Want to draw up a template for a segmental pediment to adorn the top of a puppet booth I'm building. But I have forgotten my math  .

The base is 37.5 inches and the height is 12 inches. Anyone know what the formula is?

TIA.

Had to look up segmental pediment to know what you wanted.   Is this any help to you? http://www.had2know.com/academics/arc-radius-angle-formula-calculator.html just makes my head hurt but I think the answer is in there some where. This is a bit more advanced and confusing to me but might help. http://books.google.com/books?id=Vp4PAAAAYAAJ&pg=PA315&lpg=PA315&dq=draw+a+segmental+pediment&source=bl&ots=6T000vSgK7&sig=mutA-QxR2OaK8UpdzGZyCZ-whtg&hl=en&sa=X&ei=Fb_7Ufm-CoOa9QSOsICQBg&ved=0CEEQ6AEwAw#v=onepage&q=draw%20a%20segmental%20pediment&f=false

Ahh maybe this is easier. Has a caculator on the page to get radius. http://www.mathopenref.com/arcradius.html  According to that your radius is 20.6484375  (or in my feeble mind would be the length of the string I cut to use in drawing the arc).

So, if I understand correctly you want to make a segment of a circle (had to look segmental pediment up . ) for the top of your puppet stage?  The width of your stage is 37.5" wide and you want the arch to be 12" tall?

The easiest way is to fold a large piece of paper in half to form a  straight folded edge and straight bottom edge.  I'm left handed, so I lay the paper so the folded edge is vertical to me on the right side.  Measure 12" from the bottom on the folded edge.  Half of 37.5 is 18.75 or 18 and three quarters. On the bottom from the folded edge moving horizontally, measure 18.75".  Now draw an arch from the top measurement, 12" to the bottom measurement 18.75.  Cut out. Open up and there you have it. Not to much Math.  

Julie

@ Shawn: many, many thanks. Worked it out (without the use of the calculator) before discovering the calculator on the same page. Doh! LoL.

@ Julie: Correct. Your way is similar to the solution provided by Asher Benjamin in his: "The Rudiments of Architecture: Being a Treatise on Practical Geometry" where he uses three fixed rods (equal to the radius and diameter of the segment) to describe the segment. Many thanks.
 

You'll have to show us the results once you get it all done.

BTW: Since both Julie and myself had to look up Segmental Pediment, figured I would share with everyone the link to Wikipedia that explains what we are talking about.

Pediments are something commonly seen on Punch and Judy theaters. Segmented means that it has a curved top or arch as opposed to simply being a peaked triangle.

c16thfoxe, er yeah , I had to look it up too, What are you going to make it  of? I did this tutorial on making a fake cornice that might be helpful to you. Is this sort of what you are wanting?

I did this tutorial on making a fake cornice that might be helpful.../

I should have known you had a video that would be relevant. Pretty sure that is what he is doing only he is not using a full have circle but just the upper portion of it.

Yes  He told me of his plans to do the  thing, when I stopped in to visit him. I'm not sure if he is going to use cardboard or what, and  also how  complicated he will go with it. Keep us posted c16thfoxe.