A NEW APPROACH TO GRAPHICALLY REVEAL SOME UNKNOWN PROPERTIES OF THE ORTHOGONAL COORDINATE SYSTEMS IN QUADRIC FORM, BY USING THE SQUARE ROOT SCALED CHART

The square root scaled chart (SRSC) to show the behaviour of variations changing slowly, has been in use for almost half a century for statistical data processing purposes, in which an axis only is scaled in terms of square root of any variable under consideration. In this study, as a first in the literature, some orthogonal coordinate systems (OCSs) in quadric form which are widely in use are graphically illustrated by using the SRSC in which all axes are square root scaled. The OCSs are very important having indispensable pedagogical (scientific and engineering) value to explore, formulate and illustrate the equipotential surfaces and vector flows in wide area of physics (e.g. mainly in electricity and magnetism). While the traditional linearly scaled chart (LSC) used to hide some properties of the OCSs in quadric form, the use of SRSC contributes towards facilitating drawing by revealing the hidden properties and provides a good understanding how the variables interact with each other (and the physical phenomena to which they are attributed). The suggested usage of the SRSC in the OSCSs has the potential to increase their usage mainly in teaching theoretical and applied physics (in the area of potential theory) and geometry.