[PW] circumference question: DIY solution

[Nichael Cramer]

1] A quick bit of googling has convinced me that, alas, the only way to
solve this *exactly* is with a goodly amount of math ending with a
numerical (i.e. non-analytical) solution.

2] However, that said...

If I needed to solve this in the real world, here's what I'd do:

-- Lay the quilt piece out smoothly on the floor.

Now, using a pencil and piece of string, find the center of the circle
of which the quilt piece is a part.

-- That is, take a piece of string and tie it to a pencil.   (If the previous
calculations are correct this needs to be about 5-1/2 or 6 feet long; but
surely anyone attempting this project has sufficient thread for this.  ;-)

-- Make a first guess at where you think the center of the circle
might be.   Now holding the end of the thread at that point, take
the end with the pencil and try to trace out a circle near the quilt piece.

(You might find it easier if you have a helper for this part --any kids
or grandkids available?   Alternatively, you could hold the "center end"
of the thread under a weight, e.g. your copy of the OED.)

-- The goal here is for the path of your pencil to match the inner edge
of the quilt piece.  Your first guess at the center of the circle will likely
be wrong; but you just adjust your guess and try again.

When the path of your pencil traces out the inner edge of the quilt piece
you've found the center of the circle.

-- Congratulations.

-- Finally, place a piece of paper under the newly-found circle-center.
Stretch the string from the center of the circle to one end of the arc on
the quilt piece.   Now draw a straight line along the string
starting the newly-found center.  Repeat using the other end of the arc.
The angle on the paper will now form the angle that we've
been trying to find.  With a protractor you can now measure
the angle that the quilt piece represents.

(Also, while you're here, you might as well measure the distance
from the edge of the quilt-piece to the center in order to find the
"real" diameter of the circle.)

-- If the 17 pieces really do make up a complete circle the answer should
be a smidge more than 21 degrees.

(If you don't have a protractor, you can take the piece of paper
with the angle to a friend who does.   On the other hand, once
you've copied the angle onto the paper, you can make a stack of
17 pieces of paper --with the sheet with the angle on top-- and cut
the stack into 17 wedge-shaped pieces [each having the angle of interest].
You can now try to fit the paper-wedges together to see if they
form a complete circle.)

(Frankly, my guess is that they won't form a complete circle.  17 is just
too weird a number for something like this.   I'm betting you're either
missing one or more pieces, or, more optimistically, you have extra
pieces for the project.)


So, in short, while doing all the trigonometry can be a great deal of
fun[*] in its own right , surely it's overkill here.   And while I'm
sure Nancy Jo is an expert quilter (who else would tackle such a
project?) my experience with having lived around several quilters
indicates that the above method should provide more than sufficient
accuracy.   And, in the final analysis, it only matters if the pieces
neatly fit, no matter what the numbers say.

Hope this is of some help,
Nichael
[* And as an old math geek myself, I say this with no trace of irony.]

--
Nichael Cramer
Guilford VT
nichael at sover.net
http://www.sover.net/~nichael/