Specialized Tiling

Non-Euclidean geometry and planimetric mosaics

• Tiling of non-Euclidean plane
  • Euclid’s parallel postulate, non-Euclidean & hyperbolic geometry
  • Nikolai Lobachevsky, János Bolyai, Poincaré disk model, Schläfli symbol
  • Hyperbolic tiling and symmetries
  • Escher’s circle limits
• Special mosaic construction
  • Pentagonal tiling, Cairo tiling
  • Marjorie Rice, Michaël Rao
  • Origami patterns
  • Dissection tiling, planimetric mosaics

Discussion

• Non-Euclidean Geometry (Malin Christersson)
• Artistic Models of the Hyperbolic Geometry (Vladimir Bulatov)
• Creation of Hyperbolic Ornaments (Martin von Gagern)
• Hyperbolic Planes Take Off! (Vi Hart)
• How Did Escher Do It? (Bill Casselman)
• Pentagon Tiling Proof Solves Century-Old Math Problem (Natalie Wolchover)
• The Math and Magic of Origami (Robert Lang)

Assignment

Circle limit

Hyperbolic Tiling – HyperTess – KaleidoPaint – KaleidoTile – Poincaré

 

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Decorative knots  ▸