Inscribing hexagon in circle

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!

Len

On 5/21/2009 9:25 AM Len spake thus:

Thank you. That was exactly what I was looking for.

There; was that so hard?

Same proof I gave you almost a week ago.

Lew

It seems to be based on calculation (360/6), but obscures that fact; I would expect better work from a math major.

LOL!

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" .

Reminds me of a quote from a physics professor.

"You want an easy proof for the law of gravity? Step out of the window."

Obviously, that proof makes the assumption that the classroom in question is in an inertial reference frame. :)

Chris

The window was in a big frame, on the 5th floor. :-)

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. :)

Bill

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...

Chris

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

...the tenoned parts shown at the bottom of

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). Birds don't tend to be particular beyond a 16th of an inch. :)

Bill

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.

Before some smarta$$ says, what do you do with a 12' piece of crown molding.... I obviously call a couple friends to come over and hold it in place for me. duh.

What do you do with a 12' piece of crown molding on an outside corner that isn't square?

Chris

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...

completely

want a

logical

"proofs"

stated, and

negative

That's why I suggested getting a sashigane marked with for shaku/sun/bu to begin with. Once you get used to it, it has the markings on the back side for laying out this kind of stuff without a lot of fuss.

Len