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Random Voronoi (30 cells) · seed 1

χ(planar) ≤ 4

regions · 0

edges · 0

max deg · 0

step 0 / 0

The Four Colour Theorem

Every flat map needs at most four colours

Stated 1852, proved 1976 by Kenneth Appel and Wolfgang Haken. Any subdivision of the plane into regions can be coloured with at most four colours so that no two neighbouring regions share a colour. The proof was the first major theorem verified by computer — it reduces the problem to 1834 unavoidable configurations and checks each. Mathematicians argued for years over whether the proof 'really counted'.

Preset map

Number of regions

305 … 80

Colour palette

cyanambervioletrose

Auto-colourer

Speed · 60 ms / step

coloured0 / 0

backtracks0

solvedin progress

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Foldscape · An atlas of mathematical curiosities

Curated by Simon Franzen · zauberware

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