## Archive for the ‘FTI’ Category

### belling the cat

john d.~cook on sliderules.

### FTI

i can never find the doggone thing
and it comes up too seldom to’ve memorized.
the grapher won’t do multiple graphs.

$\bullet$Press [APPS} key
$\bullet$Select Transfrm from the menu
$\bullet$Press 1: Uninstall
i’m throwing away the 6-year-old piece of paper
with this info on it now. you know what they say:
if you throw anything away, xerox it so you’ll have
a copy.

### sounds like making zines

easy, fun, and free: dan meyer.

### They Are Standing Still

Here’s some calculator code for yesterday’s formulae:
AANGLE
:Prompt N,R
:(1-(1+R)^-N)/R$\rightarrow$A
:Disp A, A$\rightarrow$Frac

To produce this code, first enter the programming interface (push the PRGM button). We’re creating a new program, so select NEW and enter its name (AANGLE, say). Hit enter; we’re editing the new program. Now type PRGM again (this puts us in the PRGM submenu of the programming interface); select I/O (with the “arrow” keys; I/O stands for “Input/Output”) and then select Prompt. The symbols N and R are produced with the ALPHA key in the usual way; the comma is above the 7. The rest of the code follows easily (Disp is of course also found in the I/O submenu).

Now we can forget the formula for $a_{n\rceil r}$ (and never mind the tables in the back of the book). The first thing to notice about this procedure is how doggone easy it is. Indeed, as far as I know, it’s much easier than it would be on a Windows box. It was this easy in DOS (the predecessor to Windows) since BASIC was standard on DOS boxes. Several generations of computer coders have a great deal to answer for.

### Today’s Lemniscate Problem

… is essentially an example from the text, first of all. So hopefully, that’ll inspire some reading (nobody had the right slope on this one). Here are some other remarks.

In Calc III (here’s an old blog by me), one considers polar co-ordinates (so skip the rest of this paragraph if you prefer not to think about ’em yet). Our curve $(x^2+y^2)^2 = 50xy$ “translates” into $r^4 = 50(r\cos(\theta))(r\sin(\theta))$, so we can put $r =5\sqrt{2\cos\theta\sin\theta}$ into a grapher. The “Draw” feature can then be used to produce the desired tangent line ($(x,y) = (2,4)$ gives us $\theta =\arctan({4\over2})$; input this at the prompt); this feature also produces the display ${{dy}\over{dx}}=.181818$ (or words to that effect); being translated (via the “Frac” feature, say), one has y’=2/11.

The Calc I version: differentiating both sides of the given equation gives
$D_x[(x^2+y^2)^2] = D_x[50xy]$
$2(x^2+y^2)\cdot D_x[x^2+y^2] = 50x\cdot D_x[y] + D_x[50x]\cdot y$
$2(x^2+y^2)(2x + 2yD_x[y])=50xD_x[y] + 50y\,.$
One now easily isolates the $D_x[y]$ (or ${{dy}\over{dx}}$) terms, “factors out” ${{dy}\over{dx}}$ (and “cancels” a 2): dividing by the other factor on both sides of the equation gives ${{dy}\over{dx}} = {{25y - (x^2+y^2)\cdot 2x}\over{(x^2+y^2)\cdot 2y - 25x}}$. Finally, substituting the given values gives ${2\over 11}$—by Calc I methods (and without a calculator). “Plug in” on the point-slope form; done.

### Oh, P.S.

Yesterday I posted some ramblings about presenting rational-number arithmetic to battle-scarred victims of the math wars. But I left out the saddest part. Here it is: the expensive calculators required for this class can carry out the computations in question (${2\over3}-{1\over4}$ and ${6\over7}-{5\over8})$ very easily! The code for the first, e.g., is “2/3 – 1/4$\rightarrow$Frac” (the “Frac” feature is the first option in the “Math Menu” and so requires two keystrokes; everything else is right there in front of us on the keypad—and just as it appears on the printed page, with no “implied parenthesis” or what have you [by way of contrast, in order to code, e.g., ${{5x -1}\over7}$ one must recognize that the “fraction bar” acts as a “grouping symbol” and enter (5X-1)/7; the usual mistake—5X-1/7—of course represents $5x -{1\over7}$ according to the “order of operations” conventions … and all this might very well seem sort of overwhelming, I suppose]).

