Look, I haven't mentioned Zeus, Buddah, or some religion.
I think this is just really cool. A "Smith hat" is a 13-sided polygon that fits the bill: a single shape that can cover a surface without ever repeating. Somebody came up with the idea of shining light through a transparent surface covered by the Smith hat shape. . .Quote
Researchers from the Institute of Industrial Science, The University of Tokyo experimentally demonstrate unique optical behavior from a long-sought aperiodic pattern. Credit: Institute of Industrial Science, The University of Tokyo
In a study published in Nature Communications, researchers from the Institute of Industrial Science, The University of Tokyo, and collaborating institutions built optical structures inspired by the "Smith hat." This unusual shape is known for solving the so-called Einstein problem in mathematics. When the team illuminated the structures with laser light, they observed diffraction effects unlike those seen in conventional quasicrystals.
The Einstein problem asks whether a single tile shape, known as a "monotile," can cover an entire surface without creating a repeating pattern.
Familiar tilings such as checkerboards and honeycombs repeat in a regular way. An aperiodic monotile, by contrast, can fill a surface without ever settling into a repeating arrangement.
[. . .]
"What is especially fascinating about the hat tile is that, although the resulting pattern appears irregular at first glance, it is actually constructed from the honeycomb lattice," says lead author Yuto Moritake. "We wanted to see whether this unique shape could also produce any unexpected physical phenomena."
To test that possibility, the researchers created nanoscale versions of the pattern on silicon nitride films using electron beam lithography.
When laser light was directed at the structures, the resulting diffraction patterns formed distinctive pinwheel-like shapes. These patterns directly revealed the chiral character of the aperiodic structure.
Chirality refers to a form of handedness in which a structure and its mirror image cannot be perfectly matched. In this case, the unusual arrangement of the monotile pattern caused the light itself to display a chiral response.
"We found that the diffraction patterns themselves become chiral because the structure lacks mirror symmetry," explains senior author Masaya Notomi. "This kind of optical response is fundamentally different from that observed in conventional quasicrystalline materials."
[Continues . . .]
That kind of sang froid is something I don't have. It was a Waldorf school, and I didn't want to terrorize the students. At least beyond a little math. Please don't judge, I just needed the money. I modified my previous post. It should have read ..."thought came to me..." I missed to the word "came".