I posted a question last night about laying out a hexagon floor. I’ve now decided to lessen the amount of work invloved by changing the lighthouse I have to build from a 6-sided to a 5-sided structure.
does anyone know an easy way to lay out a polygon on the ground?
Thanks again
paul
From building boxes and fitting face frames to installing doors and drawers, these techniques could be used for lots of cabinet projects.
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Replies
How big is the polygon?
I would start by making a T square that's longer than the room's diameter (in the case of a round room). Whatever number of sides it will have, you'll need to find the center of the room. Then, you can lay out the angles and any accents.
Can you post a diagram of what you want to do?
I'll take a crack at it.
A polygon could be multisided. A pentigon has five sides for example. A triangle has three.
1. Depending on how many sides you want......I would divide the number of sides into 360
a pentigon for example 360 divided by 5 = 72 degrees
2. Start at the middle and draw the first leg how ever long
lets say 2 ft
Tangent of a triangle is opposite over adjacent or... (tan 72 ) x (7ft)=3.07 or the opposite side is three times longer than the adjacent side
(if it would help some folks refer to a triangle as a,b,c or A squared +B squared= C squared . A = adjacent B= opposit C= hypotuse)
draw your line out 2 ft. then draw at the end of the line a right angle with the line 6 ft. connect the end to the starting point it should look like a really tall triangle
measure from the starting point up the new hypontuse 2 ft and make a point
connect that with the point at the end other two foot point and you have the first triangle of five
just repeat these steps repeating starting on the hypotuse of the new traingle
(a drawing would help but have no idea how to import one I drew it paint )
Edited 5/30/2006 10:13 pm ET by curley
Edited 5/30/2006 10:15 pm ET by curley
Remember all regular polygons have equal sides. So draw a circle with a diameter of how large the points of the polygon are to be. Such as for a 2' Diameter use a 1' radius. Then devide 360 degrees by the number of sides (5 in this case so 360/5=72). Decide where you want one of the points to be, put a mark on the circle and draw a line from there to the center of the circle. Now you can start from there and lay out spokes every 72 degrees. Next connect the ends of the spokes where they touch the circle together & you have a regular polygon.
Edited 5/30/2006 10:23 pm ET by jimcco
How wide do you want the sides?
Paul,
Here's one example of what you can do with a Pentagon using a Construction Master Calculator if you give me the side measurement you want or the diameter of a circle.
Once you have one triangle you can lay the rest out.
Framer, I'm thinking of using 8' as the diameter. I may increase it slightly. I'm also thinking of using 54" as the size for each side. Tell what diameter 54" sides will result in.
Thanks kindly
Paul
"I'm also thinking of using 54" as the size for each side. Tell what diameter 54" sides will result in."Paul,The diameter would be 7' 7-7/8"Here's a drawing.Joe Carola
I hate math.Here's the way ya do it if'n yer not a mathmagician...Decide how long the sides will be.Cut 5 sticks of wood, bullnose, pvc, whatever... to the correct length.Lay them out in the pentagon shape on the ground. Don't worry, ya don't gotta be a rocket scientist. It'll get there, even if it looks funky at first.Lay them out, 1,2,3,4,5...Then measure opposite corners. Move around to the next opposite corners, and measure. Then the next opposite corners, etc.When you have measured all five, you should have some idea which corners need to be moved.It actually works a bit better if you use some duct tape and tape the ends of the pieces of wood together. That way, when you move something, all the other parts tend to kinda move the way you want them to. It don't matter what color the duct tape is. You might want to mow the grass real low first, though. And git them beer cans out of the way.Once all the opposite corners measure the same, drive some stakes in the ground, yer done.This is the design-on-the-fly-with-the-materials-you-have-at-hand-method, of course. LOL In which you decide the length of the five walls by the length of the materials you have at hand.;o)If you want precise, ask a rocket scientist. I think Art is still in the house. Although I daresay his method of design would be pretty much like mine, but he throws some of that math stuff in too.
The destination is not the point. The completion is not the point. Enjoy today. If you can't enjoy today, then what is the point ?
Luka, we often use a variation of the system you've described when we have to frame octogon rooms.
I'm capable of calculating the exact sides needed, but the foundation guys rarely are. Consequently, the footings and blockwork vary somewhat. For them, it's good enough, but for us, it isn't. We can't afford to have one wall an inch bigger because it shows up when the windows are set and the distances vary.
