Judy Davis in the Marabar Caves
See also "Resplendent Triviality" in this journal.
Saturday, November 8, 2025
Monday, August 4, 2025
Tesseract Art
Some background for the NotebookLM video "Tiles to Deep Space" —
See posts tagged Quantum Tesseract Theorem, Multiplane Structure,
and March 26-29, 2006.
(The diamond theorem on a 4×4 square array involves arbitrary
permutations of rows, columns, and quadrants. These structures
correspond to sets of four parallel hypercube faces, and other such
sets, though less easily pictured, might be used instead.)
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Monday, March 11, 2024
Fundamental Figurate Geometry: Triangle Subdivision
Click to enlarge.
See as well "Triangles are Square," at
http://finitegeometry.org/sc/16/trisquare.html.
(I happened to find the Basu-Owen paper tonight
via a Google image search for "congruent subsets" . . .
as opposed to the "congruent subarrays" of
the previous post.)
Update of 3:54 PM ET Monday, March 11, 2024 —
This Stanford version of my square-to-triangle mapping
is the first publication in a new Zenodo community —
Citation for the research note:
Cullinane, Steven H. (2024). Fundamental Figurate Geometry:
Triangle Subdivision (Version 2). Zenodo.
https://doi.org/10.5281/zenodo.10822848
(latest version as of March 15, 2024)
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Sunday, March 10, 2024
Permutations of Congruent Subarrays
The groups generated as above are affine groups in finite geometries.
What other results are known from this area of research,
which might be called "groups generated by permutations of
congruent subarrays"? (Search phrase: "congruent subarrays")
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