FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W2017443311> ?p ?o ?g. }

• W2017443311 endingPage "818" @default.
• W2017443311 startingPage "799" @default.
• W2017443311 abstract "Aristotle contended that (regular) tetrahedra tile space, an opinion that remained widespread until it was observed that non-overlapping tetrahedra cannot subtend a solid angle of 4π around a point if this point lies on a tetrahedron edge. From this 15th century argument, we can deduce that tetrahedra do not tile space but, more than 500 years later, we are unaware of any known non-trivial upper bound to the packing density of tetrahedra. In this article, we calculate such a bound. To this end, we show the existence, in any packing of regular tetrahedra, of a set of disjoint spheres centered on tetrahedron edges, so that each sphere is not fully covered by the packing. The bound on the amount of space that is not covered in each sphere is obtained in a recursive way by building on the solid angle argument. The argument can be readily modified to apply to other polyhedra. The resulting lower bound on the fraction of empty space in a packing of regular tetrahedra is 2.6…×10−25 and reaches 1.4…×10−12 for regular octahedra." @default.
• W2017443311 created "2016-06-24" @default.
• W2017443311 creator A5009624693 @default.
• W2017443311 creator A5060735452 @default.
• W2017443311 creator A5079752291 @default.
• W2017443311 date "2010-10-14" @default.
• W2017443311 modified "2023-09-25" @default.
• W2017443311 title "Upper Bound on the Packing Density of Regular Tetrahedra and Octahedra" @default.
• W2017443311 cites W1968836887 @default.
• W2017443311 cites W1981804590 @default.
• W2017443311 cites W1994442402 @default.
• W2017443311 cites W2034430120 @default.
• W2017443311 cites W2053911766 @default.
• W2017443311 cites W2072920688 @default.
• W2017443311 cites W2083379047 @default.
• W2017443311 cites W2138706582 @default.
• W2017443311 cites W2142823388 @default.
• W2017443311 cites W2159130720 @default.
• W2017443311 cites W3098845077 @default.
• W2017443311 cites W3100999267 @default.
• W2017443311 cites W4211043430 @default.
• W2017443311 doi "https://doi.org/10.1007/s00454-010-9304-x" @default.
• W2017443311 hasPublicationYear "2010" @default.
• W2017443311 type Work @default.
• W2017443311 sameAs 2017443311 @default.
• W2017443311 citedByCount "14" @default.
• W2017443311 countsByYear W20174433112012 @default.
• W2017443311 countsByYear W20174433112013 @default.
• W2017443311 countsByYear W20174433112014 @default.
• W2017443311 countsByYear W20174433112015 @default.
• W2017443311 countsByYear W20174433112016 @default.
• W2017443311 countsByYear W20174433112017 @default.
• W2017443311 countsByYear W20174433112018 @default.
• W2017443311 countsByYear W20174433112020 @default.
• W2017443311 countsByYear W20174433112021 @default.
• W2017443311 countsByYear W20174433112023 @default.
• W2017443311 crossrefType "journal-article" @default.
• W2017443311 hasAuthorship W2017443311A5009624693 @default.
• W2017443311 hasAuthorship W2017443311A5060735452 @default.
• W2017443311 hasAuthorship W2017443311A5079752291 @default.
• W2017443311 hasBestOaLocation W20174433111 @default.
• W2017443311 hasConcept C105239961 @default.
• W2017443311 hasConcept C111919701 @default.
• W2017443311 hasConcept C114614502 @default.
• W2017443311 hasConcept C115624301 @default.
• W2017443311 hasConcept C121332964 @default.
• W2017443311 hasConcept C1276947 @default.
• W2017443311 hasConcept C130253271 @default.
• W2017443311 hasConcept C134306372 @default.
• W2017443311 hasConcept C183893376 @default.
• W2017443311 hasConcept C185592680 @default.
• W2017443311 hasConcept C198819137 @default.
• W2017443311 hasConcept C2524010 @default.
• W2017443311 hasConcept C2778572836 @default.
• W2017443311 hasConcept C33923547 @default.
• W2017443311 hasConcept C41008148 @default.
• W2017443311 hasConcept C45340560 @default.
• W2017443311 hasConcept C54829058 @default.
• W2017443311 hasConcept C72422203 @default.
• W2017443311 hasConcept C77553402 @default.
• W2017443311 hasConcept C8010536 @default.
• W2017443311 hasConceptScore W2017443311C105239961 @default.
• W2017443311 hasConceptScore W2017443311C111919701 @default.
• W2017443311 hasConceptScore W2017443311C114614502 @default.
• W2017443311 hasConceptScore W2017443311C115624301 @default.
• W2017443311 hasConceptScore W2017443311C121332964 @default.
• W2017443311 hasConceptScore W2017443311C1276947 @default.
• W2017443311 hasConceptScore W2017443311C130253271 @default.
• W2017443311 hasConceptScore W2017443311C134306372 @default.
• W2017443311 hasConceptScore W2017443311C183893376 @default.
• W2017443311 hasConceptScore W2017443311C185592680 @default.
• W2017443311 hasConceptScore W2017443311C198819137 @default.
• W2017443311 hasConceptScore W2017443311C2524010 @default.
• W2017443311 hasConceptScore W2017443311C2778572836 @default.
• W2017443311 hasConceptScore W2017443311C33923547 @default.
• W2017443311 hasConceptScore W2017443311C41008148 @default.
• W2017443311 hasConceptScore W2017443311C45340560 @default.
• W2017443311 hasConceptScore W2017443311C54829058 @default.
• W2017443311 hasConceptScore W2017443311C72422203 @default.
• W2017443311 hasConceptScore W2017443311C77553402 @default.
• W2017443311 hasConceptScore W2017443311C8010536 @default.
• W2017443311 hasIssue "4" @default.
• W2017443311 hasLocation W20174433111 @default.
• W2017443311 hasLocation W20174433112 @default.
• W2017443311 hasOpenAccess W2017443311 @default.
• W2017443311 hasPrimaryLocation W20174433111 @default.
• W2017443311 hasRelatedWork W127055905 @default.
• W2017443311 hasRelatedWork W1528525296 @default.
• W2017443311 hasRelatedWork W1636978544 @default.
• W2017443311 hasRelatedWork W2058731360 @default.
• W2017443311 hasRelatedWork W2114219845 @default.
• W2017443311 hasRelatedWork W2155866854 @default.
• W2017443311 hasRelatedWork W2281068894 @default.
• W2017443311 hasRelatedWork W2953340823 @default.
• W2017443311 hasRelatedWork W3022331864 @default.
• W2017443311 hasRelatedWork W4252191520 @default.
• W2017443311 hasVolume "46" @default.
• W2017443311 isParatext "false" @default.

• next