Question 205500
If the Diameter of each shape is 1
then the area of the circle is pi and the "square" is 1
   so the ratio of circle to "square" is pi/1
if D=2
then the ratio is pi/2
if D=3
then the ratio is pi/3

it appears that it is a series where if D=n then the ratio is pi/n

when D=1/4 the circle is .723 larger
when D=1/2 the circle is  1.31 larger
when D=1 then the circle is about 2.142(let's say square inches for fun) larger
when D=2 the circle is about 2.283 larger
when D=3 the circle is about .423 larger
when D=4 the circle is 3.437 smaller
when D=5 the circle is ...

i used microsoft excel to extrapolate or get more values and here is what i came up with

Diameter	difference
0.00390625	0.0123
0.0625	0.1924
0.250	0.7229
0.500	1.3208
1.000	2.1416
1.500	2.4624
2.000	2.2832
2.500	1.6040
3.000	0.4248
3.500	-1.2544
4.000	-3.4336
4.500	-6.1128
5.000	-9.2920
5.500	-12.9712
6.000	-17.1504
6.500	-21.8296
7.000	-27.0089
7.500	-32.6881
8.000	-38.8673
8.500	-45.5465
9.000	-52.7257
9.500	-60.4049
10.000	-68.5841
10.500	-77.2633
11.000	-86.4425
11.500	-96.1217
12.000	-106.3009
12.500	-116.9801
13.000	-128.1593
13.500	-139.8385
14.000	-152.0177
14.500	-164.6969
15.000	-177.8761
15.500	-191.5553
16.000	-205.7345
16.500	-220.4137
17.000	-235.5929
17.500	-251.2721
18.000	-267.4513

then i used excel to graph them but i don't think i can paste a graph into this but the line appears to be a parabola the limit as x->0+ is 0 i think the equation to sum up the relationship would be...
i went to another website and used a regression tool and calculate the exponential regresssion (yes i did check the equation by plugging them back in)
and the equation is y = -1 x^2  +  3.1416x + 3.2226e-7

i hope that helps