Contents

• Preface
• Philosophy
• Organization
  • People
  • Scheduled meetings
  • Discussion groups
  • Texts
  • Other materials
  • Journals
  • Constructions
  • Final project
  • Geometry room/area
• Bicycle tracks
• Polyhedra
  • Discussion
  • Homework
• Knots
  • Discussion
• Maps
  • Euler numbers
  • Discussion
• Notation for some knots
• Knots diagrams and maps
• Unicursal curves and knot diagrams
  • Assignment
• Gas, water, electricity
• Topology
  • Letters
• Surfaces
  • Discussion
• How to knit a Möbius Band
• Geometry on the sphere
  • Discussion
• Course projects
• The angle defect of a polyhedron
  • Discussion
• Descartes's Formula.
  • First proof
  • Second proof
  • Discussion
• Exercises in imagining
• Curvature of surfaces
• Gaussian curvature
  • Discussion
• The celestial image of a polyhedron
  • Discussion
• Clocks and curvature
  • Clocks
  • Curvature
  • Where's the beef?
• Photographic polyhedron
• Mirrors
  • Discussion
• More paper-cutting patterns
• Summary
• The Euler Number
  • Descartes's Formula
  • The Gauss Map (Flashlights)
  • Curvature (Kale and cabbage)
    • Curvature for Polyhedra
    • Curvature on surfaces
  • Discussion
• Symmetry and orbifolds
  • Discussion
• Names for features of symmetrical patterns
  • Mirrors and mirror strings
  • Mirror boundaries
  • Gyration points
  • Cone points
• Names for symmetry groups and orbifolds
• Stereographic Projection
  • Description
  • Discussion
  • What's good about stereographic projection?
    • The algebraic proof
    • The geometric proofs
• The orbifold shop
• The Euler characteristic of an orbifold
• Positive and negative Euler characteristic
• Hyperbolic Geometry
  • Defining the hyperbolic plane
    • The Upper Half-Plane
  • Discussion
  • Distance
• Distance recipe
  • Examples of distances
  • The Unit Disc Model
  • Passing from one model to another
• A field guide to the orbifolds
  • Conway's names
    • The prefix
    • The descriptor
  • How to learn to recognize the patterns
  • The manuscript
• About this document ...