facenian said:I'm not sure if I understand you question but regarding rotational symmetry both systems are physically the same(disrigarding direccions on the axes)
Yes, they can serve as the axes of a coordinate system. There's a formal mathematical definition of "coordinate system" which is very general and allows for all sorts of weird configurations.rkmurtyp said:Let me pose my question in a different way. Do two intersecting lines constitute a coordinate system?
does it have four quardents? or just one region in which coordinates of any point has positive numbers (for example (3.23,4)) only?
Nugatory said:Yes, they can serve as the axes of a coordinate system. There's a formal mathematical definition of "coordinate system" which is very general and allows for all sorts of weird configurations.
Four regions.
HallsofIvy said:Oblique coordinates can be useful if there are two non-orthogonal lines upon which you are given special information. Another example is in solving a hyperbolic differential equation where it would simplify the equation to use the characteristic lines as axes. And they are not generally orthogonal.
Also, while one can always find coordinates on a general surface that are orthogonal at a specific point but not generally orthogonal anywhere else.
An oblique coordinate system is a type of coordinate system that uses two intersecting axes to locate points on a plane or surface. Unlike standard coordinate systems, the axes in an oblique coordinate system are not perpendicular to each other.
In a standard coordinate system, the axes are perpendicular to each other, creating a right angle at their intersection. In an oblique coordinate system, the axes are not perpendicular, which allows for more flexibility in representing curved or tilted surfaces.
Oblique coordinate systems are commonly used in cartography, navigation, and geology. They are also used in computer graphics to represent 3D surfaces with more accuracy.
In an oblique coordinate system, points are located by measuring the distance from the origin along each axis. The coordinates of a point are typically written as (x, y), with x representing the distance along the horizontal axis and y representing the distance along the vertical axis.
Oblique coordinate systems allow for more accurate representation of curved or tilted surfaces, making them useful in many fields such as geography, architecture, and engineering. They also offer more flexibility in representing complex shapes and structures that cannot be easily represented in a standard coordinate system.