My problem is the following... This is basically a question regarding macroscopic structures and Van Der Waals interactions - But I only need to prove the geometry. Essentially what I am asked to do is to prove that the geometry of 2 crossed cylinders is the same as a sphere over a surface at distance D from the surface.

To make the picture simpler: If 2 cylinders are crossed and I look at the end of one cylinder, then it will look like a circle and a straight line. Now, what I have to prove is that the geometry of 2 crossed cylinders is locally equivalent to the sphere-surface geometry mentioned above, but not only from those perpendicular cases. So far I have presumed that the distance between each cylinder is D, the radius of the cylinders are R, and once I find the distance I will have to do a Taylor Expansion to make them locally equivalent... But my problem is finding an expression for the distance if the cylinders are viewed from a 45 degree angle.