Math question

[T*O*F]

My geometry is rusty.
Given a regular hexagon with line AB being 1.125"......how long is line BC?

[Black Hand]

Right angle triangle A²+B²=C²
in this case:
Length of (AC)²+(CB)²=(AB)²  Solve for CB

See http://www.mathsisfun.com/pythagoras.html for more info.

[Larry Pletcher]

TOF,
I count 8 sides.  You mean octagon, right?
Larry

[BrentD]

There is enough info there to do it w/o measuring A, but if you can measure A, you can measure C. 

Doing it w/o measuring A is going to take some trig and that means more work than it's worth. 

[Acer Saccharum]

Depends who drawfiled the barrel.  

Once I get my CAD system up, I can tell you.

Isn't that sad? We used to know all this stuff, and now all we know is 'google it'?

The number is.......by the way, I forgot all those trigonometric formulae......but I did once know how to do the calculations....and the number is.....all those charts, and .... the number is....1.0384"

Tom

[Acer Saccharum]

By the way, I saw Roger Fisher at Lewisburg. What a great guy. Love you, Roger.

Sorry, I'm off topic...again.

Tom

[BrentD]

The number is.......by the way, I forgot all those trigonometric formulae......but I did once know how to do the calculations....and the number is.....all those charts, and .... the number is....1.0384"

Tom

THe trig function is 1.125sin(A)

But I don't know for sure what the angle A happens to be. 

How is it one knows the diagonal and not the flat-to-flat (BC) distance?  That is the measure by which octagon barrels are sold.   Kinda curious what you need the AB dimension for?

[smart dog]

Hi TOF,
Based on your drawing the answer is 1.039".  Each angle of an octagon is 45 degrees so BC is simply 1.125*cos(45/2 degrees).

dave 

[Jerry V Lape]

Interesting Dave.  The interior angle within the octogon appears to me to be 135degrees and since the angle of BAC is half of that the sine is .9207 X 1.125 = 1.036".  

[Larry Pletcher]

I got 1.0394.  Found the length of AC and used pyth. theorem:

square root of ( 1.125^2 - .4305^2 )

Regards,
Pletch

[T*O*F]

How is it one knows the diagonal and not the flat-to-flat (BC) distance?  That is the measure by which octagon barrels are sold.   Kinda curious what you need the AB dimension for?

Brent,
The answer is simple. I don't need the AB dimension, I need the BC dimension. I have a LRML blank that is 1-1/8" round and I'm trying to decide which way I want to go with it.  This answered one of my questions, namely which breechplug to use, how much of the barrel would I have to mill off for the tulip and then taper from there.  From the BC measurement it appears a one inch breechplug is called for and I don't want to go that small.

Conversely, if I use an 1-1/8" plug, I can forego the tulip, file the corners off the plug and go with a round profile.  The max weight allowed for the gun is 15 lbs and I want to crowd that as close as possible.

[smart dog]

Hi Jerry,
The angle that I am referring to is the interior angle at the hub of the spokes connecting each corner of an octagon.  They are 45 degrees (360/8).  Each pizza pie-slice internal triangle created by those spokes has one 45 degree angle and 2 other internal angles that are equal.  The sum of internal angles of a triangle is 180 degrees, therefore, the other 2 angles must be 67.5 degrees.  That gives you angle A in TOF's diagram, angle C is 90 because it is a right triangle and thus angle B must be 22.5 degrees.  The answer to TOF's question is simply 1.125*sin(67.5) or 1.125*cos(22.5).  Using that method you don't have to measure any lengths or angles other than what TOF showed as long as the shape is a true octagon.

dave

[Jerry V Lape]

Dave, right that is what I said - and after reading your first post again so did you.  We agree!

Jerry

[Blacksmoke]

I doubt if any of the "old makers" would have had to figure out that dimension using pyth. theorem!? ;
     Hugh Toenjes

[KentSmith]

I am not so sure Hugh.  I think people had a much better handle on math functions back then because they had to.  No calculaters, google, etc.  I know my Dad and Grandpa had trig functions memorized - both were die makers - and could never understand why trig was so hard for me.  They could do it in their heads because they used it every day to do their work.  I would expect part of what an apprentice learned in the 18th century was the math he would need to do his job in a workmanlike manner.  The Pythagoran theorum is fairly basic in a non-electronic world.

[Trkdriver99]

  Dog gone all this has give me a headache. I never was good at Fancy math.    Ain't this why they made rulers?

