The Concept Of A Circle

Calling the relationships between numbers social constructs is an outright blunder that, if the claimant is consistent, reduces to the gravest error of all: the dismissal of reason as a construct of the human species.  Nevertheless, not only is the linguistic side of mathematics--the set of words assigned to numeric values--nothing but an arbitrary human creation, but it is also the case that entire sections of the geometry taught in schools are nothing but constructs themselves.  Consider the numeric values associated with the concept of a circle.

Calling a full circle a 360° angle is an arbitrary way to numerically define the shape, as one could call a circle 270°, 623°, or any other number of degrees without actually contradicting the concept of a circle.  No one can prove that a circle is 360° all the way around; they can only define degrees in such a way that 360 of them form a circle, the concept of a circle being something that does not depend on human acknowledgment.  This is because the concepts of shapes and numbers are not dictated by human language and convention, even though 360° is regularly equated with a circle as if it is a logically necessary part of the definition.

The concept of a perfect circle is always that of a shape where a point is surrounded on all sides by a unbroken, curving line that is always an equal distance from the center--but this does not prove that a circle contains a 360° angle.  That is simply the value that humans have assigned to the idea of a full circle.  None of this affects the fact that no matter what any person calls the angle of a circle, the idea of a circle is objective, reducing to the laws of logic rather than to linguistics or other social constructs.

Mathematical concepts (and, of course, logical concepts as a whole) are not invented by individuals or societies, but the descriptions of them can only be expressed in an arbitrary manner either within the communicative norms of a given society or in an individual's own words.  Classifying a circle as a 360° angle is merely useful for schooling and other practical purposes.  What matters more than the arbitrary number of degrees one labels a full circle is the fact that the concept of a circle is untouched by the customs of language.