pythagorean Theorem, Similar Triangles, Coordinate Geoboard, Isometry Transformations, Composition Transformations
SOURCE: Lawrence O. Cannon, James T. Dorward, E. Robert Heal, Leo Edwards, Utah State University
TECHNOLOGY: Java applets
• Native American Geometry
SOURCE: Chris Hardaker
• Neutral and Non-Euclidean Geometries
ADD. KEYWORDS: Spherical Geometry, Logic and the Axiomatic Method Incidence Geometry, Betweenness Axioms, Congruence Theorems, Axioms of Continuity, Neutral Geometry, Hyperbolic Geometry, Classification of Parallels, Inversion in Euclidean Circles, Models of Hyperbolic Geometry, Hypercycles and Horocycles, The Pseudosphere, Hyperbolic Trigonometry, Hyperbolic Analytic Geometry
• The Nine Point Circle
• Non-Euclidean Geometry
ADD. KEYWORDS: Poincare Disk Model, Geodesics, Isometries
• On-Line Math Learning Center - On-line Quizzes
ADD. KEYWORDS: Lines, Angles, Squares and rectangles, Parallelograms, Trapezoids, Triangles, Circles, Volume, Pythagorean Theorem, Similar triangles
• Open Problems
ADD. KEYWORDS: Existence Problems, Combinatorial Problems, Algorithmic Problems
SOURCE: Jeff Erickson, University of Illinois
• Origami and Math
• Origami Mathematics
• Partnership for Excellence - Rediscovering Geometry
ADD. KEYWORDS: Lesson Plans, Course Materials
SOURCE: Partnership for Excellence Project, University of South Carolina Spartanburg
• The Peanut Software Database Project
ADD. KEYWORDS: Lab materials, Inscribed Circles, Centroid, Triangles, Exterior Angle, Similarity, Circle Geometry with WinGeom, WinGeom Exercises on Angles, WinGeom Lab Manual
SOURCE: Meighan I. Dillon, et al., Southern Polytechnic State University
• Picture Gallery of Map Projections
ADD. KEYWORDS: Cylindrical equidistant projection, Mercator's cylindrical conformal projection, Galle's cylindrical projection, Polyconic projection, Azimuthal equidistant projection, Orthographic projection, Stab-Werner projection, Apianius' projection, Collignon's projection, etc.
• Planimeters
ADD. KEYWORDS: Area of planar regions
SOURCE: Robert Foote, Wabash College
TECHNOLOGY:Animated gifs
• The Platonic Solids
ADD. KEYWORDS: Euler's Polyhedron Theorem, Dodecahedron
• Poincaré Disk
• PoincaréDraw
ADD. KEYWORDS: Compass and straightedge constructions in the Poincaré disk model of the hyperbolic plane
SOURCE: Robert Foote, Wabash College
TECHNOLOGY: MSDOS program
• Polyhedra Collection
ADD. KEYWORDS: Uniform polyhedra, Duals, Johnson's solids, Stellations of Icosahedron, Stellations of deformed dodecahedron, Spherical Platonic polyhedra, Polyhedral Kaleidoscope, Symmetrical compounds, VRML, Interactive building of polyhedra compounds
• Polyhedral Solids
ADD. KEYWORDS: Platonic Solids, Archimedean Solids, Kepler-Poinsot Polyhedra, Compound Solids, Stellated Polyhedra
• Polyominoes
• Probability/Patterns Learning Units
• Project Interactivate - Activities - Geometry and Measurement Concepts
ADD. KEYWORDS: Lines, Rays and planes, Working with tessellations, Fractals
SOURCE: The Shodor Education Foundation, Inc.
TECHNOLOGY: Java Applet
• A Project to Transform 6-12 Mathematics Education: Vertically-Integrated, Inquiry-Based Geometry
ADD. KEYWORDS: NSF Teacher Enhancement project, Teaching Scenarios
SOURCE: Richard Allen, et al., St. Olaf College
• Projective Geometry
ADD. KEYWORDS: Tutorial, Proofs (using animated gifs)
• Pythagoras' Theorem
ADD. KEYWORDS: Geometry, history, interactive pages
• Pythagorean Theorem
• Pythagorean Theorem
SOURCE: Tom Richmond, Western Kentucky University
TECHNOLOGY: Animated Gif
• QuasiTiler
• School Geometry in Java
ADD. KEYWORDS: Ruler and compass constructions
• Science U - Geometry Center
ADD. KEYWORDS: Interactive Models of Platonic and Archimedean Solids, Interactive Triangle Tiling Maker, Kali: Symmetry group, Tilings, Tetrapuzzle, Isometries, Geometry Formulas
• SCORE Mathematics - Geometry
SOURCE: SCORE - Schools of California Online Resources for Education
• SCORE Mathematics - Measurement and Geometry
SOURCE: SCORE - Schools of California Online Resources for Education
• Seventeen Kinds of Wallpaper Patterns
• SMILE Program Mathematics Index
• Spatial Concepts
ADD. KEYWORDS: Euler's Law (V+F=E+2), Descartes' Angular Deficit, Taxonomies of Polyvertexia (=polyhedra), Symmetry, Architecture
• Steiner Surfaces
ADD. KEYWORDS: Roman surface, cross-cap, real projective plane, Whitney's Umbrella, Plücker's Conoid, Boy Surface
• Stellated Icosahedra
ADD. KEYWORDS: Mathematica, Enumeration of all stellations of the icosahedron
• Symmetric Patterns at the Alhambra
• Symmetry and Pattern - The Art of Oriental Carpets
ADD. KEYWORDS: Glossary, Bibliographies, Student Projects, Asymmetry and Symmetry-Breaking, The Four Basic Symmetries, Border Patterns, Field Patterns, Grids and Tessellations
• Symmetry and the Shape of Space
ADD. KEYWORDS: Isometries of the plane, Regular Patterns, Orbifolds, Software, Kali, Geometer's Sketchpad
• Symmetry and Tessellations - ACTIVITY LINKS
• Taking Geometry Seriously!
