So I woke up Saturday morning thinking about long skinny triangles. Specifically, the pennants our Children's Pastor asked me to make for him to use in the kids sanctuary. He gave me 4 yards each of blue and red fabric, and asked me to make two pennants from each color one layer thick (so he could shine lights through them) 1/2 the width of the fabric wide on the fat end and tapering to a point. He said they could be three- four yards long, whatever worked best. But as I kind of drifted out of whatever I'd been dreaming, I had a feeling that would be really hard to cut accurately. Then I started thinking about how long that pennant would be...and how skinny.
So while I drank my coffee before I hopped off to church for more costume sewing, I pulled out a piece of scrap paper and My Sweet Baboo's old HP calculator and did some math.
I drew up the sample, assumed it would be the shorter version (3 yards = 108" long) and exercised my rusty trigonometry to discover that the angle at the point would be 12 degrees; 10" out from the point it would be 2.06" wide and 2 feet out it would be all of about 5" wide. Waaaaayyyy too skinny to either be reasonably easy to cut and sew or look good when it was done.
So I came up with a new design; a swag that's a 3-yards-long rectangle with a pointy section at the end. I can put rod pockets on the swag at the square end and where the angled section starts; the rectangle will then be drapeable, with a one-yard long pennant hanging at the end.
The scrap paper with all the angles and arrows and thetas and 'sin theta's and 'tan theta's' and equations looked really impressive. Not bad for a SAHM. Unfortunately I forgot to take it with me to church yesterday to propose the alternate design, so no one but me saw the inner mathematician emerge. So, despite the hard-to-scan pencil marks, here it is for you (if I made a boo-boo, don't tell me! The only thing I *think* I might've done wrong was forget that the angle I was working with was half the whole angel at some point. It has been a *really long time* since I regularly worked with these things). I darkened the scan somewhat; pencil doesn't scan well.(My 7th grade math teacher refused homework that wasn't done in pencil so now I have a permanent aversion to using anything but a pencil for math).
But Pastor Dave was amenable to the suggestion just the same. So I took about half an hour yesterday afternoon and tore the fabric into four half-width lengths, then folded each width in half and stacked them carefully to cut the one-yard-long triangle out of the end with one pass of the rotary cutter. So now all I need to do is serge the edges and fold and stitch the rod pockets.
I just have to change the serger thread first.