Search Results

1. Geometry of the 4x4 Square - Elements of Finite Geometry 

   Mar 18, 2004 ... Each octad occurs within a 24-set: an array of 4 rows and 6 columns. ... a nice picture of the 35 lines in the finite projective space PG(3 ...
   finitegeometry.org/sc/16/geometry.html 

2. The Miracle Octad Generator - Elements of Finite Geometry 

   1979 AMS Notices abstract, of how the 35 4x4 structures in the MOG may be ...
   finitegeometry.org/sc/24/MOG.html

3. The Diamond Theorem in Finite Geometry 

   Jan 6, 2006 ... Finite projective geometry explains why certain graphic ...
   finitegeometry.org/sc/16/dtheorem.html

4. Cases of the Diamond Theorem - Elements of Finite Geometry

   The 35 structures of the 840 = 35 x 24 G-images of D are isomorphic to the ...
   finitegeometry.org/sc/gen/dtcas.html 

5. Notes on Finite Geometry (Site Map)

   For a finite-geometry version of the 28 bitangents to a quartic, see "Solomon's cube" below. 35. For a model of the 35 lines in the projective 3-space over ...
   finitegeometry.org/sc/map.html 

6. Diamond Theory: Symmetry in Binary Spaces - Elements of Finite ...
   

   J. W. P. Hirschfeld, Finite Projective Spaces of Three Dimensions, 1985 .... isomorphic to the 35 lines in the 3-dimensional projective space over GF(2). ... Other details on the Miracle Octad Generator are given in the reference file ...
   finitegeometry.org/sc/gen/dth/DiamondTheory.html

7. Notes Related to Diamond Theory - Elements of Finite Geometry

   Generating the octad generator The Miracle Octad Generator (MOG) of R. T. Curtis ... the 35 partitions of an 8-set into two 4-sets and the 35 lines of PG(3,2). ... Twenty-one projective partitions The author's model of the 21-point ...
   finitegeometry.org/sc/pg/dt/ 

8. “Octad Generator” « Search Results « Log24 

   Apr 28, 2011 ... ABSTRACT: Finite projective geometry explains the surprising symmetry properties of ... to the 35 lines in the 3-dimensional projective space over GF(2). ...
   

   www.m759.net/wordpress/?s=%22Octad+Generator%22

9. “latin squares” « Search Results « Log24

   Mar 13, 2011 ... ABSTRACT: Finite projective geometry explains the surprising symmetry ... to the 35 lines in the 3-dimensional projective space over GF(2). ... is closely related to the Miracle Octad Generator of R. T. Curtis– used in ...
   www.m759.net/wordpress/?s=%22latin+squares%22

10. eightfold symmetry « Search Results « Log24

    ABSTRACT: Finite projective geometry explains the surprising symmetry properties of ... to the 35 lines in the 3-dimensional projective space over GF(2). ... to the Miracle Octad Generator of R. T. Curtis– used in the construction of ...
    www.m759.net/wordpress/?s=eightfold+symmetry

11. “Solomon's Cube” « Search Results « Log24

    Sep 1, 2010 ... Whitehead on Fano's finite projective three-space: ...... isomorphic to the 35 lines in the 3-dimensional projective space over GF(2). ... to the Miracle Octad Generator of R. T. Curtis– used in the construction of the ...
    www.m759.net/wordpress/?s=%22Solomon's+Cube%22 
    

12. “79T-A37″ « Search Results « Log24

    Nov 20, 2010 ... ABSTRACT: Finite projective geometry explains the surprising symmetry ... to the 35 lines in the 3-dimensional projective space over GF(2). ... is closely related to the Miracle Octad Generator of R. T. Curtis– used in ...
    www.m759.net/wordpress/?s=%2279T-A37%22
    

13. The Diamond Theorem - a knol by m759

    Jul 24, 2008 ... Finite projective geometry explains the surprising symmetry properties of ... to the 35 lines in the 3-dimensional projective space over GF(2). ... is closely related to the Miracle Octad Generator of R. T. Curtis-- used ...
    knol.google.com/k/m759/the-diamond-theorem/.../2 
    

14. The Diamond Theorem

    The Miracle Octad Generator http://finitegeometry.org/sc/24/MOG.html ... Finite projective geometry explains some remarkable symmetries of graphic designs. ...
    www.scribd.com › Research › Math & Engineering
    

15. Geometry

    Mar 18, 2004 ... Apart from the octads that are themselves bricks, ... array also provides a nice picture of the 35 lines in the finite projective space PG(3 ...
    www.scribd.com/doc/54536748/Geometry
    

16. Steven H. Cullinane's Harvard Weblog

    Sep 22, 2005 ... isomorphic to the 35 lines in the 3-dimensional projective space over ... correspond to the 35 three-point lines of the finite ... of the 4x4 patterns is closely related to the Miracle Octad Generator (pdf) ...
    blogs.law.harvard.edu/m759/page/2/
    

17. Cullinane Journal 2002 Jul. 15-31

    ABSTRACT: Finite projective geometry explains the surprising symmetry properties of ... to the 35 lines in the 3-dimensional projective space over GF(2). ... of the 4x4 patterns is closely related to the Miracle Octad Generator of R. T. ...
    log24.com/blog/0207b.html
    

18. Diamond Theory References
    

    Sep 27, 2001 ... Curtis, R. T. Eight octads suffice Journal of Combinatorial ...
    log24.com/notes/refs.html

19. Kernel of Eternity

    Aug 13, 2007 ... (It induces A8 on the octad, the kernel of this action being the ... the group of 6 automorphisms of the projective line over the 2-element field. ... system of 35 objects (not unlike the 35 lines of the finite geometry ...
    log24.com/log07/saved/070813-Kernel.html
    

20. Diamond Theory: Symmetry in Binary Spaces

    Jun 21, 2000 ... 51E20, Combinatorial structures in finite projective spaces. ... isomorphic to the 35 lines in the 3-dimensional projective space over GF(2). ... Other details on the Miracle Octad Generator are given in the reference ...
    m759.tripod.com/theory/dtheory.html
    
    
21. [PDF] Sonderdruck aus Arch. Math., Vol. 42, 89—9B (1984) 0003-8SQ4Xf8 ...
    

    File Format: PDF/Adobe Acrobat -
    
    (projective) dimension n over a finite field with q elements (cf. ... The particular space PG(3, 2) has 15 points, 35 lines and 15 planes. .... we arrange coordinates such that the 8 last coordinates form an octad X. We Write ...
    www.mat.univie.ac.at/~neum/scan/29