Tuesday, April 2, 2013

Baker on Configurations

Filed under: Uncategorized — Tags: , — m759 @ 11:11 AM

The geometry posts of Sunday and Monday have been
placed in finitegeometry.org as

Classical Geometry in Light of Galois Geometry.

Some background:

See Baker, Principles of Geometry , Vol. II, Note I
(pp. 212-218)—

On Certain Elementary Configurations, and
on the Complete Figure for Pappus's Theorem

and Vol. II, Note II (pp. 219-236)—

On the Hexagrammum Mysticum  of Pascal.

Monday's elucidation of Baker's Desargues-theorem figure
treats the figure as a 15420configuration (15 points, 
4 lines on each, and 20 lines, 3 points on each).

Such a treatment is by no means new. See Baker's notes
referred to above, and 

"The Complete Pascal Figure Graphically Presented,"
a webpage by J. Chris Fisher and Norma Fuller.

What is new in the Monday Desargues post is the graphic
presentation of Baker's frontispiece figure using Galois geometry :
specifically, the diamond theorem square model of PG(3,2).

See also Cremona's kernel, or nocciolo :

Baker on Cremona's approach to Pascal—

"forming, in Cremona's phrase, the nocciolo  of the whole."

IMAGE- Definition of 'nocciolo' as 'kernel'

A related nocciolo :

IMAGE- 'Nocciolo': A 'kernel' for Pascal's Hexagrammum Mysticum: The 15 2-subsets of a 6-set as points in a Galois geometry.

Click on the nocciolo  for some
geometric background.

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