The Missing Piece.

The article discusses the discovery of a new shape called the "hat" in mathematics, which has led to further discoveries and deepened the understanding of tiling theory. The researchers used computer software to study the hat and found recurring patterns that hinted at a possible substitution system for proving its aperiodicity. They also discovered related shapes called the "turtle" and "Tile(a,b)" that are all aperiodic monotiles. The discovery of these shapes has generated excitement and inspired artists, designers, and puzzle creators. The authors hope that their work will stimulate further research and encourage others to explore mathematics. [Extracted from the article]

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