monotile
English
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Etymology
[edit]Pronunciation
[edit]Noun
[edit]monotile (plural monotiles)
- (geometry) A prototile tiling monohedrally; any shape able to completely tile some space on its own (allowing for translation, rotation, and reflection).
- Hyponym: einstein
- 1995, Marjorie Senechal, Quasicrystals and Geometry, Cambridge, Cambridgeshire: Cambridge University Press, →ISBN, page 208:
- In the following section we will describe families of tilings by a curious three-dimensional aperiodic monotile whose matching rule — for some values of its parameter — is weak but not strong.
- 1997, Rudy Rucker, Freeware (Ware Tetralogy; 3), New York, N.Y.: Avon Books, →ISBN, page 69:
- And I am sorry I never delivered on the four-dimensional Poultry design. It turns out John Horton Conway found four-dimensional and five-dimensional aperiodic monotiles sixty years ago, but it's not too well documented.
- 2007 March, Joshua E. S. Socolar, “More ways to tile with only one shape polygon”, in The Mathematical Intelligencer, volume 29, number 2, New York, N.Y.: Springer, , →ISSN, →OCLC, page 33:
- This naturally led to serious rumination about the possible existence of a single tile, or monotile, that forces non-periodic global structure.
- 2023 April 4, Matthew Cantor, “'The miracle that disrupts order': mathematicians invent new 'einstein' shape”, in The Guardian[1], London: Guardian News & Media, →ISSN, →OCLC, archived from the original on 2023-04-04:
- An aperiodic monotile never repeats a formation, no matter how long the pattern.
Related terms
[edit]References
[edit]- Siobhan Roberts (2023 March 28) “Elusive 'Einstein' Solves a Longstanding Math Problem”, in The New York Times[2], New York, N.Y.: The New York Times Company, →ISSN, →OCLC, archived from the original on 2023-04-04: “Dr. Goodman-Strauss had raised this subtlety on a tiling listserv: "Is there one hat or two?" The consensus was that a monotile counts as such even using its reflection.”
Further reading
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Einstein problem on Wikipedia.Wikipedia
