by Sam Ioannidis
Start off with the equation for a sphere with radius r in mm:
x2 + y2 + z2 = r2
From the diagram below you can see that a single lego unit is not a cube.
Allowing for space between blocks you can consider the width of the base
of the block to be 8mm.
To go from dimensions in mm to dimensions in lego units then consider:x = number of lego blocks across (X) * 8mm
y = number of blocks high (Y) * 9.6mm
z = number of lego blocks deep (Z) * 8mm
where X and Z and are dimensions horizontally in lego units and Y is the height in lego units,
(8X)2 + (9.6Y)2 + (8*Z)2 = R2
solving for X gives
X = √ R2 - 1.44Y2 - Z2
where R is the total radius of the sphere in lego units horizontally or radius in mm divided by 8
converting this to a spread sheet formula gives
X = sqrt(R*R - 1.44*Y*Y - Z*Z)
If you want to download the spread sheet that I used then click here. I used openoffice calc show you might also need to download this if your spreadsheet software doesn't read that format. Follow the instructions below to make a sphere of any radius and thickness.