On Tue, 17 Aug 2004 05:56:37 -0400, "Mark Hopkins"
......and in reply I say!:
remove ns from my header address to reply via email
Iiiii Knoooowwwww! My donkey kicked me in the behind just the other
Marriage. Where two people decide to get together so
that neither of them can do what they want to because
of the other one.
Now if you live in Indiana, you can simplify
your Pi calculations.
If you've never heard this story, it's an interesting read:
Interesting read. About that same time there were a number of
states who considered similar legislation; and (I've heard but
haven't confirmed) at least one state who actually enacted a
statute defining pi to be exactly three.
| and (I've heard but haven't confirmed) at least one state who
| actually enacted a statute defining pi to be exactly three.
Tennessee, and only in Robert Heinlein's "Stranger in a Strange Land." It
didn't actually happen. The Indiana story is true enough, but it has
spawned numerous spurious copycat stories that are standard April Fool's Day
fare. Heinlein's is just the most immediately credible. The state in
question is always some state presumed inhabited by rustics. But no state
in the U.S. has ever had a law passed legislating the value of pi. Indiana
I annoyed my HS geometry teacher by announcing I could trisect an angle.
True, a Carpenter's Square is illegal under the rules of "Geometric
Construction", but I could easily prove that it worked.
There are other methods, using other tools, but a carpenter's square is
probably the easiest to prove correct.
| There are other methods, using other tools, but a carpenter's square is
| probably the easiest to prove correct.
Hence the original masons used three tools: the straightedge, the compass,
and the square. It's amazing what you can do with those tools and a little
"secret" geometretic knowledge.
I'm still a neophyte, but I'm increasingly reaching the conclusion
that a little geometric knowledge is all you *want* to have. Because
of a misspent youth, I can do a lot of what people tell me is fairly
complex mathematics in my head. So I wind up designing furniture that
contains 18.7457 degree angles, or better yet, angles that are
arctan(5.75/11) or lengths that are (5+sqrt(7))/2 or something. I
actually computed a fifth order polynomial approximation to the chair
leg curve I wanted on a table I made for my mother-in-law last year.
Unfortunately, I have learned that I can do the math, but I can not
cut these crazy dimensions accurately. From now on, it's 90 degrees
or 45 degrees or re-design it because it's wrong.
Then your own designs are fairly simple. I admire people who do their
own design. It's not the math, it's art. The math I can do easily,
and often apply it in the shop, or on the computer or wherever, but
the art? Stick people are beyond me. I need plans with numbers on
them mostly. I did figure out how IKEA designed their neat folding
I knew the shape I wanted, but I can't draw (as you say, stick people
are also beyond me), so the only way I could represent it was
mathematically. I wanted the leg to be two inches wide at the top,
one inch wide at the bottom and one-and-a-half-inch wide halfway down.
I also knew I wanted the first derivative to be zero at the top and at
the bottom, and I wanted the second derivative to be zero halfway
down. That's enough to define a fifth order polynomial. The fun part
was going to be to try to do it on two faces of the leg to get the
three-dimensional shape I wanted.
So I got out Matlab and plotted the thing, then I tried to draw it on
the leg with a pencil. Then I contemplated actually cutting it with
my crappy jigsaw. Then I decided my mother in law would be very happy
with a tapered leg. :)
It's not quite that my designs are simple. It's just that I have to
take my original crazy designs and simplify them until they contain no
parts that I can't make. Right now, that means it has to require no
skill. I need a fence or guide or something to follow or the results
are not pretty. I understand from my reading that people typically
cut curves by following a hardboard template. I'm not sure how this
solves the problem, since you first have to get the template right.
I have also learned that two or three hours with coarse sandpaper can
make anything look good. :)
Plot your design. You can either superimpose it on a grid and
scale it; or you can find a way to plot it full size. If
necessary run it out on your printer in pieces, one piece per
page, and then tape the printed pieces together...
Now you can transfer the design to the hardboard. Did you know
that you can get hardboard with a slick white surface at the
lumberyard?) I have a piece tacked to the wall that I sketch on
with dry erase markers - lets me re-draw to my heart's content.
Practise makes (more) perfect. (-:
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