This article appeared first in the November Issue of Muzzle Blasts Magazine in 1979. NMLRA Members can read this and every other article ever published. Sign up today
By "Pryor Mt. Bill" Newton
Leonardo Fibonacci, born in Pisa in 1180, historians consider the mathematical genius of his time. Fibonacci, already well versed in the knowledge of those preceding, such as Archimedes, introduced the Arabic system of numerals to the western world (Europe), up to that time encumbered with the muddle of Roman Numerals. Later Leonardo Fibonacci made another scientific revolution by introducing letters along with numbers, we now call algebra, which most students hated if forced to study the subject in high school. The year 1299 in Florence saw the populace passing laws against the newfound figuring, and when we consider the present push for the metric system, what's new?
In an experiment to mathematise the precise harmonies of the earth, Fibonacci developed a progressive system of numbers. Begin with 1 + 2 = 3, then add the last and preceding 3 + 2 = 5, and so forth, yielding 1-2-3-5-8-13-21- 34-55, and on into infinity, a job for a computer.
Later, scholars pondering the naturalness, discovered in Fibonacci's system, that if the higher number were divided into the previous, the proportion would be exactly the same each time, .618034, and a basic mean of the most pleasing kind, for the measurements of buildings, sounds, movement, etc. The proportion of a line of two parts was termed, "the Golden Mean". The mean exists in the Egyptian pyramids, and is commonly found in the best designed rectangular Grecian temples.
With the demise of the Grecian period, the proportion disappeared until rediscovered by one more familiar to us, Leonardo de Vinci, artist, inventor of war machines, who left to us the first recorded sketch of the portent of the wheel lock. In 1509 de Vinci produced a book, Divine Proportion, based on the Golden Mean.
Following, in the seventeenth century, Jakob Bernoulli, about the time of Newton (a little pun there), contributed to calculus, and analytical geometry, suspecting the Golden Mean connected with nature, developed what he called a golden logarithmic spiral, or the most pleasing, rhythmic curvature, based on geometric science.
To begin with, a golden rectangle is set up with the short side .618034 the length of the intended long side. Square the upper, then the lower corner, and so on, leaving smaller proportionate golden rectangles. (see illustration). If we find the center points of the squares, and connect them with straight lines, lastly adding the curves, assumingly we have the most perfect, and gracious of forms. Look familiar?
German psychologists in the early eighteen-hundreds, experimenting with proportions of the Golden Mean, found that with common rectangular objects, such as books, and pictures, most people will select the object closest to the ideal rectangle as the most pleasant.
More contemporary writers and scientists have also postulated on the theory. Sounds are picked up by the cochlea of the inner ear, a spiral shape, while the major sixth note E vibrates with the ratio of .62500 to C, is considered by the majority of listeners as the most satisfactory sound In natural phenomena, horns of the mountain sheep spiral, appears in shell, animal claws, waves, beavers' teeth, and so forth. The spiraling of a bullet from a gun (we have gain twist as used by Colt and other makers). Could this also be what the Indian felt as living within the circle of the earth? We might also apply the theory further if desired, to the proportion of barrel to stock, those eyes delighting scrolls of the better carved Kentucky rifles.
Perhaps we are glimpsing the earth's wonderful rational harmony, if we let it, and mysteries beyond our present scope. We must also note that these esthetic pleasantries are the things down-to-earth muzzle loading people take to heart.