Photo on 11-28-15 at 10.22 AM

Photo on 11-28-15 at 10.23 AM #2

Photo on 11-28-15 at 10.20 AM

Photo on 11-28-15 at 10.20 AM #2

Photo on 11-28-15 at 10.21 AM

Photo on 11-28-15 at 10.23 AM

Photo on 11-28-15 at 10.34 AM

(seven chords seven ways, part mercury)

Photo on 11-27-15 at 2.57 PM

seven signs in seven positions.
and days-of-the-week and ages-of-
-man and whatnot… the trivium &
quadrivium… may be superimposed
in various interesting ways.
the seven principles of UU will
eventually be invoked if this
is ever (again) the basis of a
sermon by me. “window crayons”
on cardboard box; 2015.

seven stories, part zero.

Photo on 11-27-15 at 11.33 AM

three newish guitar-stands arranged in such a way
that any two will fall down without the third.
and madeline’s “three women” statue, having a
similar property. blessings from our happy home
to yours if you’ve got one; double blessings if
you’re doing without. happy “black friday”.

the linking and not-linking rings
(blogpost of 05/03/014).
flickr shot.

Photo on 11-24-15 at 6.14 PM

that 7-space has seven-way symmetry is obvious
(rotate the drawing by 2\pi/7—about 51.43\degrees—).

but the *three*-way symmetry isn’t so obvious.
here it is in its 7-color wonder.

we’ve chosen to fix the “Mud” point at the top.
we then chose the “secondaries” line
{Green, Purple, Orange} and permuted;
the “primaries” permute accordingly;
a 2-way symmetry can be displayed by “swapping”
each primary with its “opposite”:

i call this one “reflection in the Mud”.

(one may also… of course… reflect
in any of the other colors;
for each (there are three)
“line” through a given color,
interchange the positions for
the other two colors.
the lines-on-blue are
{bgy, bmo, bpr}, so
“reflection in the Blue” has
as its permutation-notation.)

the orange blend

Photo on 11-24-15 at 2.28 PM

exercise: draw the other six lines.

about time these guys got some names.
ROY (this one) is obvious.

let’s see.
green blend.
bgy byg gby gyb ybg ygb;
GABY, then.

gop gpo ogp opg pgo pog;
PEGGIE-OH, then, maybe.

the orange blur.
bmo, bom, mbo, mob, obm, omb.
JIMBO comes to mind.

submissions welcome. yes, it’s the great
name-the-lines contest of ought-fifteen!

i’ll be forced for the sake of my own peace
of mind to type out the rest of the exercise
and make up three more names. “the purple
blur” isn’t much of a *name* for a line.
more like a *secret identity*.

Photo on 11-23-15 at 6.18 PM

or, the fano plane presented symmetrically.

each of the three triangle-edges
found along any of the “long lines”
(joining vertex-to-vertex
on the biggest 7-point “star”)
is a “line” of rainbow-space.

check it out. the “points” are
Mud Red Blue Green Purple Yellow Orange
the lines are MRG, RBP, BGY, GPO, PYM, YOR, OMB.

here’s a version from last year.
this new one’s much cooler.

Photo on 11-20-15 at 3.32 PM

formed by my right hand. i got a new shipment
of strings today… thanks, madeline!… so i
(finally!) tuned up one of my guitars “lefty”.

if i try to *play* it that way, it sounds like
day one. but if i play it *right* handed, i
can make it sound like music. the chords and
the dynamics are different, though. so, cool
trick, it sounds like somebody else playing
(while still sounding a lot like me).

or maybe that’s the cough syrup talking. whee!


Photo on 11-17-15 at 10.44 AM

while you still can.

Photo on 11-17-15 at 10.43 AM

consider ordinary (x,y,z) space.
co-ordinatize a “unit cube” in the all-positive octant.
put “primary colors” on the axes. next slide.

from the edges of the cube, “cut out” the three that
pass through the Origin of our system—i.e., (0,0,0).

distort the resulting diagram so that the “top face”
(and the “missing” bottom face) remain *square*. i’ve
shown this “flattening out” in two steps: once as a
truncated-pyramid in a “3-D” view, and then as a
fully-flattened 7-vertex “graph”.

meanwhile, introduce the secondary colors… in the
“natural way”.

all this is pretty old hat around here. you could
look it up.

the novelty here is the stick-figure iconography
(each of the “icons” has the “top of the cube”
represented by the square-in-the-middle; the
three nonzero vertices of the “bottom” of the
cube appear along the top and right-hand “sticks”
of a given icon).

each of these 7 icons now represents a
*linear equation*; these are precisely
the equations of the 7 2D-subspaces-
-through-the-origin of the vector-space
{(0,0,0), (0,0,1), … , (1,1,1)}
having exactly eight vectors.

one can calculate directly on the icons
(rather than the triples-of-numbers or
the colors) using “set differences”.

but that’s it for today.

Photo on 11-17-15 at 10.46 AM

saturday night i colored in the corners of this cube.
the underlying black-and-white is based on a work of
the great dutch artist m.~c.~escher. the cardboard
cut-out version is from a collection by the american
mathematician doris schattschneider.

anyhow, i’ve had the whole “5 platonic solids” set
from this work on display in the front room at home
for a while. the others are in color already, right
out of the book. i’ve had *another* set of these,
too: it’s a great “book” and might still be in print
for all i know. i had two editions, from years apart,
years ago.

i took this one to church on sunday and used it in my talk.
there wasn’t time to explain why i’d colored it the way i
did. but i *did* count the symmetry group of the cube,
two ways. any talk by me should have a theorem in it;
i’m happy to count that as a theorem.

24 because any of the 6 faces can be “face down”,
and each such choice-of-face allows for any of 4
remaining faces then to “face front” (all but the
“face-up” one *opposite* to our “chosen” face).

but also 24 because
1 identity
6 180-degree “flips” that fix two edges
(one for each pair of opposite edges)
8 120-degree “corner-turns”
(fix a pair of opposite corners;
there are 4 such; one may “turn”
right or left)
6 90-degree “face turns”
(fix opposite faces—3 ways; again,
one can go “right” or “left”)
3 180-degree face turns.

and this messy version is actually quite clear when
one is actually holding up an actual cube and pointing
at the drawing on the board. or in this case, at one’s
own sweatshirt. canvas makes a good whiteboard.

you can do it all without even mentioning “group theory”…
and i *sure* didn’t get to prove that this set of 24
“moves” gives a version of “the symmetric group on 4
objects”. anyway, part of the point is that one need
not have introduced any “math code” into the discussion
at all to arrive some some *very* useful results.

i learned the symmetry-groups-of-solids trick from an
old master
. i mentioned this book in the service.

but mostly i talked about stuff like bible studies and music.

stuff that people actually show up at church *for*. bring what
you love to church and share it. food and money are particularly

Next Page »

  • (Partial) Contents Page

    Vlorbik On Math Ed ('07—'09)
    (a good place to start!)
  • Categories


Get every new post delivered to your Inbox.