Length in two-dimensional space (in other words, length in a plane) defines distance. If the distance is referenced from a point, then the circle is the set of all points that are this particular distance away from that point, or center. The radius is the length or measurement of the distance from the center to […]
It’s generally understood that, when the time dimension is subtracted from spacetime, we are left with Euclidean 3-space. This is usually interpreted to mean that, once we look at spacetime without the time component, we’re left with space, or what in SI units is called volume. The SI unit for volume is which is consistent […]
Figure 2.1 – NIST Subway Diagram So, what is direction, really? Currently, direction is an orphan when it comes to understanding physical quantities and how they relate to one another. The basic unit that is used to define an angle, the radian, is the disconnected unit at the lower right in the NIST diagram. […]
So, what is direction, really? We can call it angular position, and we can call the change in angular position angular velocity, and we can call the change in angular velocity angular acceleration. In case it isn’t obvious, there is a stunning symmetry with length here. We can call it linear distance, where we can […]
Direction is currently considered to be a ratio between lengths. This is different (mathematically and conceptually) from representing direction as a quantity. Ratios are not quantities. They are a comparison between two or more quantities, which is fundamentally different from how quantities themselves are represented.
The way that it’s mathematically expressed, space actually comprises a set of three 2D planes, arranged orthogonally. In this usage, each individual “dimension” is actually a plane, or a set of two perpendicular directions, where each direction is also called a “dimension.” The x and y dimensions combine to form the xy-plane which is perpendicular […]