## Archive for February, 2010

jesse johnson: slide rules with john ewing.

the inert and the eternal at gyre & gimble.

### a question both deep and profound

is whether a circle is round.
in a paper by erdos
published in kurdish
a counter-example is found.

a question both real and complex
is whether a sphere is convex
the problem’s proposer
the famed leo moser
believes it depends on the sex.

lucky for you, that’s all i’ve memorized.
here’s sue v.’s math poetry wiki.

### restrict the “range” for a famous isomorphism

z:= x+yi
w:= a+bi

zw = (xa-yb) + (xb+ya)i

u:= xa-yb
v:= xb+ya

$f: \Bbb C \rightarrow M_2(\Bbb R)$
$f(p+qi) := \begin{pmatrix} p & q \\ -q & p\end{pmatrix} (p, q \in \Bbb R)$

$f(z)f(w) = \begin{pmatrix} x & y \\ -y & x\end{pmatrix} \begin{pmatrix} a & b \\ -b & a \end{pmatrix} =$

$=\begin{pmatrix} xa-yb & xb+ya \\ -ya-xb & xa-yb \end{pmatrix} = \begin{pmatrix} u & v \\ -v & u\end{pmatrix} = f(zw)$

f(z)+f(w) = f(z+w) trivially.

PS

$\begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix} \begin{pmatrix} \cos\psi & \sin\psi \\ -\sin\psi & \cos\psi \end{pmatrix} =$

$=\begin{pmatrix} \cos\theta\cos\psi - \sin\theta\sin\psi & \cos\theta\sin\psi+\sin\theta\cos\psi \\ -\cos\theta\sin\psi -\sin\theta\cos\psi & \cos\theta\cos\psi - \sin\theta\sin\psi \end{pmatrix}=$

$=\begin{pmatrix} \cos(\theta+\psi) & \sin(\theta+\psi) \\ -\sin(\theta+\psi) & \cos(\theta + \psi) \end{pmatrix}$

### go with the flow

s:=
[1^2, 2^2, 3^2, 4^2, …]=
[1,4,9,16,…]=
[n^2]_(n \in \Bbb N).

$\Bbb N$ =: “\Bbb N”
NB: 0 \in \Bbb N.
******************************************

S := x + 4x^2 + 9x^3 + …

($S = \sum_{i = 1}^\infty i^2x^i$)
******************************************
(1-x)*S = x + 3x^2 + 5x^3 + 7x^4 + …
(1-x)^2*S = x + 2x^2 + 2x^3 + 2x^4 + …
(1-x)^3*S = x + x^2

S = (x+x^2)/(1-x)^3
******************************************
(
x = 1/10

S = .1 + 4*.01 + 9*.001 + 16*.0001 + …
S ~ .150892
S = (.1+.01)/(.9)^3
S ~ .150892
OK
)

### numbertwopencil-dot-net

(pdf) “the worst test in the world” (ssat), by jesse spooneye! fuchs.
tic-tac-totality and elucidation.
this guy is unstoppable.

### bucky on zero

“… the 400 year battle
from 1200 to 1600
between the Church and science
in which the Church tried by decree laws,
torture and death
to prevent the lay use
of the cipher in calculations.

For the cipher or zero,—
brought to our civilization by the Arabs
from the Hindus,
along with their simple numerals and algebra,—
was symbol for all the non-sensorial world
soon to be popularly revealed
as a natural rather than mystical phenomenon.”
—r. buckminster fuller
untitled epic poem on the history of industrialization (1962)

### january 2010

I Relaunch(01/05) as MathEdZineBlog at the site… vlorbik.wordpress.com… of my quit-in-a-fit-of-frustration Vlorbik On Math Ed of ’07 to ’09. I offer subscriptions to the then-purely-imaginary MathEdZine (and, though of course this isn’t revealed in the post itself, I get no takers. I am not at all surprised. Heck, I’m not at all discouraged, even. “Disappointed” might not be going too far.) In Where Did That Amazing Blogroll Go? (01/05) I offer a backhanded apology for having deleted the blogroll for the relaunch; this was probably the feature I’d’ve found most attractive about VME if somehow I’d found one just like it done by somebody else before I’d ever started blogging. A fellow mathblogger with better net chops than mine… “sumidiot”… had already modified it for the new feedbased formats anyhow, so my work was finished (“feeds” are part of what I’d been so frustrated at when I’d quit, I’ll go ahead and mention). Also WDTABG? was the first in what promises to be a pretty steady stream of links lists. Probably I shouldn’t drop links here in this post for all of ’em… here’s the WordPress Archive for Jan ’10.

In Songs For Beginners: Pascal’s Triangle (01/05) I hinted at one of my ideas for the first issue of the zine. “Lectures Without Words” is a phrase I’d been dropping here and there already… for example in this post from Open A Vein (my “homepage” blog) back in December. I have indeed gone on to create four zines on this theme and have convinced myself I could probably do one a week or so… on the model of the hugely-popular-though-nobody-knows-about-it cartoon diaries of recent years… indefinitely and love doing it. Not that I will. I’ve got plenty of other ideas about math, and ed, and zines. Unless this is some monster hit, I’ll move on pretty quick I imagine. One never knows. Where was I.

in lovely dark and deep (1/07)
i slip into my “ramble” style for some
discussion of early drafts of issue zero.
i crossposted this
in order, i think, to cause a link to show
up in twittr or facebook or some other
“social” site that i’d caused to be linked
but had lost track of (this problem has
of course grown even worse in the
ensuing weeks).

then in comment thread reprint (1/08)
i continued my very-intermittent conversation
with the frighteningly-successful dan meyer
about sizzle and steak; i followed up immediately
with “continued from…“, yet another
in a never-ending line of luddite ravings.
what am *i* gonna do with it?

Vlorbik On Math Ed(1/13) is the title of this post; its contents are actually a list of links to selected posts from the blog of that name… much like this one though much better organized. I’ve revised it substantially from the version of its posting date. Usually I avoid doing this but in this context it looks like plain common sense to go ahead and over-ride that “house style” rule.

prehistory of MEdZ, part i (1/19)
tells, rather, the prehistory of the ten page news
(volume iii), with some math ed thrown in.
prehistory of MEdZ, part ii (1/21)
is a dismal failure wherein i tried to put
a photo in and it was there briefly and
even drew a comment from JD (one of
thanks jonathan). further fiddling…
specifically this photo-post (1/25)…
clobbered the picture; to heck with it.
i’ve gotten a little better at moving
pictures around with flickr and tumblr
but it’s infuriatingly “intuitive” and
i can still barely work any of it at all.
the picture that stuck… not at all by
the way… is of madeline’s scanner/printer.
i’ve made some mighty cool zines with
this thing already but i’ll probably
have to beat it to death with a goddamn
hammer before too much longer.
when it can be made to work at all…
at random as far as i can tell…
it makes gorgeous copies but
gohd knows what they cost and
anyway i can’t stand the aggro
and when it breaks soon i’m done.

### go on to have a fun time

cotton socks edition of ten cheap lessons.
Ξ meets sue v at the joint meetings.

### beneath the surface of the mud

le radical galoisien on singapore math in KTM. gatto mentioned favorably.

• ## (Partial) Contents Page

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