Conchoid of Nicomedes

Stu put up a post a few days ago about trisecting an angle using standard geometric drawing techniques. I looked at it and wondered if I could validate this technique using algebra. So I dinked around for awhile, but didn't come up with a solution. Well, surely I can validate it using trigonometry, and I did. I put the calculations in a spreadsheet, and to the limits of Google's math capabilities, it does appear to be correct.

But this is really a simple looking problem. We just have three triangles, surely I can solve this problem using algebra. So I fiddled with it for another day, and eventually I did come up with something, but it has an exponent of 4, and there is no nice way to solve an algebraic equation like that.

So I have a solution of sorts, it will still require a computer to work out the actual numbers, but it doesn't require any trig. Let's see what we can find on the net. First stop is Mathematica, where they use two constants, but don't tell you where they fit in this picture. Second stop is Wikipedia, where I find this line:

"They are called conchoids because the shape of their outer branches resembles conch shells."

As for the trisection, I did pick up one insight. As angle BAC approaches 90 degrees:

• line segment j goes to zero,
• line segment AD goes to 2, and
• line segment a goes to 1,

so now triangle CAD is half an equilateral triangle, and angle BAD is 30 degrees, which is indeed 1/3 of 90.

Update May 2015: Replaced the missing diagram. Updated the quote from Wikipedia and added a link to their article. Removed the kibitzing about the original quote. Fixed a typo. Replaced the link to Stu's article.

Two Trillion Dollars

Conspiracy theories are so much fun. You can use them to explain almost anything, they are unprovable, and if you have a cynical turn of mind, they make perfect sense.

Take 9-11 for instance. The day before, Secretary of Defense Donald Rumsfeld gave a press conference complaining about the two trillion dollars that had disappeared down some rat hole in the Pentagon. The next day, 9-11 happened, and all of a sudden we are at war, and everyone forgets about the two trillion dollars. Coincidence? I think not.


Donald Rumsfeld 2.3 Trillion Dollars Just Gone Sept 10, 2001
Actually I do think it was a coincidence, but hey, it makes good fodder for conspiracy theorists. Of course, it could also be explained by black projects. The goal of any defense contractor with larcency on his mind is get his project classified as secret. That way there is no accounting for the money that is spent on it. It's just part of the budget for secret stuff. Wouldn't surprise me if that's where the two trillion dollars went.

Jody dropped me a note about foreign countries not using dollars for oil any more and pointed me to The Drudge Report where I found several links on the subject. Here we have a report that all the big consumers and producers, except the US, are conspiring to stop using the dollar for oil trading, which is of course denied by official sources. I found a couple of quotes I really liked in the story by Robert Fisk. Here we go with the two trillion dollars again:

An indication of the huge amounts involved can be gained from the wealth of Abu Dhabi, Saudi Arabia, Kuwait and Qatar who together hold an estimated $2.1 trillion in dollar reserves.

And here's the conspiracy theory:

Iran announced late last month that its foreign currency reserves would henceforth be held in euros rather than dollars. Bankers remember, of course, what happened to the last Middle East oil producer to sell its oil in euros rather than dollars. A few months after Saddam Hussein trumpeted his decision, the Americans and British invaded Iraq.

Then there's this story about the UN wanting to move away from the dollar. Ain't this stuff just great?

Update January 2017 replaced missing video. I think I got the right one, I remember seeing all those pallets stacked with money before. Half the links are dead, but I don't have the energy to track down replacements right now.

Water Car

This is not your putt-putt amphi-car, this one is a real go-getter. The music sucks, but what can you do? Via StreetFire.


Fastest Amphibious Cars in the World - www.WaterCar.com - Python Edition (prototype only)
Update January 2017 replaced missing video, removed dead link.

The Ayatollah of Rock´n Rolla

This phrase popped into my head when I heard John playing his guitar this afternoon, and I got to wondering just where it came from. The Road Warrior, aka Mad Max 2, that's where. The phrase comes from the flunky's introduction.


Mad Max 2 - The Lord Humungus
Update January 2017 replaced missing video.

Fall Falls With a Tink

Yesterday I decided it was cold enough to turn on heat, so I went to the gas fireplace and noticed that the pilot light was out. No surprise there, open the door, turn the knob, push, and then push spark ignitor. Hold for a minute.... release, pilot light goes out. Try again. Still no go. Something is broke, gonna have to look into it. Meanwhile turn on the furnace. Fortunately it seems to be working.

This morning I roll out of bed and something is tinking on the night stand. It sounds like a clock ticking, except it is more of a tink sound, and it's faster than a clock, but just as regular. Weird.

Go in the bathroom and turn on the light and two bulbs burn out simultaneously with a series of tinking noises. Look at the bulbs and I can see longish wires lying in the bottom of the bulb. These aren't just the filaments, these are supports for the filaments. Weird.

Eventually I go back to investigate the clock noise on the bedside table. It's the lamp. It's one of these turned brass things that has a bunch of pieces all held together by a threaded rod running through the center. The whole thing is loose. It must be right on some balance point because any little tremor sets the whole thing to tinking again.

Update January 2017 replaced missing picture.

G-20

Jody sent me a link to a story about the riot at the G-20 Summit in Pittsburgh last month. I went poking around for some more information about the G-20 and I stumbled over this little pamphlet: Meet The G That Killed Me (16 pages). It gives a pretty clear explanation of just what's going on. It does give a couple of paragraphs to the social injustice of it all, but the opinions are clearly separated from the facts. I give it an A+.

The crux of the matter:

"Needless to say, these policy prescriptions have not helped to stabilize developing economies. Instead these IMF-imposed structural adjustment policies have caused even further destabilization for developing economies. And more significantly, they have opened the doors for multinational corporations to come into developing countries to exploit people and resources.

"IMF loans rarely turn out to be ‘quick fixes’ for developing countries facing severe economic trouble. Instead, as debtor nations are unable to pay up on the impossible terms of their loans they sink deeper and deeper in debt falling into a condition of perpetual debt."

I don't know how true that is, but I do suspect these guys of lending money to charlatans who just take it and spend it on themselves instead of investing it in their economy like they are supposed to. Foolish IMF.

As to whether the G-20 is really evil or not, well, of course they are. They haven't given ME a billion dollars. And the numbers mentioned don't strike me as all that big. The biggest one was $750 billion. Didn't we (the US Government) shell out more than that to shore up our own collapsing economy? Or was that the amount we gave DOD to spend on black projects?

An Open & Shut Case

The Opening of the American Mind

The Closing of the American Mind

We were at Powell's last night and I happened across these two books about two shelves apart. Make of it what you will.