The coordinates of points are recorded in a coordinate system. A coordinate system is the set of coordinate
system axes that spans the coordinate space. This concept implies the set of mathematical rules that
determine how coordinates are associated with invariant quantities such as angles and distances. In other
words, a coordinate system implies how coordinates are calculated from geometric elements such as
distances and angles and vice versa. The calculus required to derive angles and distances from point
coordinates and vice versa in a map plane is simple Euclidean 2D arithmetic. To do the same on the surface
of an ellipsoid (curved 2D space) involves more complex ellipsoidal calculus. These rules cannot be specified
in detail, but are implied in the geometric the properties of the coordinate space.
NOTE: The word ‘distances’ is used loosely in the above description. Strictly speaking distances are not invariant
quantities, as they are expressed in the unit of measure defined for the coordinate system; ratios of distances are
One coordinate system may be used by multiple coordinate reference systems. A coordinate system is
composed of an ordered sequence of axes, the number of axes being equal to the dimension of the space of
which it describes the geometry. Coordinates in coordinate tuples shall be listed in the specified axes
sequence and units.
The dimension of the coordinate space, the names, the units of measure, the directions and sequence of the
axes are all part of the Coordinate System definition. The number of coordinates in a tuple and the number of
axes in a coordinate system shall be equal.
Example: It is therefore not permitted to supply a coordinate tuple with two heights of different definition in the same