Geometry, one of the oldest branches of classical mathematics, is concerned with the properties of space that one relates to distance, motion and the relative positions of individual figures. Most significantly, it instructs a method of problem-solving by rational analysis and the process of logical deduction, by the application of universally accepted principles (axioms) to attain the desired conclusions. Those who have studied Euclidian Geometry will undoubtedly agree that its salient value consists in its instructive discipline for the solution of presenting problems, but that it also has a lesser, additional utility in its concepts and principles, employed in the dynamics of life in speech and writing.
But first, we feel the need to take the opportunity of voicing our view on a somewhat related, frequent, and tiresome waste of human inquiry, not relevant to logic, geometric or otherwise. If we had the authority to do so, we would dispense with the trite, irrelevant, and useless problem, “What is the meaning (or purpose) of life.” To the degree that such questions make any rational sense at all, they seemingly are founded on some storybook or reductive view, that society’s pragmatic value, assigned to productive purpose is relevant to the metaphysical existence of man or nature. The Darwinian meaning and purpose of life are merely to live. The faux issue is not resolved logically (or geometrically) since it is not a rational issue. However, the topic of this writing is man’s pattern of life to the extent that it acceptably mimics and utilizes geometry.
Indispensable to the useful application of reason to the solution of problems is, initially, the accurate perception and understanding of the intrinsic problem. A not uncommon human failing with using geometric reasoning is the frequent confusion or misapprehension of the specifically presenting problem. The analytical capability to objectively discern the basic problem, possibly submerged in a quagmire of irrelevant and superfluous detail, or unproductive, thought impairing emotion, is the primary and quintessential prerequisite to resolving the problem.
Once the basic problem has been analytically discerned, the next geometric step is the application of relevant facts and principles, universally proven to be accurate, in theory, or empirical experience. In geometric or any logical system of thought, the ability to marshal (only) useful and relevantly known facts and experience is vitally essential. Once the acceptably known facts or experiences, relevant to the problem, are correctly applied, the solution to be deduced becomes accessible.
In addition to the existential value of problem-solving, the discipline of geometry in its illustratively applied forms has augmented a vocabulary, employed in literary and philosophical conceptions. The applicability of the expression, ”the circle of life” is descriptive of an often- stated use of the 360’ geometric form. The concept as applied to man’s lifetime, refers to his predictable physical condition from new-born to old age, viz., naps, gain and possible loss of teeth, physical limitations, eating, digestion, memory decline and toilet habits. It also has an acceptable application to man’s (hopeful) advances in knowledge, from “tabula rasa” to mature perception. A geometric circle upon completion returns to its starting point, and the life of homo sapiens empirically emulates that formulation.
In a similar fashion, the expression, “circular reasoning,” (use of the geometric figure, circle) is used to describe a form of fallacious reasoning in which the premise validates or ratifies the conclusion. For example, if it is accepted that the Bible is infallible, its premises are necessarily true, or you must obey the law because it is illegal to break it and, America is the best place to live because it is better than any other country. In essence, it describes is a useless restatement or repeated confirmation of the originally stated premise.
A form, indispensable to any study of geometry, and part of our vocabulary, is of course, the triangle. The term is figuratively used in man’s speech and literature, to describe a three-way relationship, such as occurs in marriages involving an unfaithful spouse (love triangle) or a menage a trois. In business, it is a fixed and established relationship between a manufacturer, shipper, and seller. It is also used for certain small geographic locations, a small metallically ringing percussion instrument while, the noun, “triangulation,” is used for a process or technique of location.
The concept of the adjective, “parallel,” is employed, frequently, in the study of geometrical forms and as, well, employed in descriptive and analytical speech. Many people live identically appearing, or “parallel” lives. Thoughts, futures, opinions, and careers are often deemed to be parallel, or “in sync.” The term may also permissibly be used as a designation of a mutual sense of agreement. The geometrics of viewed experiences are numerous: curvy roads, angular stance, parallel streets, circular driveways, village squares, traffic circles, square dances, linear perception, and the like.
The importance of any attribution to geometrical mathematics, however, pales in significance when weighed against the utility of its instructive discipline in problem-solving, as observed at the early part of this writing. The application of known useful and relevant principles to the accurately discerned issue, to deduce the logical solution to problems, is the guaranteed route to knowledge and mature discernment. The rational path provided by the mathematical discipline of Geometry, thus, may anthropologically, exceed the value of all practical mathematic disciplines; it is the rational roadmap to mankind’s aspirational advancement toward the cherished gold medal of acquired wisdom.