# A New Slant on Lebesgue’s Universal Covering Problem

@article{Gibbs2014ANS, title={A New Slant on Lebesgue’s Universal Covering Problem}, author={Philip Gibbs}, journal={arXiv: Metric Geometry}, year={2014} }

Lebesgue's universal covering problem is re-examined using computational methods. This leads to conjectures about the nature of the solution which if correct could provide a blueprint for a complete solution. Empirical lower bounds for the minimal area are computed using different hypotheses based on the conjectures. A new upper bound of 0.844113 for the area of the minimal cover is derived improving previous results. This method for determining the bound is suggested by the conjectures and…

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