How would you go about describing a precise position?

[OAQfirst]

Say you have a point on a surface, such as somewhere on the tip of your fingernail, and you needed to express that position to within an atom. How would you do it? I was wondering if anyone even does this sort of thing.

I understand that some position would need to be chosen relative to the point, but beyond that I'm stumped.

 

[mgb_phys]

You need to choose a set of axis and some way to fix them and a zero position to measure from. In all you need 6 fixed values.

You could measure the position of an individual atom on a finger tip with an AFM (but you might need to remove it first)

 

[Borek]

You need to choose a set of axis and some way to fix them and a zero position to measure from. In all you need 6 fixed values.

Can you elaborate what you mean by "6 fixed values"? Especially why 6, as 4 points seems to be enough. Could be I am missing something.

 

[mgb_phys]

An x,y,z of the origin and roll,pitch,yaw angles for the axis.
Alternatively two xyz points.
To lock down 6 degrees of freedom you need 6 values.

 

[Borek]

I don't get it :sad:

I can't see how can I use just two points to define three axes. One axis OK, but nothing more, coordinates of every point that doesn't lie on the axis are ambiguous (at best, giving distance from both points, I can show circle on which the point lies). Three points - and I can have two axes (or I can give correct coordinates of every point on the plane, that's assuming my three points are not colinear). Finally, four points can define three axes, and that will allow me to give coordinates of every point in 3D.

 

[OAQfirst]

I've been thinking this over and I believe a six axis coordinate would work for my project (book). I searched Google, but all I find are links for that PS3 controller.

I would really like to see an example of what that would look like on paper. What search strategy should I be using? And what unit of measurement is used for very short distances between atoms?