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About: Dividing a circle into areas     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatCirclesyago:Abstraction100002137yago:Attribute100024264yago:Circle113873502yago:ConicSection113872975yago:Ellipse113878306yago:Figure113862780yago:PlaneFigure113863186yago:Shape100027807 New Facet based on Instances of this Class

In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem, has a solution by an inductive method. The greatest possible number of regions, rG = (n4) + (n2) + 1, giving the sequence 1, 2, 4, 8, 16, 31, 57, 99, 163, 256, ... (OEIS: ). Though the first five terms match the geometric progression 2n − 1, it diverges at n = 6, showing the risk of generalising from only a few observations.