Something else to think about

If you have a piece of material that measures 48" x 48"
what is the largest paired diameter you can cut from that square?



:shrug:

:cry: Because I am no damn good at geometry!

Are you going to tell us the answer?

:loveya: :hug:

Work with the radius of the two circles; call that r. I'll call the side of the
square s for now, because it's easier to work with as a symbol.

First you notice that a line connecting the center of the two circles is the
diagonal of a square of side (s - 2r). The diagonal of a square has a length
of (sqrt 2) times the side. So the distance between the centers of the circles
is (sqrt 2)(s - 2r). But the distance between the centers is also just 2r, because
the circles touch. So you have 2r = (sqrt 2)(s - 2r). A tiny bit of algebra and you get
2r(1 + sqrt 2) = (sqrt 2)s, or 2r = (diameter) = (sqrt 2)s/(1 + sqrt 2).
That could be simplified a little more, but never mind. If I put in the numbers,
I get (diameter) = 0.58579 s = 28.12"

:applause: :applause: