On 5/20/2009 7:20 PM firstname.lastname@example.org spake thus:
Like more than half the respondents to this thread, you completely
missed the point.
I know how to do that. I wasn't asking for a demonstration; I was asking
for a *proof*.
(Even though your description contains some of the elements of a proof.)
Found--the gene that causes belief in genetic determinism
State the axioms you wish to start with, and we'll take it from there. I'm
sure someone here knows how to write a proof. A calculation based
explanation is a good proof if one axiomizes high school geometry. This
seems like the right approach here in rec.woodworking!
Obviously, as your previous post hinted, the OP didn't really want a
formal proof. (He may not realize that is not what he wanted, but the
fact that this question was raised because of not having an old
geometry text is a pretty good clue.) What he wanted was a logical
demonstration based on facts he accepted, with steps he didn't have to
figure out. Note the range of logically identical responses here that
have been dismissed as "mere demonstrations" or accepted as "proofs"
depending on the number and detail of the steps explicitly stated, and
whether the steps were numbered and labeled "proof" <g>.
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
Your LOL is well taken. I'm not sure whether one needs the numbers in
between the fractions (like sqrt(2)) for woodworking, nor any negative
numbers, imaginary numbers, non-real complex numbers, nor probably any
numbers bigger than 500. Maybe that's why those aren't marked on the ruler.
sqrt(2) is useful to find the length of the long side of a 45/45/90
triangle. Similarly, 1/2/sqrt(3) are the sides of a 30/60/90 triangle.
Numbers bigger than 500 are useful when working in millimetres.
I'm up in Canada and I know a guy who does everything in mm. Although
the initial conversion of regular North American lumber dimensions to mm
is a bit of a pain, it makes subsequent math a lot simpler. And of
course all the Euro stuff just works...
Do you think 1 53/128 would suffice (somebody with good eyesight might be
able to mark it off a ruler with 64th's). I'd do better with a micrometer.
I hope the wood is very stable. :)
Similarly, 1/2/sqrt(3) are the sides of a 30/60/90 triangle.
It might depend on what you're doing. The ribs at
needed to be cut so that the length along the parabola was exactly four
feet (the mirror width) and with accuracy to provide a good optical
focus along the entire eight-foot length - and...
...the tenoned parts shown at the bottom of
were for silverware trays with diagonal dividers; these were the divider
blanks, and they needed to /exactly/ fit (on /both/ ends :) ).
And no, none of the numbers needed were marked on any of my rulers. :)
Interesting projects! My wife is supportive of amost any outlay for tools
as long as I build her some "bird-related" stuff (feeders, houses, etc).
don't tend to be particular beyond a 16th of an inch. :)
Am I the only one would rather mark than measure?
Like if I have a piece of trim that needs to fit between A and B,
I don't measure A to B then measure that out on the trim.
I hold up the trim between A and B and mark the trim.
"Playing is not something I do at night, it's my function in life"
If it'll help you feel better, I neither marked /nor/ measured for those
projects - everything was cut from unmarked stock and then assembled as cut.
I did have drawings for the silverware trays because the customer needed
something to sign off on, but the drawings for the parabolic trough came
along after the fact, to document what had been done.
For stuff I don't need to be fussy about, I've had to switch to a light
touch with a knife - my eyes just aren't good enough any longer to split
a pencil mark...
HomeOwnersHub.com is a website for homeowners and building and maintenance pros. It is not affiliated with any of the manufacturers or service providers discussed here.
All logos and trade names are the property of their respective owners.