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Definitions
Items directly below are considered to be strictly Mathematical / imagined.
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active version ( Galilean) Starting with only one point when coincident systems. Cartesian coordinate system A standard x,y,z grid. coincident coordinate systems Two Cartesian coordinate systems occupying the same mathematically imagined space at the same time. Galilean transformation Is a set of mathematical equations, to numerically characterize, the corresponding coordinate points from one frame (coordinate system) to another. passive version ( Galilean ) Starting with two points when coincident systems. point A specific x,y,z location of a Cartesian coordinate system Wherein, the coordinate values are determined, not through the naming of them, but by their relative distance from their origin. transformation A coordinate transformation is a conversion from one system to another, to describe the same space. (wiki). Whereas space itself is considered to be a duality in characteristics...possessing both an imagined mathematical space aka Euclidian space and a corresponding physical space. Euclidian space The imagined mathematical points of an imagined mathematical Cartesian coordinate system. Mathematically, any point is suitable as origin, as well as any delineation value for a unit length. Even a rotational variance between two Cartesian coordinate systems can be dealt with exact mathematical precision. physical space [ Not pertinent to this math challenge. ] The actual physical locations in space, each unique location, of which can be assigned a mathematical, one to one relationship, to a corresponding point in an imagined mathematical Cartesian coordinate system. |