How to lay out an octagon

I was flipping through a neighbor's library and opened a book called "101 DIY Projects" or something like it, and there was a good way to lay out an octagon (it was for a picnic table). Here goes:
1. Lay out a square, and measure the diagonals. E.g., our square has sides of about 4 1/2 feet and diagonals of 6 feet exactly.
2. Measure and mark 3 feet (half the diagonal) from both sides of each corner, for a total of 8 measurements and marks.
3. Connect the dots, cut off the corners, and wahlah (sic)! You've got a perfect octagon!
I usually overthink things like this, so it struck me as particularly simple and helpful.
-Phil Crow
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I suspect that the measuring will guarantee that the resulting octagon will not be perfect given the state of most shop's measuring equipment. Maybe close enough but nothing I'd want to guarantee perfection for.
I suspect that one might get closer by laying out a circle, bisecting it with a line through the center, erecting a perpendicular to the first line also through the center thus dividing the circle into four quadrants. Bisect the quadrants and you have eight equal divisions. Connect the points where the lines cross the circle and you have an octagon. All of these steps can be done using a straightedge and either a compass or a set of trammel points to fit onto the straighedge. Or so my vague recollections of junior high geometry class suggest...
--
John McGaw
[Knoxville, TN, USA]
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stated wide-eyed, with arms akimbo:

Tell Phil it's "Voilà!", will ya? (pronounced "vwala")

Yes, layout via bisecting the circle is actually quicker to do than to describe.
- Yea, though I walk through the valley of Minwax, I shall stain no Cherry. http://diversify.com
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I quite Messrs. Merriam and Webster:
sic- [L, so, thus -- more at so](ca. 1859): intentionally so written--used after a printed word or passage to indicate that it is intended exactly as printed or to indicate that it exactly reproduces an original <said he seed [~] it all>
I guess I can take that as another miserable failure in my quest to make the wRECk's most humorous list. Sigh...
-Phil Crow
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"Larry Jaques" <> wrote in message ...

Larry, the "sic" indicates it is as quoted from the original text. The simple act of inserting it indicates he knew it wasn't correct.
cheers,
Groogy
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_I_ will write it 'Viola!' -- at least when I'm stringing somebody along.
Some days, the phone gets answered "cello?", too.
I know it's _all_ off-bass.
But don't forget the luthier and tailor, who, one day when he was having a hard time concentrating on his stitchery, was reprimanded:
"Get your mind out of the guitar, and back in the sewery!"
N.B.: The quote seems to have gotten corrupted over time.
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Bisect
points
The above is perhaps the easiest to draw an octagon inside a circle. To draw an octagon inside a square, you would trace a line from opposite corners of the square, let's call "C" the point where these 2 lines intersect, then draw four quarter circles with centers on each of the square's corners, start from one side of the square, ending on the other side and passing exactly on the intersection "C", finally join all points where the quarter circles intersect the sides of the square.
Guillermo
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