Allan Collins_Appel–Haken_6.jpg

Appel–Haken

Each Drawing is Unique

Material: Ink Drawings on Isometric Paper

Size: W21cm x H29.7cm

Appel–Haken is a series of works exploring the scientific phenomenon of the four colour theorem and the divine beauty that emerges from the proof of the theorem.

The Rule - The four colour theorem states that, given any separation of a plane into contiguous regions, producing a figure called a map, no more than four colours are required to colour the regions of the map so that no two adjacent regions have the same colour. Could this theorem be applied to three colours on a geometrical map? Could the geometrical map have evenly sized components?

The Outcome – The Hexagon is able to be subdivided by three factors into evenly sized components. When the three colour theorem is applied to the subdivided hexagon over 3 factors the proof that no two adjacent regions have the same colour is true.

The Presentation – The artworks use the three primary colours, Red, Yellow & Blue to illustrate the proof of the theorem.

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