More Math Help wanted........

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Baer Charlton

SPFG, Supreme Picture Framing God
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The opening of the circle mat is 10"

The mat width is 2" so a frame size of 14"

But how long are the legs on an Octagon frame
if I need them to be equal length?

Yes, I'm lazy.... I don't want to go up to
the shop, fire up the wizard, and let it do the math,
and cut a test mat to give me the sizes.
 
trig

I think it's:

2[7tan (22.5 degrees)]= 5.8ish (per leg of an octagon)

wish there was a graphing calculator function on here to show you

Chris

P.S.
360/8 = 45 degrees (top angle of one of the pieces)

Divide that piece in half, making two right triangles, with the smaller top angle 22.5 degrees - you only need one of the triangles standing on its short side.
The length of that long side is 5 (radius of the circle whose diameter is 10) + 2 (the extra amount you need to reach the edge of the 14' mat) = 7.
You need to find the length of the short side from the info you know - that is the tall side (7) and the top angle (22.5 degrees).

tangent of an angle (22.5) = opposite side/adjacent side = x/7

So, 7 tan(22.5 degrees) = 2.899 or approx 2.9

BUT this is only 1/2 of that leg of the octagon, so now multiply by 2 = approximately 5.8 (for the length of each leg)

The length of the slanty side (for those who want to know the distance from the center of the circle to the outside "corner" of the octagon, it's 7.6ish. The hypotenuse is always the longest side of the right triangle.

And this may be all wrong or TIM.

Of course the Wizard will be much more accurate in the cutting!
 
5.79899"


http://www.calculatorsoup.com/calculators/geometry-plane/polygon.php
 
CAD - click polygon, click 8 sides, click 14 inches - measure with dimension tool.
 
Bandsaw.... my CAD is made out of linen and is usually used at the table....

but as a CAD...... Child Applied Diaper....... is not an option in our house....
so drawing on the linen COULD occur.... but I really hate sleeping on the couch.
 
I cheated and looked in my "Barton's Multi-Angle Framing Guide" circa 1986.
It says for a 14" frame, the inside measurement of each side is 5.799".
Or in "technical terms" a "hair off of 5 25/32".
 
neilframer said:
I cheated and looked in my "Barton's Multi-Angle Framing Guide" circa 1986.
It says for a 14" frame, the inside measurement of each side is 5.799".
Or in "technical terms" a "hair off of 5 25/32".
Click to expand...

That is a great book. When you need to know, and don't want to repeat Geometry, it's the text to have at hand.
 
I would have done it with a straight edge and compass, scribing the 1st leg and setting the stops from it. I did well in geometry, but my drafting training serves me better.
 
The bartons book is great. on the bottom of the octagon page is the constant for the side. x.414
It was our area code for a long time so it's the one I can always remember. If not a stop sign then just add the difference between the measurements to get the size for the longer legs.
14 x 18 14 x .414=5.8 plus 4 = 9.8 for 2 long sides
 
2 weeks ago a customer brought in an octagon frame we did 27 years ago - Christmas X-stitch - 16" circle.
Updated to a square frame, completely redone, new mount, mats, museum glass.
Really appreciate those long term customers.
 
Sorry, late to the party.

The radius of the circle is 7” so with an octagon, the internal angle of each side is 45°, then you have an isosceles triangle with 67.5° on the other two sides. Each length of the octogon would be ~ 5.359 inches (5-11/32”).
 
Pat Murphey said:
Octogon internal or external to the radius Bill? Baer is looking for external.
Click to expand...

Actually, I never saw that he said. "Frame Dimension" only references rectangular frames in FACTS GEN 1998. AFAIK there is no accepted single standard for measuring non-rectangular polygons. In general science regular polygons can be defined with inscribed or circumscribed dimensions when referring to "diameter", or leg length as is being sought here.

I use CAD because it was waaay too many years ago I did that kind of stuff...

Here are both solutions:

View attachment Octagon.pdf

Dunno why the thumbnail is black, it opens w/white background...
 
neilframer said:
I cheated and looked in my "Barton's Multi-Angle Framing Guide" circa 1986.
It says for a 14" frame, the inside measurement of each side is 5.799".
Or in "technical terms" a "hair off of 5 25/32".
Click to expand...

Baer Charlton said:
Sorry Bill, it measures just between 5-3/4 and 5-7/8.
Click to expand...

Exactly. That's a "hair off of 5- 25/32":thumbsup:
 
Oh my gosh, I'm sooooo impressed with you math wizards!! All this talk of sin, tan, etc. I loved geometry and was really good at it but I'd be long dead before I remembered those formulas. Way to go you smartsters!
 
Amy... there is just some simple rules and it all makes sense.

1) Tangent is that customer who just got back from the Caribbean from two weeks of vacation on the beach.
2) Hypotenuse - - - this is the most important thing in the morning. Before you start doing anything
that may involve brain cramping activity.... make sure you High Pot (20 cup coffee urn) is in use.. or perking along.....
 
Pat Murphey said:
Octogon internal or external to the radius Bill? Baer is looking for external.
Click to expand...

Okay, the problem as stated was unclear to me. If each leg of the octagon is to be tangent to the 14” ‘circle’, then the equation should be:

b = 7 * 2(tan(45°/2)) = 14 * tan(22.5°) = 5.798” (or, as Neil said, "a smidgen over" 5-25/32") :)
 
Pat Murphey said:
...Baer's original request was for a 2" mat around a 10" circle...
Click to expand...

I still could not accept an order with that much (little) information. 2" where? The narrowest point or the widest point? An octagon with 10" circle, 2" mat and 14" frame describes two possible outcomes.
 
As my wife chastises me all the time for using jargon and industry short-hand,
so is this glaringly obvious a framer thing David.

That is why I'm the framer, and you are a wood stick guy.

Mat measurements are always across the smallest reach of the mat,
not out to the corners.

Well, not for normal framers. Bill, Bob and Pat may be exceptions.
or like Manny, Mo and Jack... just pulling our tires for the fun.
 
Did it give you a laugh and make you feel like the snot nosed youngin'
that you are? LOL

For decades I aspired to be a crotchety old f*rt.... now that I are one...
I'm working on becoming curmudgeon.

So, frame is made..... I didn't like the way the mat looked so I increase the
legs to 6.18394.
Now.. interestingly... the gauge on my tablesaw... is not that "special"...
so I built a jig.... and shimmed until the test blocks looked right with a 2"
sight opening.....

And then I realized that my jig could only work with one end of the moulding...
so I took the little blocks.. and built a saw buck.. and cut the other end with
my Japanese hand saw.
Hmmmm got a better cut... time to send the table saw blade out for sharpening..
So glued and V-nailed in a complicated jig I built for the V-nailer....
(4" square of 1/2" thick foam core.. drew the center line, and lined up the moulding,
drew two more lines and cut it... )
A little wax and rottenstone in the morning.. and fit in the afternoon.
Maybe next year I'll knock out a few dozen more.... :kaffeetrinker_2: not.
 
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