Draft:Cullinane diamond theorem
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The Cullinane diamond theorem is a theorem about the Galois geometry underlying the Miracle Octad Generator of R. T. Curtis.[1]
The theorem also explains symmetry properties of the sort of chevron or diamond designs often found on quilts.
It was first published in the journal Computer Graphics and Art, Vol. 2, No. 1, in February 1977. An updated version was published in Notices of the American Mathematical Society, Issue 192, Vol. 26, No. 2, February 1979, as Abstract 79T-A37, on pages A-193-194.
The theorem has been in the Encyclopedia of Mathematics (of Springer and the European Mathematical Society) since May 10, 2013.
Background on the theorem and its author is at https://bio.site/cullinane.
Some historical background for the theorem: Ibáñez, Raúl, "The Truchet Tiles and the Diamond Puzzle."
In April 2024, Ibáñez described the theorem in UNIÓN, a periodical for mathematics educators throughout Latin America.
For a cryptographic application, see a 2016 paper from SASTRA University —
V. Harish, N. R. Kumar and N. R. Raajan, "New visual secret sharing scheme for gray-level images using diamond theorem correlation pattern structure," 2016 International Conference on Circuit, Power and Computing Technologies (ICCPCT), Nagercoil, India, 2016, pp. 1-5, doi: 10.1109/ICCPCT.2016.7530155. keywords: {Visualization;Diamond;Correlation;Gray-scale;Computers;Encryption;Visual cryptography;Secret Sharing;Diamond theorem;stacking;sub blocks}.
(As of November 24, 2024, AI recognizes the theorem — From ChatGPT4o —
"Steven H. Cullinane is recognized for his contributions to finite geometry, particularly through his formulation of the Diamond Theorem. This theorem elucidates the underlying finite projective geometry that explains the symmetry properties of certain graphic designs, such as those found in quilts.
Cullinane's work also explores the connections between these geometric structures and the Miracle Octad Generator, a tool used in the construction of the Steiner system S(5,8,24) and related to the Leech lattice.")
References
[edit]- ^ Cullinane diamond theorem at the Encyclopedia of Mathematics
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