515.15 Complementary Angles

515.151 The initial angle and its cyclically complementary angle are defined by the relative proportions of one whole circle into which the whole circle is divided by any two different radii of the circle.

515.152 The greater the even number of equal intervals into which the circumference of the circle is divided, the more accurately may the proportioning of the circle’s central-angle-divisioning be described. If the circle is divided into 360 degrees and if the initial angle considered is 60 degrees, then its complementary angle is 300 degrees. If the initial angle is 90 degrees, its complementary is 270 degrees. If the initial angle is 180 degrees, its complementary is also 180 degrees. This ambiguity, if not thoughtfully considered, can bring about fatal “wrong-way” errors of direction-taking in navigational calculations. What looks like a local fragment of a “straight” line constitutes a complementary pair of 180-degree angles generated around the center-point of the line.

515.153 An assumedly straight line both of whose ends are hypothetically considered to be leading in opposite directions to infinity also may have an arbitrarily selected dividing point located (locally conceptually) upon it from which the oppositely extending lines emanateor upon which point the opposite lines converge to form a 180-degree angle. Both of the oppositely-and- outwardly-bound lines of extension from the 180-degree angular convergence point are inferentially interminable. Ergo, as hypothetically assumed to be “straight” lines, they are paradoxically half-finite and half-infinite. This is a paradox consequent to humanity’s misassumption of the existence of the phenomenon of “straight” lines, an error that occurred in turn only as a consequence of the inadequate experience of people at the time they adopted the fallacious assumption. Such misconceptions are the logical consequence of humans having always been bom naked, helpless, and ignorant, though superbly equipped cerebrally, utterly dependent upon only trial-and-error-based exploration and survival stratagems.