04/12/2023
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Did you Know? ๐ค
๐ฉโจ "The Hat" Solves a 60-Year Geometry Puzzle! โจ๐ฉ
In a surprising turn of events, a retired printing technician from northern England, David Smith, may have cracked a 60-year-old geometry problem using a newfound 13-sided shape affectionately dubbed "The Hat." Resembling a fedora, this shape is classified as an "einstein," capable of flawlessly covering a surface without any repeated patterns, an accomplishment previously unattained with a single tile.
Smith, not a professional mathematician, stumbled upon this breakthrough in November 2022. Collaborating with two academics, he published a self-published scientific paper about "The Hat," sparking excitement in the mathematical community.
๐ง From 20,426 to One: Aperiodic Tiles Unveiled
Most wallpapers or tiles are periodic, featuring repeated clusters. However, "The Hat" breaks the mold as an aperiodic tile, covering a surface without gaps and resisting periodic repetition. Historically, mathematicians believed aperiodic sets were impossible until the 1970s when physicist Roger Penrose reduced potential shapes to two in what is now known as Penrose tiling.
๐ต๏ธโโ๏ธ The Unexpected Mathematician
Smith, not a math enthusiast, started delving into the problem in 2016 through a blog. In 2022, he reached out to Craig Kaplan, a professor at the University of Waterloo. With the help of software, they recognized the significance of "The Hat."
๐จ Artistic Impact and Open Source Accessibility
Dubbed a simple polygon, "The Hat" has inspired artistic renditions, quilts, cookie cutters, TikTok explainers, and even made it into a Jimmy Kimmel monologue. Publicly available, including for 3D printing, "The Hat" is not copyrighted, encouraging its use in various creative endeavors.
๐ง What's Next? "The Turtle" Sequel
Already exploring a "sequel" named "The Turtle," Smith's constant quest for new shapes demonstrates his passion for mathematical discovery.
๐ฌ Awaiting Peer Review
While the scientific paper, coauthored with Joseph Myers and Chaim Goodman-Strauss, awaits peer review, the potential impact across various research fields, including physics and chemistry, has mathematicians and scientists eagerly anticipating the confirmation of this groundbreaking discovery. Stay tuned for updates on "The Hat's" journey through peer review and its potential ripple effects in the world of mathematics and beyond! ๐๐
Reference: https://edition.cnn.com/2023/04/06/world/the-hat-einstein-shape-tile-discovery-scn/index.html
Prepared and Designed by: Aloysius Francois R. Reyes
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