[PW] circumference question

[Brian Whatcott]

Nancy,
I interspersed responses:

At 01:48 PM 11/28/2007, you wrote:
>This is for me.  I bought an item at a yard sale. When  all parts are
>  attached to the wall, it will make a wreath.  There are 17 "arcs"
>quilted out of various red gingham materials. The arcs would lie flat
>against a wall. Picture something shaped like a crescent moon turned
>on its side. The outer curve has a scalloped edge. The inner curve
>is 25.5" long along the curve, and 23" in a straight line going from
>  point to point of the crescent. I have 2 questions:
>
>1. Is my logic correct that (17 * 25.5) divided by pi is the diameter
>of the inner circle? That would be approx. 11.5 feet wide.

That would be true if the arcs were from a circle of this diameter.
They are not, however.

>2. Is there a way I can tell if the 17 pieces will indeed form a circle?

Yes, the trigonometry given leads to the conclusion that the arcs would
  lie closest to a circle of diameter 33.4 inches.
That would only take four pieces.

>That is, since I got it at a yard sale, how can I tell if all the 
>pieces are there?

It is not possible to deduce the original decorative intention: whether is was
to get multiple small circles of four pieces, so that three pieces are missing:
of five pieces with 2 missing; of six pieces with one piece missing etc....
or one circle of least inner diameter 10.43 ft from 17 pieces, giving 
a scalloped
interior diameter as well as a scalloped exterior curve.

>I have a large blank wall I'd love to decorate with the wreath, but 
>I do not have
>  11+ feet of floor space (sans heavy pieces of furniture) to lay it out on.
>
>Any help would be greatly appreciated.
>
>Nancy Jo Leachman


Brian Whatcott    Altus OK    Eureka!