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Dennis:
 
We've found good historical notes a bit hard to come by.  Maybe because the pioneers were also protagonists in a battle of words, as champions of the old and the new methods, so had to watch what they said in print!?  Anyway, I'll include what references (below) I can lay my hands on, even referring to myself as you suggest!  (Some are not quite on the subject....but are in the general area of the geometry of statistics.)
 
Re 6 and 12, you stump me there!  Luckily Richard has come to the rescue.  My only thought had been that the term N(N+1) is common, with 6=2x3 and 12=3x4.  But Richard's ideas are much better and more specific.
 
Kind regards,
Dave
 
 
REF LIST

Box, J.F. (1978).  “R.A. Fisher, The Life of a Scientist.”  New York: Wiley. [See pages 122-129.  Biographical material (by Fisher’s daughter).]

Box, G.E.P., Hunter, W.G. and Hunter, J.S. (1978).  “Statistics for Experimenters: An Introduction to Design, Data Analysis and Model Building.”  New York: Wiley.  [See pages 197-203.]

Bryant, P. (1984). “Geometry, statistics, probability: Variations on a common theme.”  The American Statistician 38: 38-48.

Durbin, J. and Kendall, M.G. (1951).  “The geometry of estimation.” Biometrika 38: 150-158. 

Fisher, R.A. (1925).  “Applications of ``Student's'' distribution.”  Metron 5: 90-104.  [Foundations of statistics type material.]

Heiberger, R.M. (1989).  “Computation for the Analysis of Designed Experiments.”  New York:  Wiley.  [See geometry sections.] 

Herr, D.G. (1980).  “On the history of the use of geometry in the general linear model.”  The American Statistician 34: 43-47.

Saville, D.J. (2001). “A hands-on, interactive method of teaching statistics to agricultural researchers.”  In: C. Batanero (Ed.), Training Researchers in the Use of Statistics (pp 197-213).  Granada, Spain:  International Association for Statistical Education and International Statistical Institute.  [Mostly deals with my heuristic-based workshops, but has a small final section on teaching via geometry.]

Saville, D. J.; Wood, G. R. (1986).  “A method for teaching statistics using n-dimensional geometry.”  The American Statistician 40: 205-214.  [General interest paper.] 

Saville, D.J. and Wood, G.R. (1991).  “Statistical Methods: The Geometric Approach.”  New York: Springer-Verlag, 560 pp.  [Textbook for 2nd year university applied statistics courses.]

Saville, D.J. and Wood, G.R. (1996).  “Statistical Methods: A Geometric Primer.”  New York: Springer-Verlag, 268 pp.  [Easier reading introduction to the geometric approach.]