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SUMMARY:Plato’s cube and the natural geometry of fragmentation -  Prof G
 abor Domokos\, Budapest University of  Technology and Economics
DTSTART:20201106T140000Z
DTEND:20201106T150000Z
UID:TALK151717@talks.cam.ac.uk
CONTACT:Hilde Hambro
DESCRIPTION:Plato associated regular  polyhedra with the classical Element
 s\, in particular\, he associated Earth with the cube. His views have been
  broadly regarded\, at best\, as metaphors.\n\nHowever\, if we approximate
  natural fragments by convex polyhedra and count the respective numbers fo
 r faces\, vertices and edges then in most cases we find averages close to 
 6\,8\,12\, the values corresponding to the cube.\n\nI will explain this ph
 enomenon by using the theory of convex mosaics\, geometric computer simula
 tions of such mosaics\, discrete element simulations of fragmentation and\
 , last but not least\, field data from over 4000 fragments.\n\nWe found [1
 ] that stress fields determine fragmentation patterns (albeit in an averag
 ed sense) and a vast majority of naturally occurring stress fields produce
  patterns which yield fragments with cuboid averages.\n\nWhether and to wh
 at extent these findings vindicate Plato's views and how they are related 
 to the Gömböc are interesting subjects which I am happy to discuss if ti
 me admits.\n\n[1] https://www.pnas.org/content/117/31/18178.short\n\n
LOCATION:zoom 853 4440 7455 - for password email  hh463@cam.ac.uk 
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