Beautiful Geometry

Fall in love with geometry by uncovering elegant solutions to beautiful geometric problems.

Infinite Areas

Polyomino Tiling

Guards in the Gallery

Regular Tessellations

Semiregular Tessellations

Transforming Tiles Part 1

Transforming Tiles Part 2

Irregular Tiles


Infinite Arithmetic

Tiling a Chessboard

Counting All Possible Solutions

Bigger Polyomino Blocks

Challenging Packing Puzzles


Tiling and Cutting

Congruent Cutting

Mathematical Origami

Dragon Folding

1D Flat Folding

2D Holes and Cuts

2D Single-Vertex Flat Folding (I)

2D Single-Vertex Flat Folding (II)

Strange Polygons

Convex vs. Concave

Quadrilateral and Pentagonal Galleries

Efficient Guard Placement

Worst-Case Designs

Fisk's Coloring Proof

Further Art Gallery Research

Pegboard Rectangles

Pegboard Triangles

Pick's Theorem Generalized

Pick's Theorem with One Hole

Pick's Theorem with Multiple Holes

Course description

Are you ready to start loving geometry? This course is here to guide you through some of the magic of geometry, revealing the thought processes that lead to clever solutions to beautiful geometry problems. By the end of this course, you'll have explored polyominoes, tessellations, origami folding, art gallery problems, and lattice polygons.

Topics covered

  • Convexity and Concavity
  • Deconstructing Origami
  • Fisk's Coloring Proof
  • Fractals
  • Lattice Polygons
  • Packing Puzzles
  • Pick's Theorem
  • Polyominoes
  • Reptiles
  • Tessellations
  • The Art Gallery Problem
  • Triangulation


  • Measurement

Next steps