start one dimension up and form a quotient space. or start with ordinary n-space and add “infinite” points.

Photo on 2011-01-31 at 19.49

so here’s my latest version of P_2({\Bbb F}_3),
the two-dimensional projective space constructed on
the field of three elements.

and the story. there are thirteen “windows”.
through each window, one sees a “line”.
each line is associated with four windows;
these in their turn, upon “looking through”,
show the four lines through the original window.

i went through essentially the same explanation
(on an earlier drawing of a different space) here
(and left a bunch of footnotes).

my post, “some finite projective spaces”
consists of a bunch of photos of zines with pictures
of projective spaces in them; some of these could
be considered “drafts” of this version of P_2(F_2).

i’m trying to make stuff simple where possible.
there’s been some progress since *this*:

Photo on 2011-01-31 at 20.08


  1. one might as well mention *verbal* descriptions
    (bypassing the “y = mx + b” formalism):
    our left-hand column, top-to-bottom, reads
    “across the middle,
    across the top,
    across the bottom,
    straight-up on the left”
    and is followed by
    “rise from the middle,
    rise from the top,
    rise from the bottom,
    straight-up from the middle”.
    sometimes there’s no chalk.

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