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Wednesday, November 26, 2014

A Tetrahedral Fano-Plane Model

Filed under: General,Geometry — Tags: — m759 @ 5:30 PM

Update of Nov. 30, 2014 —

It turns out that the following construction appears on
pages 16-17 of A Geometrical Picture Book , by 
Burkard Polster (Springer, 1998).

"Experienced mathematicians know that often the hardest
part of researching a problem is understanding precisely
what that problem says. They often follow Polya's wise
advice: 'If you can't solve a problem, then there is an
easier problem you can't solve: find it.'"

—John H. Conway, foreword to the 2004 Princeton
Science Library edition of How to Solve It , by G. Polya

For a similar but more difficult problem involving the
31-point projective plane, see yesterday's post
"Euclidean-Galois Interplay."

The above new [see update above] Fano-plane model was
suggested by some 1998 remarks of the late Stephen Eberhart.
See this morning's followup to "Euclidean-Galois Interplay" 
quoting Eberhart on the topic of how some of the smallest finite
projective planes relate to the symmetries of the five Platonic solids.

Update of Nov. 27, 2014: The seventh "line" of the tetrahedral
Fano model was redefined for greater symmetry.

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