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Smith emailed Kaplan less than a week after the publication of their paper informing him of the apparent properties of a new shape. This shape, nicknamed "the spectre", was found at the midpoint of the team's spectrum of shapes published in their paper. It was an anomaly within the spectrum of shapes
91:. Kaplan proceeded to further inspect the polykite shape. During this time, Smith informed Kaplan that he had discovered yet another shape, which he nicknamed "the turtle", that appeared to have the same aperiodic tiling properties.
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in order to help complete the proof. Myers realised that "the hat" and "the turtle" were in fact a part of the same continuum of shapes, which possessed the same aperiodic tiling properties but with sides of varying lengths.
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as it produced a periodic pattern when tiled with its reflection. However, Smith had discovered that it would produce an aperiodic pattern when tiled without its reflection.
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The team worked on a proof that confirmed the chiral aperiodic tiling property of "the spectre" and published a preprint paper in May 2023.
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to experiment with different shapes. After further experimentation using cardboard cut-outs, he realised that the shape appeared to
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The team published their proofs in a preprint paper called 'An aperiodic monotile' in March 2023.
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Smith, David; Myers, Joseph Samuel; Kaplan, Craig S.; Goodman-Strauss, Chaim (2023-03-20).
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By mid-January 2023, Kaplan enlisted software developer Joseph Samuel Myers from
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261:"'The miracle that disrupts order': mathematicians invent new 'einstein' shape"
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236:"Discovery of Elusive "Einstein" Tile Raises More Questions Than It Answers"
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380:"With a New, Improved 'Einstein,' Puzzlers Settle a Math Problem"
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is an amateur mathematician and retired print technician from
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but seemingly without ever achieving a regular pattern.
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in
November 2022 whilst using a software package called
145:"Elusive 'Einstein' Solves a Longstanding Math Problem"
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183:"Hobbyist Finds Math's Elusive 'Einstein' Tile"
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111:Publication and further proofs
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208:"Aperiodic Monotile"
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303:2024-09-26
278:2023-09-12
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