SDW BP Glossary Issue 189: Dimension

1. Dimension (geometry)
As mentioned in CRS issue, dimension is usually defined in term of number of coordinates needed, whereas coordinates are defined in terms of the dimension. ISO19107 breaks out of this by having a rigorous mathematical definition which is incomprehensible to non-mathematicians. I propose that we stay with the Wikipedia article paraphrase, as definition by example is valid. I suggest adding a torus to the cube, sphere and cylinder examples to show a bit more generality. (Note 'doughnuts' are not well defined globally!) Also, tidy up both the highlighted comments:

"Dimension (geometry): In physics and mathematics, the dimension of a mathematical space (or object) is informally  [[https://en.wikipedia.org/wiki/Dimension|defined]] as the minimum number of coordinates needed to specify any point within it. Thus, a point has no dimension (0D) as there is no inside, whereas a line has a dimension of one (1D) because only one coordinate is needed to specify a point along it – for example, the point at 5 on a number line. A surface such as a plane or the surface of a cylinder, torus or sphere has a dimension of two (2D) because two coordinates are needed to specify a point on it – for example, both a latitude and longitude are required to locate a point on the surface of a sphere. The inside of a cube, cylinder, torus or sphere is three-dimensional (3D) because three coordinates are needed to locate a point within these spaces. For a formal rigorous mathematical definition see the ISO definition<http://registry.it.csiro.au/sandbox/iso-tc211/terms/213>. [[ISO-19107]]"

Of course we now need a Coordinate System definition:
“Coordinate System: collection of all possible ordered lists of n numbers designating the position of a point in n-dimensional space. [[ISO TC211]]”

Chris