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Saturday, August 17, 2013

Up-to-Date Geometry

Filed under: General,Geometry — Tags: — m759 @ 7:24 PM

The following excerpt from a January 20, 2013, preprint shows that
a Galois-geometry version of the large Desargues 154203 configuration,
although based on the nineteenth-century work of Galois* and of Fano,** 
may at times have twenty-first-century applications.

IMAGE- James Atkinson, Jan. 2013 preprint on Yang-Baxter maps mentioning finite geometry

Some context —

Atkinson's paper does not use the square model of PG(3,2), which later
in 2013 provided a natural view of the large Desargues 154203 configuration.
See my own Classical Geometry in Light of Galois Geometry.  Atkinson's
"subset of 20 lines" corresponds to 20 of the 80 Rosenhain tetrads
mentioned in that later article and pictured within 4×4 squares in Hudson's
1905 classic Kummer's Quartic Surface.

* E. Galois, definition of finite fields in "Sur la Théorie des Nombres,"
  Bulletin des Sciences Mathématiques de M. Férussac,
  Vol. 13, 1830, pp. 428-435.

** G. Fano, definition of PG(3,2) in "Sui Postulati Fondamentali…,"
    Giornale di Matematiche, Vol. 30, 1892, pp. 106-132.

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