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...Non euclidean geometry and indra s pearls millennium mathematics project university of cambridge permission is granted to print copy this page on paper for commercial use other uses including electronic redistribution please contact us june features by caroline series david wright many people will have seen been amazed the beauty intricacy fractals like one shown right particular fractal known as apollonian gasket consists a complicated arrangement tangent circles few know however that pictures are intimately related tilings what mathematicians call hyperbolic space such tiling in figure below contrast b shows ordinary flat plane article which first appeared proceedings bridges conference held london we explore maths behind these how they give rise beautiful images disc regular heptagons image created hexagons round lines strange distances not measured usual way metric shortest distance between two points no longer along straight line but different kind curve whose precise nature ll ne...