### same space, different day

probably my best-looking version
of $P^2(\Bbb F_4)^*$ so far
(but is graph paper “cheating”?).
[* this paragraph has no footnotes;
that’s a “star” standing for “dual”
rather than an asterisk: “the *dual* of
the two-dimensional projective space on
the field of four elements”]

meanwhile, i’ve played 21-tac-toe
right on the board a couple times

once one had memorized the board
(all 21 “lines”… the five circles in any
of the 21 “cross” diagrams here
are arranged in the pattern of a line
in the “big space” consisting of
the “crosses” [points of the space]),
the game would begin to very-closely-
-resemble “ordinary” tic-tac-toe:
just sketch a single cross and start
alternating X’s and O’s in the usual way.

all five points of any line wins;
otherwise count sets of four-on-a-line.

the last point isn’t played
(since there are an odd #

so far the alphabetical version is easier.