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The extensive use of coordinate systems for the algebraic analysis of geometric curves originated with René Descartes (1596 1650).
Further development of coordinate systems (see figure) in mathematics emerged only after algebra had matured under Islamic and Indian mathematicians.
Instead, we use a sequence of coordinate changes.
Denote, where and in a neighborhood of coordinate origin.
In each subdomain a transformation of coordinate is used.
Palter (1972) first broached the Phoronomy from the modern standpoint of coordinate transformations between frames.
Why, after all, should any genuine physical phenomenon depend on the choice of coordinate system?
The problems of coordinate positioning when assembling large-sized constructions are considered.
First, a scaling gain is introduced into the system under a set of coordinate transformations.
Properties of sections of coordinate maps are discussed in [21, Section 3].
In fact, however, the main different point comes from the independent choice of coordinate.
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