^ I've looked at the curve produced with the points I currently have.

It looks similar to y=hyperbolic cosecant(x), but it's not correct.

Here is my current known data set in both fractions and decimals:

Code:

y x
32/1 sqrt(2)/16
16/1 1/8
8/1 sqrt(2)/8
4/1 1/4
2/1 sqrt(2)/4
1/1 1/2
1/2 sqrt(2)/2
1/4 1/1
1/8 sqrt(2)/1
1/16 2/1
1/32 sqrt(2)/0.5
32 0.088388347648318440550105545263106
16 0.125
8 0.17677669529663688110021109052621
4 0.25
2 0.35355339059327376220042218105242
1 0.5
0.5 0.70710678118654752440084436210485
0.25 1
0.125 1.4142135623730950488016887242097
0.0625 2
0.03125 2.8284271247461900976033774484194

There's certainly a pattern here. I just do not know how to put it in an equation so I can solve for one variable if I have the other.

I found it!

y=((1/x)^2)/4

x=1/sqrt(4*±y)