System Representation of Physical Quantities: Visualization of Dimensional Relationships of Physical Laws

The principle of geometric-dimensional representation of physical quantities in the dimensions of the International System of Units in the form of separate system cells on an LT-dimensional basis is described. Depending on the ratio of the dimensions of quantities in the International System of Units and the LT representation, physical quantities are combined into separate clusters that form the multilevel content of most system cells. Physical quantities within a cluster have the closest dimensional connections through length, time, and speed. It is shown that long-range dimensional relationships of physical quantities expressing physical patterns (without digital coefficients) are selected parallelograms or selected lines. In this case, the additional coefficients of the cluster groups eliminate each other, and the products of the dimensions of physical quantities located on opposite sides of the selected parallelogram are equal to each other. Such a systematic principle of representing physical quantities allows not only to illustrate known physical patterns, but also to discover new ones, as well as to identify certain properties and features of the arrangement of quantized and constant physical quantities in various versions of their systemic representation. The results of the work can be applied in the educational process and exploratory research.