Google cullinane zenodo to . . .
View "The Square Model" or download "Notes on finite geometry."
Tuesday, February 21, 2023
For Harlan Kane: The Zenodo Files
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Friday, October 27, 2017
Monday, April 8, 2024
Alexandria Quartets*
For my own arrival at CERN, see Zenodo in this journal.
* A title suggested by the work of Lawrence Durrell and by
geometric quartets in figurate geometry.
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Thursday, April 4, 2024
Figurate Geometry: Order-5 Triangle Labelings
See also Figurate Geometry at Zenodo —
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Thursday, March 28, 2024
An Old Sci-Fi Question
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Friday, March 15, 2024
Corrections to Post from Monday, March 11
The post, on triangles and figurate geometry, has had some
minor image corrections, and these corrections have now
also been made in a new Zenodo version.
(Some aesthetic background: In the words of Alan D. Perlis,
that post concerns "a conception that embodies action and
the passing of time in the rigid and timeless structure of an
art form.")
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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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Tuesday, January 17, 2023
Alexandria Quartets
"Remember your epiphanies on green oval leaves,
deeply deep, copies to be sent if you died to all
the great libraries of the world, including Alexandria?"
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Tuesday, March 15, 2022
The Rosenhain Symmetry
See other posts now so tagged.
Hudson's Rosenhain tetrads, as 20 of the 35 projective lines in PG(3,2),
illustrate Desargues's theorem as a symmetry within 10 pairs of squares
under rotation about their main diagonals:
See also "The Square Model of Fano's 1892 Finite 3-Space."
The remaining 15 lines of PG(3,2), Hudson's Göpel tetrads, have their
own symmetries . . . as the Cremona-Richmond configuration.
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Friday, October 8, 2021
Thursday, May 13, 2021
New Code Link
Notes on finite geometry
by Steven H. Cullinane:
m759.github.io is the URL
for the displayed website.
A release of the site's GitHub code
now has a Digital Object Identifier (DOI) —
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Thursday, April 22, 2021
A New Concrete Model for an Old Abstract Space
The April 20 summary I wrote for ScienceOpen.com suggests
a different presentation of an Encyclopedia of Mathematics
article from 2013 —
(Click to enlarge.)
Keywords: PG(3,2), Fano space, projective space, finite geometry, square model,
Cullinane diamond theorem, octad group, MOG.
Cite as
Cullinane, Steven H. (2021).
“The Square Model of Fano’s 1892 Finite 3-Space.”
Zenodo. https://doi.org/10.5281/zenodo.4718182 .
An earlier version of the square model of PG(3,2) —
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Monday, December 11, 2017
The Diamond Theorem at SASTRA
The following IEEE paper is behind a paywall,
but the first page is now available for free
at deepdyve.com —
For further details on the diamond theorem, see
finitegeometry.org/sc/ or the archived version at . . .
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