If I try to build all the walls to the theoretical dimensions, they might not land on the foundation! So, we are perpetually forced into some sort of compromise. My solution is to measure the perimeter of the walls that the foundation guy has provided, then divide the total length by the number of walls that I'm building. I then theoretically cut all the plates at that length and lay them on the foundation, tweaking them into their true 45 degree angles. The plates hang over some of the foundation and hang in on some, but usually it's not a problem.
It would be better if they let me lay the block on those sections but I'm okay with my own method of fudging.
blue
Sounds like fine homebuilding to me !=0)
The destination is not the point. The completion is not the point. Enjoy today. If you can't enjoy today, then what is the point ?
Hate to say it, but if you are having trouble figurin' the floor, what's gonna happen when you get to roof?
I like Luka's method, but when you get to the roof, I doubt you are gonna be able to 'fake it in there' :-)
He he heYou haven't seen the master of kludge at work yet.;o)I'd geterdone ! And without a mathmagician...=0)
The destination is not the point. The completion is not the point. Enjoy today. If you can't enjoy today, then what is the point ?
I hear ya! I've seen framers frame all kinds of stuff with nothing more than a tape, stringline, speed square, skill saw, and a nailgun :-)
OK, maybe a hammer too for the beat to fit phase...
I just love that term though... "fake it in there". :-) I'm not the master, but I can make due when necessary :-) Oh- OH!!! - this is FHB Shusssh before someone hears us :-)
Dude!
Just draw it out in CAD and cut out the pattern with some scissors.
Databoy
A fine structure would/could still be had.The issue isn't whether you wrapped yer noggin around enough numbers... The issue is how well you built it, and how nice you made it look.=0)
The destination is not the point. The completion is not the point. Enjoy today. If you can't enjoy today, then what is the point ?
Draw a circle using your tape. Call the center C.
Pick a point on the circle to be one of the vertices of the pentagon. Call this point A.
Draw a line from this point through the center (C) and to the opposite side of the circle. Call the point where the line crosses the circle point B. Call this line AB.
Bisect line AB and extend the new line to the circle on both ends. This will look like crosshairs. Label the points D and E. Call the line DE. (see below how to bisect a line if you don't have this in your bag of tricks already.)
Bisect line CE (from the center to point E). Call the middle of this line point F.
Now draw an arc, using point F as the center and using the line AF as the radius.
Where This arc crosses line DC, label a point G. Almost done!
Now draw an arc with the center at point A and using line AG for the radius. Where the arc crosses your circle in two places, you will have the next two vertices of your pentagon.
Just swing an arc with the same radius from each of these two points to get your remaining points.
Bisecting a line:
Let's start by calling the line AB, to match the circle as shown above.
Hook your tape over a nail at point A and extend it about 3/4 of the way to point B. Draw an arc across line AB. Then do this again using the same length of tape, but with point B as the center of the arc.
The two arcs will cross in two places. If not, adjust the arcs so that they do cross. Be careful to keep the radiuses the same.
Call the two points where the arcs meet X and Y. Draw a line from X to Y. This line bisects line AB. As a bonus, it is perpendicular to line AB, forming crosshairs for your convenience!
Trigonometry. The formulas in the attached images will work for any regular polygon with an odd number of sides.Joe Bartok
Paul: Forgot to add something in my last post that will help you with the layout. For a regular pentagon:
Diagonals = Length of Side × 1.618034 ... the Golden Ratio.Joe Bartok
Sas...Thank you for the "hands-on" method you describe.THAT... I would be comfortable doing.
The destination is not the point. The completion is not the point. Enjoy today. If you can't enjoy today, then what is the point ?
No problem.
Actually, once you know this method, you can do it with a string and a pencil.
Try to convince a neighbor or friend that it has something to do with the Da Vinci code, and if they could only incribe the perfect pentagon on the floor for you, the mystery would be solved...
Paul,
With the measurements of the triangle you can cut a triangle out of a sheet of plywood or cardboard with the bottom 4'6" and come up 3'1-3/16" and the two angles would be 3'9-15/16".
Use that triangle for all 5 triangles to lay it out on the ground and you have your full Pentagon. Or if it's confusing make 5 triangles the same and lay them on the ground and your done. Your mason can't go wrong, he has patterns.
Paul, here's a web-based Regular Polygon Calculator to test the dimensions.
Check the link to the diagrams for the meaning of "width", "inscribed" and "circumscribed" in each different case. For example, in most books or drawings, the term "across flats" or "across corners" is the correct name for the measurements I'm showing as the "width" on even sided polygons such as hexagons or octagons.Joe Bartok