areslagae said:Thanks.
Is "4-D spherical coordinates" established terminology?
Is this the "standard" transformation? I guess there are other ones?
A 4D angular coordinate system is a mathematical system that allows for the representation of four-dimensional space, which includes three spatial dimensions (length, width, and height) and one temporal dimension (time). In this system, each point is defined by four coordinates, typically denoted by (x, y, z, t).
In a 4D angular coordinate system, there is an additional dimension (time) that allows for the representation of changes over time. This means that in addition to the three spatial dimensions, the coordinate system also includes a temporal dimension, allowing for a more comprehensive understanding of events and phenomena.
A hypervolume element is a mathematical concept that represents the infinitesimal volume in a four-dimensional space. It is analogous to a three-dimensional volume element but accounts for the additional dimension in a 4D angular coordinate system. It is denoted by dV or dV4D.
In a 4D angular coordinate system, the hypervolume element is calculated by multiplying the infinitesimal changes in each of the four coordinates (dx, dy, dz, and dt). This can be represented mathematically as dV = dx * dy * dz * dt. The resulting hypervolume element is a four-dimensional measure of the volume in space and time.
A 4D angular coordinate system and corresponding hypervolume element have various applications in different scientific fields. For example, in physics, it is used to study the behavior of particles in four-dimensional space-time. In biology, it can be used to analyze the growth and development of organisms over time. Additionally, it has applications in engineering, computer graphics, and many other areas of research.