Ronnie

[Gaeckle]

Isn't that sad? We used to know all this stuff, and now all we know is 'google it'?

Tom

That is pretty sad...I used to know all kinds of math stuff, diffy Q's, how to use a slide rule, calculus...oh well.

What the heck, I can stll wash dishes, change oil in my truck, fix a flat tire, figure out how to fix things at work, be a pain in the neck to my boss, treat my wife good, send my kids to school, pay the mortage, figure out ways to increase my 401K, make a rifle, and a whole bunch more.....


Guess I'm not too sad.

[P.W.Berkuta]

Ah -- I think the angle is 22.5 degrees. So 22.5 (degrees) X 8 (sides) = 180 degree

Hi TOF,
Based on your drawing the answer is 1.039".  Each angle of an octagon is 45 degrees so BC is simply 1.125*cos(45/2 degrees).

dave 

[Jerry V Lape]

P,W.  not quite - 180 degrees is only half of a circle.   

[Rootsy]

an octagon with 8 equal sides and 8 equal angles will have 1080 total degrees when summing all angles.  IE each corner angle is 135 degrees.  Derived from the fact that every time you add an additional leg to a polygon you can form another triangle within it whose sum of angles is 180 degrees... IE, triangle = 180, 4 sided polygon = 360, 5 sided equals 540, so on and so forth.

In a regular octagon with 8 equal sides, if you draw a line from one vertex to the opposite vertex you have a bisector.  IE that 135 degrees is split equally (67.5 degrees).

Then it becomes a simple trig solution...

Sin (theta) = Opp / Hyp = X / 1.125, rearranging, 1.125 x sin (theta) = X =>  1.125 x sin (67.5 deg) = 1.0394

[P.W.Berkuta]

 --DAH --sorry I was only half right - forgot the other half - I'm not a muti - tasker - I could not get back in time to correct it -- thanks for the correction    .

[smart dog]

Dave, right that is what I said - and after reading your first post again so did you.  We agree!

Jerry

Hi Jerry,
Right you are my friend.  My problem is that I actually use this math all the time.  It is how we triangulate the position of radiomarked animals using directional bearings on the radio transmissions.  Of course the new staellite tracking GPS collars take all the fun out of it.

dave

[Herb]

I laid this problem on my friend, Greg, who is an engineer and worked 14 years for Hughes Aircraft.  It only took him about 3 hours, interrupted by my catfish and shrimp dinner and 4 or 5 glasses of cabernet sauvignon wine, to come up with the answer.  It is 1.0394 inches, and I can't remember my trigonometry from 1951-2, but he solved it two different ways.

[omark]

an octagon with 8 equal sides and 8 equal angles will have 1080 total degrees when summing all angles.  IE each corner angle is 135 degrees.  Derived from the fact that every time you add an additional leg to a polygon you can form another triangle within it whose sum of angles is 180 degrees... IE, triangle = 180, 4 sided polygon = 360, 5 sided equals 540, so on and so forth.

In a regular octagon with 8 equal sides, if you draw a line from one vertex to the opposite vertex you have a bisector.  IE that 135 degrees is split equally (67.5 degrees).

Then it becomes a simple trig solution...

Sin (theta) = Opp / Hyp = X / 1.125, rearranging, 1.125 x sin (theta) = X =>  1.125 x sin (67.5 deg) = 1.0394

  sorry rootsy, but an octagon is just a circ le with corners and a circle only has 360 degrees, the more corners, the less angle in each corner, but still totals 360 degrees

[omark]

an octagon with 8 equal sides and 8 equal angles will have 1080 total degrees when summing all angles.  IE each corner angle is 135 degrees.  Derived from the fact that every time you add an additional leg to a polygon you can form another triangle within it whose sum of angles is 180 degrees... IE, triangle = 180, 4 sided polygon = 360, 5 sided equals 540, so on and so forth.

In a regular octagon with 8 equal sides, if you draw a line from one vertex to the opposite vertex you have a bisector.  IE that 135 degrees is split equally (67.5 degrees).

Then it becomes a simple trig solution...

Sin (theta) = Opp / Hyp = X / 1.125, rearranging, 1.125 x sin (theta) = X =>  1.125 x sin (67.5 deg) = 1.0394

  sorry rootsy, but an octagon is just a circ le with corners and a circle only has 360 degrees, the more corners, the less angle in each corner, but still totals 360 degrees

sorry rootsy, i see youre measuring inside corners, i was measuring outside angles