an EXPOSITION of the OCTorb

I drew up a little Conspiracy of my own, but decided the market was crowded and never put it into action.

Above is what I've salvaged of the original. Cheers.

There is a one-sided glass, the inside is the outside is the inside, but you can drink beer out of it and IT NEVER GETS EMPTY!

The river Pregel divides the town of Königsberg into four separate land masses, A, B, C, and D. Seven bridges connect the various parts of town, and some of the town's curious citizens wondered if it were possible to take a journey across all seven bridges without having to cross any bridge more than once. All who tried ended up in failure, including the Swiss mathematician, Leonhard Euler, a notable genius of the eighteenth-century.
http://www.contracosta.cc.ca.us/math/Konig.htm

I think that this is the same Acme Co. that the Coyote gets all of his stuff from:
http://www.kleinbottle.com/

I never would have developed my hatred of mathematics if I'd had that kind of stuff in school.

The math that is taught in school, I believe, is often taught by people who don't understand it very well themselves. Trigonometry is a great example of this: every two-year-old instinctively comprehends sines and cosines, and any teacher who can't make it seem easy, must not understand the material very well.

Klein bottles and Königsberg would be neat to learn about, but I think it would be necessary for teachers to cover the fundamentals better first.

Here's everything you need to know about trig. Consider a diagonal line:

/

Do you agree that the line travels a certain distance vertically, and a certain distance horizontally? Does it seem sensible that the exact amounts of horizontal and vertical would depend upon the angle?

That's all sines and cosines are. Sine says: "Tell me how far you go at a given angle, and I'll tell you how far 'up' you went". Cosine is the same thing, except it gives you horizontal distance.

The sine of a 30-degree angle is 0.500 -- or, if you like, 50%. That means if you draw a 12-inch line at an angle of 30 degrees, you end up 6 inches "up" from where you started.

Not all that hard. So why do math teachers make it such an ordeal? Why are story problems always written in a manner to foil comprehension? Even calculus is pretty simple if explained well, what's the problem here?

I think that everyone learns that the square of the hypoteneus is equal to the sum of the square of the other two sides, even the Scarecrow in whe Wizard of Oz says that after he gets a brain, but nobody much ever uses that. Like in surveying, if I lay-out a rectangular building, even though I turn 90° angles on the corners, I'll still measure diagonals to see that they match and also calculate a diagonal to see that the actual matches the theoretical. Instead of chopping down trees that may be on a property or a control line, it is possible to measure-off some angle and figure an arc-tangent. I like watching big radial curves take shape by chord and deflection angles. Sometimes, curves involve a Point of Curve (radial,) Point of Spiral Curve, another Point of Curve (radial,) and back to Point of Tangent. There are curves that are both horizintal and vertical, the vertical curves often being catenary curves, how a chain would hang if suspended between two points. Catenary sounds like a cross between a cat and a canary, but it's from the Latin word for chain. One surveyor
that I worked with could figure out almost anything using triangles, but he couldn't tell me the angle of inclination of the side of a pyramid. If you have four equal triangles, let them touch at the base and fall inward to make a pyramid, the angle of inclination is always the same, regardless of the size of the pyramid. The guy could figure the altitude of a triangle, but got lost with the tangent part. Anyway, since the Global Positioning System, geodesy is a lot easier, but layout, it's still useful to know some trig.

After having read Richard Feynman's anecdote books I wished I had paid more attention in physucks back in high school. I wrote a math placement test last spring for a program I never ended up going into, but was accepted anyway, despite the fact that I scored below 20% on the test: after not having used any more math than what is required to determine tax on a purchase, tips, or the "Girls = Evil" joke, the questions on that exam, that only three years ago would've been laughably (or at least deal-with-ably) easy, had me stumped beyond stumping. I can figure enough to get by with Pascal programming, and I find myself now more drawn to philosophical logic, but nonetheless few things are finah than simplifying some horrendously ugly quadratic equation into a term. But now I have to stop and think hard before doing anything beyong grade 9 algebra. When bases are multiplied their exponents are added, right? At least I can remember the terms...

One time I missed a math 12 class (the first time round), my mom had signed me out of school so I could be one of the first to see the Star Wars re-release.

Maybe Lou could post some tutorials? That trig bit was slick.

Ween last night. Ween tonight.

