3.1 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
Reptiles
Infinite Arithmetic
Tiling a Chessboard
Counting All Possible Solutions
Bigger Polyomino Blocks
Challenging Packing Puzzles
X-Only
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
Prerequisites
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3.2 Geometric Thinking
Strengthen your geometric intuition and logical reasoning skills through problem solving.
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