### for hannah on the back of an envelope

almost-symmetric desargues’ theorem.
(7-color version)

5 “flat” and 5 “tall” triangles
arranged as the 10 “intersection points”
of a (so-called) pentagram.

thus far the black-and-white “underlying
diagram” (which i probably should have
photographed before coloring it in and
erasing it… it was the best b&w version
i’ve done so far, i think… oh well…).

the b&w *already* “tells the story” (if you
know how to look): the ten “triangles” are
in the ten “positions” on the “big picture”
diagram in such a way that, mutatis mutandis
(read “line” for “triangle” & “point” for
“position, to wit), one has the well-known
points-&-lines “duality” exhibited in
purely *graphical* form: not only a
“lecture without words”, but a “lecture”,
if you will, without *code itself*.

so it’d be a pretty awesome picture, done right,
&’d make a good art project for somebody patient
enough to make actual measurements & stuff.

as would the colorized version.
so, briefly.

the letters {a, b, … , j}
are posted in “positions” in such a way
that the when the “triangles”
{abc, ade, afg, bdh, … , ijk}
are “placed in” the appropriate positions
(as is done here)
one has each letter-triple in the position
of its *dual* letter (“a” to “ijk”, eg.;
one should probably look at some other
now replace all the letters with colors
according to the scheme pictured at right.
(whose connection with the “fano plane”
[& “vlorbik’s 7 color theorem”] is solid
but we don’d have to go into it here.)

happy neighborhood of yr b’day.
thanks for your part in, you know,
teaching me to read & bringing me
back from the dead and all that.

PS the *actually* symmetric version has
the ten “lines” modeled as *diagonals
of an dodecahedron* (the “diameters”
connecting opposite vertices; there
are of course 20 such…);
the “asymmetric” (textbook) version
has a *marked* point (and, of course,
a “marked” dual line…); never mind…