Geometrical Measurements

[Jeffrey Schronce]

I must say that I feel incrediably stupid and rather lazy posting this question here. The stupid part is that I have graduate level Econometrics and Stats/Probability under my belt but have never taken the equivalent of High School Geometry. (I will add that the SAT is seriously biased toward Geo!).
The lazy part is I should read up on this some where or look it up, but I am soooooo lazy that I am just asking . . .

I have been commissioned to build a poker table. It is an octagon (thats the 8 sided one right? LOL! ((I acutally think I got that much in High School)) ) that measures 48" wide. Width measured along parallel sides.

How long should each piece of the 8 pieces be? I am 98.7653% sure my miter should be 22.5 degrees but would like that confirmed.

Again, I know I am pathetic in asking this.

[gugie]

Interior angles for equidistant sides = 360 degress divided by number of sides. For a triangle, 360/3=120, square, 360/4=90 degrees (that's the most intuitive one), octogon 360/8=45 degrees. The miter will be half of the interior angle (each side takes half of the angle), giving 45/2=22.5

You are correct!

[JeremyM]

Jeffrey,

Yeah, you're being lazy!

You are right, your miters are 22.5deg, minus a scooch. An octagon is just a circle divided up with straight legs. So, 360/8=45 and that is made in 2 cuts, so 22.5 and just a little less so you can make the miters work better.

As to length.... why are you trying to figure your miters right now? Are you putting this together so you have a "ray" pattern in the center?

I made an octagonal table about 2 years ago, and I didn't figure the math out at first. Then I got a book "Workshop Math" and saw something in there and then figured out a mathematically simple way of doing....but I forgot!

Here's what I did before I figured it out. I was making mine simply out of oak ply. I took and laid out a square. I made the cross section in the middle and then divided that with 45's. I drew very light lines where I needed out from the center on those 45's. Then I measured out the distance from the center to the edge of the board(in your case 24") and measured that out on the 45 lines and marked it. I then drew a perpendicular line each direction from that 24" mark. Where those intersected the edges of the 48"x48" board (or layout lines) then I had the shape of the table.

Yes, there is room for error here. But it was a quick and easy way of getting it done. It can actually be very accurate if you are a nut about precision marking and such. And yes, there is an easier way of calculating it, but I'm like you....too lazy right now! (book is actually packed away as I'm the midst of a move).

Hope this gives you some ideas.

[JeremyM]

Maybe this will help some. If not, it should at least help you start to solve it.

http://mathforum.org/library/drmath/view/56459.html

[jwaterdawg]

Where should I send the bill for geometrical consultation

[sacherjj]

Man, I love geometry and show up after the math is done. BTW - Norm did a real nice looking Poker table on NYW, a couple weekss ago.

[ExYankee]

This is how Nahm did it

I think it was last weekend that he built one of these, did a good job explaining the angles and joints



http://www.newyankee.com/getproduct3.cgi?0604

[Jeffrey Schronce]

Where should I send the bill for geometrical consultation

Therefore, total length of each piece is 19 5/8, if I assume I am correct in doubling the number to get the length of each piece.

[Jeffrey Schronce]

I really appreciate the help folks. While I am doing this as a favor for a friend, it is implied that I will never have to deal at the home game again, which to me is priceless!

[scorrpio]

The calculation is actually dead simple if you just vizualize it. Looking at the edge of the table, you see one of the sides at it full length, and two sides at 45 degrees. Any length viewed at 45 degrees is divided by square root of 2 (square diagonal formula), which is approximately equal to 1.4 - or 1.414 if you want extra accuracy.



So, if X is side length, X + 2X/sqrt(2) = 48
At 1.4 as root of 2, that works out to X being 20" - a nice round number. The table will be approximately 1/4" wider than requested - but I doubt anyone would notice. Besides, once you cut the miters, you can always trim 1/8" off the outsides.

A 19.5/8 side will give you a roughly 47.375" table - more than half inch too narrow. The most accurate result (47.98) will be achieved with a 19 7/8" length. I would still say go with 20" long - will leave you some room for error.

[gsmittle]

Owwwww!!

You guys are giving me a headache!

g.

[Jeffrey Schronce]

The calculation is actually dead simple if you just vizualize it. Looking at the edge of the table, you see one of the sides at it full length, and two sides at 45 degrees. Any length viewed at 45 degrees is divided by square root of 2 (square diagonal formula), which is approximately equal to 1.4 - or 1.414 if you want extra accuracy.

So, if X is side length, X + 2X/sqrt(2) = 48
At 1.4 as root of 2, that works out to X being 20" - a nice round number. The table will be approximately 1/4" wider than requested - but I doubt anyone would notice. Besides, once you cut the miters, you can always trim 1/8" off the outsides.

A 19.5/8 side will give you a roughly 47.375" table - more than half inch too narrow. The most accurate result (47.98) will be achieved with a 19 7/8" length. I would still say go with 20" long - will leave you some room for error.

Ya, I figured on rounding it to 20". Using stops on CMS, repeating should be no problem and overall size is not a factor. I was just figuring 48" seemed to be standard. This table is going to be so freaking cool that it will not matter 1/2" either way . . . LOL!

[JeremyM]

waterdawg,

Thanks for that. I knew that it was going to involve a tangent or a cosine, but didn't remember what. It appears that you had the more involved mathematical solution, but the one I was more incline towards. I know the square root of 2 answer must be right, but I sure didn't remember it.

But if someone doesn't have the math skills, you can still do it the hard way!

A question for you, Jeffery. You are asking about how long to a make the miters. Are you creating a frame that you are then dropping a table top in?

[Jeffrey Schronce]

I was asking the length, as shown in Scorrpio's diagram as x.

i believe i have the answer of, round it up to 20".