## Archive for April, 2011

a recent post in *KTM* asked why

.

i know that one.

the “graph” in the upper right is K_4…

the “complete graph on 4 vertices”…

and has *6* (so-called) edges.

its “complement” (upper left) has *none*

of the edges. obviously there’s one

(so-called) *complete* graph having

all six possible edges and one “empty”

graph having *none* of the edges.

move down to the next couple lines:

the graphs having exactly *one* edge

match up in one-to-one fashion

with the graphs having *five* edges

(because “including five (edges)”, in this context,

is the same as “leaving out *one* (edge) out”.

so on for two-edge graphs.

each is the “complement”

(via the inclusion-exclusion principle

as hinted at a moment ago)

of a *four*-edge graph.

posting; gotta go to class.

i’ve finally put the “points at infinity”

where they’ve belonged all along.

this’ll probably be the last draft

as far as “where do the points go”.

the color scheme is still almost

entirely up in the air. all i know

so far is that nobody not already

interested in maths will look

at the damn thing in b&w.

i did this before rearranging the points.

now i suppose i oughta do it again.

anyhow there sits the plane on

the field with *two* elements

in red right inside the plane

on the field with *four* elements.

another microzine 8-pager

(one side of a single sheet

of typing paper, cut & folded).

pages 6 & 7 are this new version

of . i’ve used

the (more “obvious”) ordering

00 01 0a 0b

10 11 1a 1b

a0 a1 aa ab

b0 b1 ba bb

on the “finite points”;

last time i posted a drawing

of this space i used the weird

aa ab ba bb

a0 a1 b0 b1

0a 0b 1a 1b

00 01 10 11

.

it seemed like a good idea

at the time. part of the point

is that there *are* different

ways to go about putting in

a co-ordinate system.

but mostly i just wanted

to see how it would look.

calculator thread in *walking randomly*.

john d.~cook on sliderules.

i’ve just edited in a subscript-backslash-zero

to the top line…

which now reads …

to repair an *earlier* repair, done sloppily.

somewhere along the line i tacked on the “—{(0,0)}”

*without* adjusting the “zee-cross-zee” ().

a beginner-like blunder, i confess. onward! *more* mistakes!

(just get down in the dirt and *calculate*, by golly.)

anyhow, owners of *Math Ed Zine* #0.4— by name—

should please to adjust the appropriate page in their issues.

which, being interpreted, means that

the set of *rational numbers* (**Q**) can be

represented as the collection of *lines through

the origin* (in the usual *(x,y)*-plane),

having *rational slope*. The slope condition,

for a given line, is equivalent to the condition

that there be an *integer* pair lying on the line

(nonzero; it gets to be something of a pain…).

the algebraic process whereby S…

nonzero-integer-pairs…

“maps onto” **Q**

is called “factoring by a relation”.

the relation in this case is called “tilde” (~).

tilde is defined by

” (x_1, y_1) ~ (x_2, y_2)

MEANS THE SAME THING AS

x_1 * y_2 = x_2 * y_1″

(“cross-multiplication” is in effect;

tilde is the relation we want “because”

when ).

oh heck. there’s that infinite-sloped line.

belongs to S/~, too. OK. modify the .

let’s call it , say. okay.

that’s it.

.

two hours fly by like nothing… working exercises

with one student at a time is generally the best part

of the whole lifetime-math-teacher trip.

there’s quite a bit of homework for 151 students

to work out this week… and then to digitize.

putting the answers into the computer interface

can be expected to present *lots* of problems.

but this level of coding is easy enough for *me*,

so part of how i was able to help with

in a couple of instances was translating.

handwritten work leading to

might be entered as

(-I, -3*2^.5/2)U(-3*2^.5/2,0)U(0,3*2^.5/2)U(3*2^.5,I)

—which is anyway much more trouble to type

than the handwritten version is to write out.

the student bringing this up already had (essentially)

correct code; maybe this is easier than i think.

we’ll see how it goes i guess.

PS

first quiz.

my latest rant mentioned the reason

this was postponed from tuesday to thursday

(or from T to R as i’m likely to use in handwriting):

computer security snafu. so i got a hardcopy on W

and created two slight variants in .

got those run off in the printing office.

and i spread ’em around around the room

with the allotted 15 minutes left to go

(versions alpha and beta to alternate columns).

took the roll for the first time ever and copied

names into “seating chart” order in my notes;

an old habit. everybody handed in with time

to spare; good.

i haven’t graded ’em yet (more or less of course).

but i glanced at a few of the papers and saw

*lots* of right answers including those on

at least one “perfect” paper. looks like it’ll be

“so far, so good” when i’m passing ’em around.

here’s hoping.

the procedure for TA’s administering quizzes:

log into the “secure site” with your university password;

print out hardcopies and run off copies (one does *not*

have direct access to the copying *machines*, however…

run ’em off at your own expense or wait your turn

at the department’s copy center).

so far so good if the system actually worked.

but no such luck. when i got the email with

the link to the originals over the weekend,

i went and glanced at the link; okay.

there appears to be a quiz here. but i don’t

own a printer so i waited until i was on campus

to begin creating the actual paper documents.

whoops. locked out of the system. no time

to fix it. gotta postpone the quiz.

naturally there’s some resentment from the class;

naturally i’ll take a great deal of the blame.

(fortunately for me there were others suffering

the same problem or the *administration*

would presumably go ahead and blame me, too.)

in the twentyfirst century economy there’s *usually*

a robot between me and whatever i want.

and the more i want it? the more of my time

the robots will burn up uselessly while i try

to get it. telephones? your service *will* fail

and if you try to get it fixed, prepare to wait

on hold for a long time before you can get

to the menu with no option remotely like

serving your needs. home internet connection?

same thing, but worse (on my model because

i actually *want* to be online but not to talk

on the god-damn telephone). and don’t even

try to get me to *think* about health insurance.

look, i like breathing in and breathing out

as much as the next guy. but when does

this become unacceptable?

(here’s last year’s why i don’t

live at the p.o..)