╥

One of the main characteristics of any circle is the incommensurability between its curvilinear and its rectilinear features, i. e. between its circumference and its radius and diameter, a relation represented by the number ╥. In some contexts, one or other of the terms of this relation is accorded priority. For example, because of the ease of construction of a circle in terms of an integral radius, in basic Geometry, the rectilinear features are primary and rational, while the curvilinear one is derived and irrational. On the other hand, modern Calculus connotes the rectilinear term of the curve-tangent relation as the one that is 'derivative'. Regardless, what is irrational is ╥ itself, not necessarily one or the other of its relata, e. g. both a radius and a circumference can, in principle, be irrational quantities. Now, since there seems to be neither a perfect circle nor a straight line to be found in nature, the stronger case can be made that the concept of each is a priori, rather than a posteriori. Hence, ╥ expresses an irrationality within the a priori realm, contrary to the contention of some Rationalist doctrines, and in the structure of the Circle, a symbol of Perfection in e. g. Platonism and Aristotelianism.