• Tangrams
ADD. KEYWORDS: Geometry, spatial-visualization skills, congruency, similarity, symmetry, area of polygons
• Tangrams - An Introduction
• A Teacher's Guide to Building the Icosahedron as a Class Project
SOURCE: Frederick J. Wicklin, Geometry Center
• Technology in the Geometry Classroom Course Materials
ADD. KEYWORDS: Course Materials, Geometer's Sketchpad, Monge's Theorem, Peaucellier's Linkage, Dynamical systems lab, Symmetry and Patterns, Wallpaper Patterns, Orbifolds, Videotapes, Software, Student Projects
• Tessellations Project
• Tiling Dynamical Systems
ADD. KEYWORDS: Prototiles, Shift Dynamical Systems, Penrose
• Tiling - Plane & Fancy
ADD. KEYWORDS: The 17 wallpaper groups, Tiling and Patterns from Historical Sources, Tiling arranged by Symmetry group, References,| Open questions, Pythagorean Theorem, Color Tiling
SOURCE: Steve Edwards, Southern Polytechnic State University
• Tiling With Right Trominos
• Topology and Geometry Software
ADD. KEYWORDS: Torus and Klein Bottle games, Kali, KaleidoTile, Exploring the Shape of Space, Computer Graphics in Curved Spaces, SnapPea
SOURCE: Jeff Weeks
TECHNOLOGY: Java Applets, Software packages for Macintosh, Windows, Linux and Unix
• Totally Tessellated
ADD. KEYWORDS: Decorative Use, Ancient and Modern, Historical Image Gallery, Escher, Regular and Semiregular Tessallations, Mosaics, Tilings, Related Art Movements, Dissection Tiling, Packing, Penrose Tiles, Polynominoes, Tiling Dynamic Systems
• Transformations
ADD. KEYWORDS: Rotations, Reflections, Translations, Enlargements, Combinations
SOURCE: MathsNet and AngliaCampus
TECHNOLOGY: Java applets, Cinderella
• Transformations
• Transformations
ADD. KEYWORDS: Translations, Rotations, Reflections, Glide Reflections, Symmetry, Frieze Patterns, Escher
• Triangle Centers
ADD. KEYWORDS: Schiffler Point, Exeter Point, Parry Point, Congruent Isoscelizers Point, Yff Center of Congruence, Isoperimetric Point and Equal Detour Point, Ajima-Malfatti Points, Apollonius Point, Morley Centers, Hofstadter Points, Equal Parallelians Point, Centroid, Incenter, Circumcenter, Orthocenter, Fermat Point, Nine-point center, Symmedian point, Gergonne point, Nagel point, Mittenpunkt, Spieker center, Feuerbach point, Isodynamic points, Napoleon points
• Triangle Geometers
ADD. KEYWORDS: Napoleon theorem, Ceva's theorem, cevians, cevian triangle, Clawson point, Euler line, Feuerbach theorem, Gergonne point, Kiepert hyperbola, Lemoine point (or symmedian point), De Longchamps point, Malfatti problem, Morley triangle, Morley points, Nagel point, Neuberg circles, Schiffler point, Simson line, Soddy circles, Steiner ellipse, Steiner point
• Triangle Geometry
ADD. KEYWORDS: Angles, Right angles, Pythagorean Theorem, Compass and rule constructions
• Triangles
ADD. KEYWORDS: The nine-point circle, Euler's line, Morley's theorem.
SOURCE: Alejo Hausner, Princeton University
TECHNOLOGY: Java applets
• UIMATH.grafiXlab
ADD. KEYWORDS: LATERNA matheMAGICA, Cellular Semiotics, Software, Courses, Homotopies
• Understanding Projective Geometry