Hey everyone, several years ago while framing some homes in the Dallas area, we came up with a technique and formula for calculating exact equalateral octagons (or oblong derivitives of them).
The geometry is a little convoluted, but not real difficult. However, it isn’t necessary to understand or remember the formula.
All that is needed is to look at the octagon as being within a square box of the identical exterior dimension. Then simply multiply the exterior dimension by .707 (this is 1/2 of the square root of 2). This is the length from the corner of the bounding square to the opposite corner at the start of the 45 degree angle.
I hope this will help you save some time on a project.
Replies
True, and the sides of the octagon in your drawing will be 41.4", which is 100" times the square root of two, minus one. From the corner of the big square to the near corner of the octagon is 23.9", and the diagonal of the octagon, from one corner to the opposite corner is 108.2". To put a circle around the octagon, scribe it with a radius of 54.1"
-- J.S.
Ever wonder how the old timers laid out octogons without the aid of calculaters? It is much easier to use a simple set of dividers. Take the distance from one corner to the center and use that setting to mark 8 corners. Place one leg on the corner and swivel the dividers making a mark where they cross the sides. connect the dots. Perfect octagon!!
Or, you could make two square templates of the same size as the width/height and mark them both with center lines and diagonals. Lay one on top of the other and line up the diagonals of the top one with the center lines of the bottom one. No measuring, no muss, no fuss. If the templates are made of Lucite or Lexan, you can drill small holes and make the appropriate marks and connect the dots for making whatever sizes you want. Maybe connect them at the center with a pop rivet and washer so they can rotate.Another way is with a square and a compass. Draw a circle as big as the height/width of the octagon. Lay the square on the circle and draw the right angles at the contact points(so you have a circle in a square). Draw the diagonals and/or just draw a 45 degree line where the diagonals meet the circle. Next, we can bisect any angle or dimension with a compass and divide any length into whatever number of pieces with a ruler or tape measure.
"I cut this piece four times and it's still too short."
Edited 5/19/2005 9:43 pm ET by highfigh
Yeah, thats the ticket! Throw them calculating gizzmos away and do it like grandpa did it!Much more fun that way.
Probably faster, too.
"I cut this piece four times and it's still too short."
Hey, nice work guys, sure glad I found this forum.
It is great hangin' with the smart guys!
This is pretty handy ..
http://junior.apk.net/%7Ejbarta/octagon_layout/
Jay,Dividers would work great on a piece of paper but out in the field where you have 100" as in Mike's drawing or even a 24' Octagon using math is a lot faster and easier. Mike's numbers work well and there's also a lot of other numbers that would work with about a few seconds on a calculator.I think masons should these formulas when their laying out foundations for these Octagon's to make it a lot easier on them and me as the framer because once I punch the numbers in for what the sizes of the Octagon walls should be, if the foundations out then there's a problem which I've seen many times.Joe Carola
On the older framing squares you will have an Octagon scale on the back of the tongue---I believe. I do not think I can explain it here (I have to get the book out) But it is a ratio of sides...like the original post. The Square can also be used as a calculator---that's what the 10th and 12th sides were for. Some squares had 100th scales too. I'll bet you don't know about the "Black Diamond club" from the tape measure? Are you a member? Got your secret handshake? That square is an amazing tool. The more I learn about it...the more I don't know.Do anything...even if it's wrong...It's not wrong...It's rustic!
Methods & Materials Building Co.
Authentic Timber Framing & Classic Carpentry
http://www.methods-materials.com
Black diamond gives you the lay out for placing 5 trusses per 8 ft. sheet of plywood, did'nt know there was a club.
Oh yea....There is a club....Just Kidding.A while back a guy got on here and asked what the Black Diamonds were for....and WOW was he knocked around. A very funny run of posts. Do anything...even if it's wrong...It's not wrong...It's rustic!
Methods & Materials Building Co.
Authentic Timber Framing & Classic Carpentry
http://www.methods-materials.com