The area of the square with side a equals the area of circle with radius r.
The large square they are within has area of 1.00000
What are a and r?
a=0.556, r=0.314 Purely algebraic solution that I'll post later.
Your circle and square don't fit into the big square.
a=0.5
r=0.293
by algebra i get a=0.509 and r=0.287 on first attempt. I haven;t checked it though, just 3 mins. didn;t realise how rusty i was.
I will check by autocad.
yay I think I got it.
Doug Crawford, post: 333110, member: 9 wrote: a=0.5
r=0.293
This is the answer,for a using the a quarter of big square, but the answers are
dependent, on each other.
a can be = 0 to 1
and r will vary
from .5 to 0
Doug Crawford, post: 333121, member: 9 wrote: This is the answer,for a using the a quarter of big square, but the answers are
dependent, on each other.a can be = 0 to 1
and r will vary
from .5 to 0
He also stated that the areas of the small square and the circle must be equal.
Stephen Ward, post: 333125, member: 1206 wrote: He also stated that the areas of the small square and the circle must be equal.
I stand corrected, thanks.
Now all I need are my chicken scratchings from 5:00 AM. this morning
I got Bill93's answer with a quadratic equation. a = 0.5562092371, r = 0.3138074579. For those who hate lots of decimal places, remember that it's impossible to square a circle, so there is no exact answer.
But that's not the correct answer.
I found my mistake. Darn 3-minute hurry.
Still all algebraic - no quadratic required. Just add up the pieces of the diagonal. Lots of sqrt 2 and sqrt pi factors.
Rounded to 4 places ...
a=0.5094
r=0.2874
That's what I got. An "exact answer" for r is r = sqrt(2)/(1 + sqrt(2pi) + sqrt(2)). Bill probably has a simpler expression, but I've always done things the hard way!
squowse, post: 333115, member: 7109 wrote: by algebra i get a=0.509 and r=0.287 on first attempt. I haven;t checked it though, just 3 mins. didn;t realise how rusty i was.
I will check by autocad.
No outward signs of rust!!