There's a Portland band going to play here on Oct. 6 named Quasi; they used to be Heatmiser and got an Oscar nomination for "Good Will Hunting" My brother's old band was supposed to do some soundtrack for a Clint Eastwood western, but they had great difficulty showing-up for anything in those days. I used to like this slide guitar player named Ry Cooder, he's done a boatload of movie soundtrack stuff. I guess that's one way to make a living as a musician. The Quasi show is only $8! Such a deal!

random test pattern... 55-octet... MUST QUIT JOB

Yeah, 'Motorgoat' and 'Bugskull Split' sound good!

Thanks! If you've got any math questions, sure, I'm game to entertain 'em. Our good Prussian King seems to know his stuff as well.

It's even on-topic because most people hate math.

I'd also be happy to talk about Pascal programming. Or Delphi.

I'm not an expert on math, some parts I like and understand. From learning to make topographical maps, topology was easy for me to understand. Linear algebra is not as easy as it should be, as easy as it seems for some people. I have gotten interested in nanotechnology which has meant that I have to study more physics and chemistry. Stuff like faster-than-light communication and string-theory seem to still be developed. Molecular chemistry seems very interesting, and there certainly are some spiffy computer programs to model molecules. Things like the Kline Bottle and Math Knots are nice. Also, fractals make sense to me.

If I had any say in these things, integral calculus would be known as The Lunchmeat Principle. Go to your favorite deli and ask for a pound of finely-sliced balogna. They'll give you a stack of slices, each one a circle of almost negligible thickness. Each slice could be measured, weighed, whatever; and if you add up the results, you have information about the original hunk of balogna that they cut up for you.

Integral calculus is a way to learn about the original hunk without actually slicing it. It's a Zen thing, where you slice by not slicing.

Things get interesting when they start on a new balogna. Instead of the circles being a uniform size, they change size until you're well and truly into the middle of the balogna. How much meat did they have to slice off to get to that point? Well, the area of a circle is pi-r-squared, and the thickness of each slice is a millimeter or two. Multiply area by thickness on each slice and you'll have a good measurement of the total meat involved.

The only problem is, the edge of a given slice may be on an angle, so it's hard to measure the radius exactly. Fortunately, some smarties came up with formulas to handle this contingency; all you have to do is find the formula that matches your scenario, and you're set.

So your job, as a calculus kind of person, is to describe the contours of the balogna, and then look in your calculus book to find the formula that handles that particular balogna scenario.

Calculus: The Adventure Begins.

Conic sections make sense, OK. Among the books on our home library shelf were Vector and Tensor Analysis and Class Field Theory; as a curious child, I wondered, "What are these things?" and marveled at the symbols and ciphers. From the statistics PoV, I think that the computer curve-fitting routines are the greatest thing since sliced bread; if there are a bunch of data points, you can ask the computer to fit the best curve. Or if the data points don't have much of a spread but are kind of bunched-up, cluster analysis. I went to a 5-day statistics seminar and the instructor is going on about a scatter of data points and adjusting a straight line through them which is both linear and unbiased, so I says, "The BLUE!" He says "What?" I says, "Best Linear Unbiased Estimator" He says, "What?" I don't think that he'd seen that acronym before, I wasn't trying to upstage him, but rather more, "Yes, I understand you so far. Good God! Get ON with it, man!" Also, there are some spiffy computer programs for optimization techniques, finding maxima and/or minima of curves, min/max. There was a kind of "Ah-ha!" moment for me when after doing this curve stuff, curves for different time frames were put together to make a topological map and we started looking at ridge traces, it was like coming home!

You have analysed the curvature of my skull and thereby deciphered my credit card number!

A teacup's a donut!

More from the Acme Co.
http://www.netsrq.com/~hahn/calc5_0.html

Wile E. Coyote is proof that intelligence doesn't make you happy.

It's like Pinky and the Brain: if I had to be one of the two, I truly don't know which one I would prefer to be.

You've mentioned that before, Lou. Ignorance is bliss, but I'd be happier hatching schemes, so I'd have to pick the Brain.

www.theonion.com/onion3731/not_flesh-eating_zombie.html

swallows 11 spiders per year, while sleeping. So the question to ask yourself now is, "which month last year did I NOT swallow a spider?"

First of all, it's supposed to be eight spiders.

Second, it's not true. Lady columnist, few years back, decided to show how old wives' tales could easily become fact, unattributed on web page after web page. Succeeded beyond her wildest dreams.

http://www.snopes2.com/spoons/fracture/spiders.htm

However, Fig Newtons are full of fig wasps, so it evens out.

As usual, you're right. About both. Crunchy wasps!