How do we tell where we are in 3D space. We need to be familiar with cartesian coordinates - x and y axes, before we add the z-axis.

We can think of using Pythagoras to get the distance formula - from one diagonal in a cuboid (superimposed in 3D coordinates). This requires some understanding of algebra and geometry.

Arbitrary positions in space are 'the void', and we can think in terms of going from one point to another: this consists of vectors. We can try to figure out angles between: this requires a familiarity with trigonometry.

The void requires a lot of mathematical knowledge and skill to conquer. Practical examples may help with visualisation: one corner of a cardboard box to another - how to measure that distance - compared to working it out using mathematics.

If boxes are not hard enough, what about more complex 3D shapes: cones, spheres, polyhedra...

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