Regularly repeating patterns are commonplace around us, on tile-laid pavements, on tapestry designs, on window grills, on rangolis and so on. Exploring newer and newer basic patterns to create novel designs has fascinated mankind for centuries. This talk begins by looking at the seemingly simple problem of tiling a flat floor by polygonal shapes and takes on a journey telling the story of how it leads to certain intriguing but as yet unresolved questions like finding out how many different convex pentagons are capable of tiling the plane. Along the way, one gets to hear about Penrose's aperiodic tiling, the Honeycomb Conjecture and an interesting connection with the study of crystalline structures.
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