"Tiling with Three Polygons is Undecidable"
Erik D. Demaine; Stefan Langerman 17 Sep 2024
Abstract
We prove that the following problem is co-RE-complete and thus undecidable: given three simple polygons, is there a tiling of the plane where every tile is an isometry of one of the three polygons (either allowing or forbidding reflections)? This result improves on the best previous construction which requires five polygons.
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It remains open whether tiling …
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Sonnet 089 - LXXXIX
Say that thou didst forsake me for some fault,
And I will comment upon that offence:
Speak of my lameness, and I straight will halt,
Against thy reasons making no defence.
Thou canst not, love, disgrace me half so ill,
To set a form upon desired change,
As I'll myself disgrace; knowing thy will,
I will acquaintance strangle, and look strange;
Be absent from thy walks; and in my tongue
Thy sweet beloved name n…
Sonnet 026 - XXVI
Lord of my love, to whom in vassalage
Thy merit hath my duty strongly knit,
To thee I send this written embassage,
To witness duty, not to show my wit:
Duty so great, which wit so poor as mine
May make seem bare, in wanting words to show it,
But that I hope some good conceit of thine
In thy soul's thought, all naked, will bestow it:
Till whatsoever star that guides my moving,
Points on me graciously with fair a…