MA341 -- Topics in Geometry

Course Information

• Syllabus
• Course Notes (Updated frequently)
• Visualizing Math Course Notes (From a previous course)
• Summary of Class
• Blackboard at UK
• Suggestions on Approaching Mathematics
• Example of slicing the unit sphere with a plane (SketchUp file)
• Example of finding lines in the Poincare disk model (GeoGebra file)
• Example of finding lines in the upper half plane model (GeoGebra file)
• Illustrating the result of multiplying a vector by a 2x2 matrix (GeoGebra file)
• Powers of Ten Video
  • A Question of Scale
  • Cosmic Scale
  • The Scale of the Universe
  • Cosmic Eye iPad App
• Creating an Ellipse (GeoGebra file -- move the slider)
• Modeling a Simple Planet (GeoGebra file with animation)
• Scott Kim's Symmetry Talk
• Scott Kim's Ambigram Handout
• Isometry 1 (GeoGebra file)
• Isometry 2 (GeoGebra file)
• Isometry 3 (GeoGebra file)
• Isometry 4 (GeoGebra file)
• Isometry 5 (GeoGebra file)
• Isometry 6 (GeoGebra file)
• Isometry 7 (GeoGebra file)
• Isometry 8 (GeoGebra file)
• Symmetries of Plane Patterns
• 3D Geometry
  • POV-Ray Ray Tracer
  • POV-Ray Unofficial for the Mac
  • POV-Ray Documentation
  • POV-Ray Hall of Fame
  • Some of my Examples
  • More Examples From a Previous Course
  • Some POV-Ray Textures and Colors
  • POV-Ray Predefined Colors (Click on a color to see its name)
  • Modeling Notes from a Previous Course -- Visualizing Mathematics
  • Wingeom
  • Coordinates for the Platonic Solids
    • cube.wg3 (Wingeom file)
    • tetrahedron.wg3 (Wingeom file)
    • octahedron.wg3 (Wingeom file)
    • preicosahedron.wg3 (Wingeom file)
    • icosahedron.wg3 (Wingeom file)
    • icosahedron2.wg3 (Wingeom file)
  • OpenSCAD
    • Manual
    • octahedron.scad
    • puzzlepiece.scad
    • longoctahedron.scad
  • MakerWare
  • 3D Rotation Formula
    • Maple File

  Assignments

  • Homework #1
  • Homework #2
  • Homework #3
  • Exam #1 Review
  • Homework #4
  • Homework #5
    • GeoGebra File
  • Exam #2
  • Homework #6
    • Transformation Matrices
  • Homework #7
  • Exam #3
  • Final Exam

  Other Resources

  • Books and Articles

    • Euclid's Elements
    • The Foundations of Geometry by Hilbert
    • SMSG Texts (High School textbooks)
      • Geometry, Part I
      • Geometry, Part II
      • SMSG Geometry Parts I and II Summary
      • Geometry With Coordinates, Part I
      • Geometry with Coordinates, Part II
      • Analytic Geometry
    • National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics
    • Common Core State Standards Initiative
      • Common Core State Standards for Mathematics
    • History of Geometry (Wikipedia)

  • Software and Apps

    • GeoGebra
      • GeoGebra Quickstart
      • iPad App
    • GeoGebra 5 Beta with 3D
    • Wingeom
    • The Geometer's Sketchpad
    • Cabri
    • Spherical Easel
    • NonEuclid
    • SketchUp
      • Using SketchUp
      • Jessie Clark SketchUp Project
    • Blender
    • POV-Ray
    • Wolfram MathWorld
    • WolframAlpha
    • Jing (To make short videos)
    • Dropbox (For sharing files across computers)
    • Some iPad Apps
    • Cybrary Man's Educational Web Sites -- iPad Apps

  • Miscellaneous

    • Trailer for the Movie "Contact"
    • Animusic
      • Pipe Dreams
    • BBC In Our Time: Godel's Incompleteness Theorems
    • Game of SET
      • Physical game
      • SET Pro HD iPad app
    • Engines of our Ingenuity radio program
      • Descartes
    • Origami Proof of the Pythagorean Theorem
    • Mathematics Education and Outreach Resources
    • Wff'n Proof Games
    • Scale of the Universe
    • A Question of Scale
    • Powers of Ten Video
    • Cosmic Voyage Video
    • Powers of One -- xkcd
    • NCTM Research Clips and Briefs
    • Conic Sections SketchUp file -- Doubleclick a plane and move it with the Move tool (drag a corner)
    • Doodling in Math Class: Infinity Elephants
    • Origin of the Terms Sine, Cosine, Tangent, etc.
    • How the Trig Functions Got Their Names
    • The Math Forum @ Drexel
    • Dave's Short Trig Course
    • NCTM Illuminations
      • Distance to Horizon -- NCTM Illuminations Activity
    • POV-Ray examples (Free ray-tracing software)
    • Theodolite problem
    • Core Math Tools from NCTM
    • Ambigram handout from Scott Kim
    • Music video illustrating superposition and repetition
    • Smarter Balanced Sample Items
    • Isometry Problems I
    • National Library of Virtual Manipulatives
    • Scott Kim's NCTM Talk on Symmetry
    • Data and Story Library
    • Mathed Potatoes
    • Green Bean Matherole
    • Area of Circle
    • Unrolling a Circle (GeoGebra file)
    • Scaling a Cube Building (SketchUp file)
    • On Being the Right Size
    • Flatland
    • Geometry in Utopia
    • Illustrative Mathematics

    Interesting Websites

    • Jabberwocky (Source of toves, borogoves, and gimble)