now with 5-way symmetry made obvious (version ii)

March 31, 2015 in desargues

cf

the second, smaller, sketch is from
desargues’ theorem in color (but let’s call it
desargues’ rainbow from here on
to match fano’s rainbow,
posted the next day).

in the first, newer, bigger sketch,
i’ve used my mystical “projective
geometry” powers to bend all the lines
into circles. so we now (as you can see)
have a red *circle* (at the “omega” point)
along with (arcs of) blue and yellow
*circles* (replacing the red, blue, and
yellow *lines* on the original [textbook]
drawing).

again, as one should expect from the
names-of-colors aspect of all this,
we find certain yellow-and-blue
point-pairs occurring on the arcs
of certain circles… and two such
circles meet in the *green* point
(green is the “blend” of yellow
and blue). and then likewise for
the other “secondary” colors: an
*orange* point at the intersection
of two red-and-yellow circles, and
a “purple” point where two red-and-
-blue circles meet.

desargues’ theorem is then that the
secondary colors are on one of the
“lines” of the system at hand.

[in this case, (an arc of) another
“wide circle” (our system consists of
ten circles; the “narrow circles”
appear as circles in the diagram
and arcs of three of the “wide”
circles are indicated by three-
-point arcs).]

Advertisement