I have a 30 inch square. I want to turn this into an octogan by cutting off the corners. I don’t have anything with angles but if I knew how long each side would be, I could cut the foam core board correctly. Please help me. Thanks.
I’m gonna assume the square is 30 inches on a side
if you make an X by creating lines from corner to opposite corner
then 15 inches from where they cross, toward any corner, is where the cut will cross
you just have to make the line, for the cut, so that it’s center is at 15 inches from the center of the square
http://www.ehow.com/how_4683220_construct-regular-octagon.html
That’s a formula.
I got that each side will be about 12.43", but I’m somewhat dysnumeric, so don’t take my word for it. Denny’s solution seems elegant.
Denny’s reply hurt my brain, as do all his comments. Emm’s got to the heart of the matter. Once I take the dog for a walk, I’ll see how the math worked. Thanks.
…And of course the cut should cross the diagonal line at a right angle. You’ve gotta have something with one square corner.
Edited: Denny’s solution very elegantly uses the diagonals to give you the 45% angle you need to make an octogon. Draw the diagonals, and than draw a line that crosses each diagonal 15 inches from the center, and you have a perfect octagon with no math required.
two chalk lines & a carpenter’s square is more painful than paper, pencil & protractor?
s1, I was presupposing that wasn’t I…
No, it’s sweet.
Make an x, like this: X
It runs from corner to corner in your square, crossing in the middle.
So, starting from the center of the X, measure 15" along the line toward each corner. Mark these 4 spots.
The center of each cut is on these 4 spots. You just have to make sure each of the triangles formed is isosceles…i.e., the sides of the triangles that meet at the four corners of your original square must equal each other, but the base (your cut) will be longer.
Right, this. That will make positioning the cuts easy.
emm’s answer was good enough. that worked. thanks. nothing has to be exact. this is me we’re talking about.
Wow…lookee this! (just for fun, and future reference:)
http://buster2058.netfirms.com/octagon/calc/octagon_layout_calc.htm
Indeed: sides= 1’ 7/16" Very good.
Now you can calculate ALL your octagons!
You folks amazed my friend who was helping with this project. Going to musicians for help with math problems is not anyone’s first inclination. But mine.
so ya have to have a measure, a straight edge & a pencil but ya don’t need a chalk line 
I’m keepin’ me chalk line…
a lot of the musicians I’ve known were comfortable with math/geometry…
Yep, Denny’s geometric solution is elegant. Use a T-square or protractor or a pair of compasses (my preference) to construct a perpendicular to each 15" crossing point.
The algebra is straightforward, too. Slice an isosceles triangle off each corner such that the hypotenuse of each triangle equals the length of each remaining original edge of the foam square.
If each triangle is x by x by h, then each side of the original square is
2x + a = 30", where a = the remaining edge.
For each triangle, h = sqrt(2x^2) by the Pythagorean theorem. And by definition you want a = h. So substituting for a above, you get
2x + a = 30
2x + sqrt(2x^2) = 30
2x + (x * sqrt(2)) = 30
x * (2 + sqrt(2)) = 30
x = 30 / (2 + sqrt(2)) =~ 30/3.414 =~ 8.8 inches =~ 8-13/16 inches
So you can measure and mark 8-13/16 inches from each corner of the original square, and slice across the marks. Or use that measurement to double check the geometric cuts.
I taught geometry in high school for several years. Rather than embarrass myself in front of the class on the blackboard, when I got these kinds of questions, I passed them to the smart kids in the class and pretended that I knew the answer. I wish is was that simple.
an’ then ya want Mutie to do a sqrt? 
Hush now. Doing a sqrt is not something to be discussed in polite company.
not one of those things I do in private either…
TMI, Denny. At least you don’t live in Delaware.
With Denny’s reply giving me a headache, Guru’s reply had the potential to knock me into a seizure. Before my heart surgery, I could have done the math and thought all this through, for the first year after my heart surgery, I couldn’t even do simple math in my head. I was lucky that basic math skills came back. Higher math skills will never be seen again, to no one’s loss. I regainded most but not all of my playing card counting skills too. That made me happy.
I am making a rather large octogonal shaped spinner/top to play a Wheel O’ Fortune type game at a Disabilities Conference. I wanted to make a casino type wheel with the pegs sticking out but that would have been a bit complicated and required more engineering and craftsmanship than i could handle. Instead, the octoganal spinner/top will be on the floor, just like on Wheel O’ Fortune and the spinner will tip to the chosen prize. I covered the board with that sparkly mylar wrapping paper so it will be all shiny and stuff.
Ooooh … shiny!