And I’ve more or less begged ’em, over and over, to use their calculators for these problems! (“When you’re working out homework problems, you should do the calculations by hand for practice—computing with fractions is a big part of our course [and algebra more generally]; when you’re in a hurry or—on exams or quizzes, say—need to check your work, by all means, break out the computer … look, it’s this easy …”)

And I say this that’ll never grow tired of denouncing the pernicious influence of all this high-tech folderol on math ed. Yep. That’s the saddest part. Meanwhile, as I was hinting earlier, the most will-sapppingly frustrating part is having to show up every day and talk about this kind of stuff in the face of what seems like pretty ample evidence that whatever I say is not only ignored, but actively resisted. It beats working, I guess.

### ZBox Considered Harmful

This post is intended for TI-savvy readers. Everybody else: count yourself lucky; I’ll see you next time!

Does it bother anyone else that to get the “Standard Window” you type Zoom, 6? I mean, if it’s “standard”, oughtn’t it to be “1” (so that we could just Zoom, Enter)? I mean, in light of the simple fact that we’re going to use this feature most of the time and we’ll use the “ZBox” feature that actually inhabits the “1” position … well, never?

If there’s some reasonable explanation for this, I’d sure like to know it. I’m hard-pressed even coming up with an unreasonable explanation. Here it is. They know perfectly well how useless the damn thing is, but want to call our attention to it anyway. This would also account for the way “ZFit”, which is probably the next-most useful selection in the menu—and indeed, might even be the most useful of all if textbook problems weren’t rigged to look right in the standard window—is buried out of sight (i.e., it doesn’t immediately appear in the menu; one is forced to scroll down [or memorize its location]): the designers didn’t really want this feature at all since you can use it to avoid thinking about a bunch of things that they want you to think about. It’s a B&D language we’re dealing with on this theory.

There’s much more to be said along the same lines (in particular, any amount of ranting to do on the misfeatures associated with “Trace” [ZInteger, ZDecimal]) … but once again, there’s actual work to do. How anybody actually maintains a blog with regular content is a mystery. Maybe if one had an internet connection at home …

### FTI

Tony Lucchese’s “Choking Down Technology” (recently in Pencils Down) is a brief conference report on $T^3$. I did something similar in 2001 (and reprinted it here not long ago).

Let me just take this opportunity to mention the sadly-defunct blog “Tall, Dark, and Mysterious”, whose hostess, Moebius Stripper, made frequent mention of graphing calculators.

### It Worked Until They Fixed It

Rudbeckia Hirta posted a brief description of some computer snafus she experienced yesterday. She’s amazed at her students’ patience. Well, I’m amazed at hers. And probably at yours.

Our overlords have caused these damnable devices to take over more and more of our lives and they just keep telling me, “Get out of here, Finchley!”. And what I want to know is: how much trouble would it take for your typical technophile to feel that, say, their cel phone was too much trouble? Because it looks to me like if you had to, say, wrestle an alligator every day before you were allowed to turn the thing on, why then, you’d just have to start honing your alligator-wrestling skills pretty quick, wouldn’t you. And probably start buttonholing everyone about your latest alligator-wrestling tricks before too long in the bargain.

Or maybe, and this is my last thin thread of hope on the topic, a lot more people resent having to wrestle those alligators than I imagine—and they just won’t admit it. Maybe because their living depends on it, say. I guess I could live with that.

My next rant will have something to do with actual math.

• ## (Partial) Contents Page

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