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40d:Z-axis
The Z-Axis is known in math as the "third axis".
It's easy to think of a graph with an x-axis and a y-axis, right?
The X-Axis goes left to right, whilst the Y-Axis goes down to up.
Here we can see the three axes...
The Z-Axis, as you can see, goes perpendicular to both the X-Axis and the Y-Axis to create a 3-D coordinate system, which is essentially what Dwarf Fortress is based in.
Thus, objects described with only 2 axes are 2 dimensional, whilst objects with depth measured along the Z-Axis are 3 dimensional.
In Dwarf Fortress, the Z-Axis is a fairly recent addition to the game that allows players to dig holes down into mountains, or up into mountains, see where exactly those trees are, dig ditches... etc.
The Z-Axis is also believed to be in part of the game engine that calculates accuracy of weapons based on where dwarves are, how missiles fly, and other considerations.
The Default Key-Bindings to shift what part of the Z-axis plane you are viewing are
Shift + Numpad5 (supposedly shifts viewing plane up, but I was unable to reproduce -- Alfador 21:44, 30 October 2007 (EDT))
Control + Numpad5 (shifts viewing plane down)
Shift + . (>) (shifts viewing plane down)
Shift + , (<) (shifts viewing plane up)