Martin Gardner: Adventures in Flatland


A Two-dimensional Playground
by Evelyn Lamb

Section 1: Playing Games in Two Dimensions

1.1    The Game of Hex

1.2    Ticktacktoe Old and New

1.3    Even More Ticktacktoe

1.4    The Game of Life

1.5    Another Look at Life

Section 2: Filling the Plane

2.1    Two-dimensional Rep-tiles

2.2    What Shapes Tile the Plane?

2.3    Tiling the Plane with Polyominoes

2.4    Penrose Tiles

2.5    Square Packing

Section 3: Dissecting Shapes

3.1    Dudney’s Dissections

3.2    Squaring the Square

3.3    Equal Dissections

Section 4: Imagining Two-dimensional Worlds

4.1    Meditations on Flatland

4.2    The Physics of the Planiverse

4.3    Taking a Taxi to Non-Euclidean Geometry

4.4    Euclid’s Parallel Postulate and its Modern Offspring

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