Position and Orientation: Level 5

The key idea of position and orientation at level 5 is that lines and curves (called loci) can be described in terms of their relationship to certain fixed objects.

Loci were a spur to work that led mathematicians to the discovery of calculus. This came about because of the desire to understand the movement of heavenly bodies. In particular the locus of planets are ellipses as the planets move around that fixed object, the Sun. From this it is clear that loci exist in the real world. It is also true that loci can be used to solve practical problems.

This key idea develops from the key idea of Position and Orientation Level 4 where positions, directions and distances are defined on a coordinate system.

This key idea is extended in the key idea of position and orientation at level 6 by moving from constructing loci to finding points of intersection and areas in common between two loci.