Quotes & Sayings About Ratio And Proportion

The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That's an incredible role for one number to play, but then again this one number has played an incredible role in human history and the universe at large. — H.E. Huntley

The Golden Number is a mathematical definition of a proportional function which all of nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the human skeleton, or the ages of growth in man. — R. A. Schwaller De Lubicz

Rationality or consciousness is itself a ratio or proportion among the sensuous components of experience, and is not something added to such sense experience. Subrational beings have no means of achieving such a ratio or proportion in their sense lives but are wired for fixed wave lengths, as it were, having infallibility in their own area of experience. Consciousness, complex and subtle, can be impaired or ended by a mere stepping-up or dimming-down of any one sense intensity, which is the procedure in hypnosis. And the intensification of one sense by a new medium can hypnotize an entire community. — Marshall McLuhan

She thanked God that life was not always winter, that spring always came at last to chase away the cold and heaviness, and to release one to warmth and movement again. — Janette Oke

This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have both aesthetic and mystic significance. That the Egyptians knew of it and used it seems certain. — John Pile

Socialism increases in direct ratio and proportion with the surrender of personal responsibility to neighbor. — Fulton J. Sheen

The Pythagoreans... were fascinated by certain specific ratios, ...The Greeks knew these as the 'golden' proportion and the 'perfect' proportion respectively. They may well have been learned from the Babylonians by Pythagoras himself after having been taken prisoner in Egypt. Ratios lay at the heart of the Pythagorean theory of music. — Graham Flegg

Just then, thunder boomed overhead. Lightning flashed, and the bars on the nearest window burst into sizzling, melted stubs of iron. Jason flew in like Peter Pan, electricity sparking around him and his gold sword steaming. Leo whistled appreciatively. Man, you just wasted an awesome entrance. — Rick Riordan

Central to all these interlinked themes was that curious irrational, phi, the Golden Section. Schwaller de Lubicz believed that if ancient Egypt possessed knowledge of ultimate causes, that knowledge would be written into their temples not in explicit texts but in harmony, proportion, myth and symbol. — John Anthony West

[The golden proportion] is a scale of proportions which makes the bad difficult [to produce] and the good easy. — Albert Einstein

In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov] — Alexey Stakhov

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. — Jonathan Black

Schwaller de Lubicz identifies the Golden Mean as "the fundamental scission," or division of one into two, that creates three things - the original whole and two parts, one in golden proportion to the whole and the other in golden proportion to that. — Richard Heath

The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in the Great Pyramid.

But the many measurements made by Professor Jean Philippe Lauer, says Stecchini, definitely prove the occurrence of the Golden Section throughout the architecture of the Old Kingdom.... Schwaller de Lubicz also found graphic evidence that the pharonic Egyptians had worked out a direct relation between pi and phi in that pi = phi^2 x 6/5. — Peter Tompkins

For any two portions of fire, small or great, will exhibit the same ratio of solid to void; but the upward movement of the greater is quicker than that of the less, just as the downward movement of a mass of gold or lead, or of any other body endowed with weight, is quicker in proportion to its size. — Aristotle.

Very harmful effects can follow accepting the philosophy which denies personal guilt or sin and thereby makes everyone nice. By denying sin, the nice people make a cure impossible. Sin is most serious, and the tragedy is deepened by the denial that we are sinners ... The really unforgiveable sin is the denial of sin, because, by its nature, there is now nothing to be forgiven. By refusing to admit to personal guilt, the nice people are made into scandalmongers, gossips, talebearers, and supercritics, for they must project their real if unrecognized guilt to others. This, again, gives them a new illusion of goodness: the increase of faultfinding is in direct ratio and proportion to the denial of sin. — Fulton J. Sheen

There are two ways of getting into the Cabinet - you can crawl in or kick your way in. — Aneurin Bevan

Man will never be entirely willing to give up this world for the next nor the next world for this. — William Ralph Inge

The longer I go on, the more I am aware of the power of finance. — Justin Welby

Men, who achieve much, die as do those who achieve nothing. — Clarence H. Burns

Filmmaking is a completely imperfect art form that takes years and, over those years, the movie tells you what it is. Mistakes happen, accidents happen and true great films are the results of those mistakes and the decisions that those directors make during those moments. — Jason Reitman

They were both sad that their love had died, but they agreed that there was nothing they could do about it. They would just have to part. — Siobhan Parkinson

As I explain at some length in 'The Crystal Sun' this particular angle, which we can call the 'golden angle,' is the precise value of the acute angle of of a right-angled 'golden triangle' that embodies the golden mean proportion ....

The Danish art historian Else Kielland established with conclusive and absolutely overwhelming evidence and analysis that this angle was the basis for all Egyptian art and architecture. She did this in her monumental work 'Geometry in Egyptian Art' .....

The King's Chamber inside the Great Pyramid embodies no fewer than eight occurrences of the golden angle, and the coffer in the chamber embodies yet more. — Robert K. G. Temple

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle — Samuel Colman

De Morgan was explaining to an actuary what was the chance that a certain proportion of some group of people would at the end of a given time be alive; and quoted the actuarial formula, involving p [pi], which, in answer to a question, he explained stood for the ratio of the circumference of a circle to its diameter. His acquaintance, who had so far listened to the explanation with interest, interrupted him and exclaimed, 'My dear friend, that must be a delusion, what can a circle have to do with the number of people alive at a given time?' — W. W. Rouse Ball

The Golden Mean was considered a fundamental constant by the Egyptians and the fundamental division of the whole into two parts. — Richard Heath

I get satisfaction when I write something I like, when I'm happy with it. — Al Franken

The crickets got quiet and the wind died down. It was so still, I felt like the world had stopped.

-Russell Ray Teague, When Saigon Surrendered:
a Kentucky Mystery — James Aura

The Golden Proportion, sometimes called the Divine Proportion, has come down to us from the beginning of creation. The harmony of this ancient proportion, built into the very structure of creation, can be unlocked with the 'key' ... 528, opening to us its marvelous beauty. Plato called it the most binding of all mathematical relations, and the key to the physics of the cosmos. — Bonnie Gaunt

The golden era of the golden number was the Italian renaissance. The expression divine proportion was coined by the great mathematician Luca Pacioli in his book 'De divina proportione', written in 1509. — Midhat Gazale

Men don't change. They just learn to disguise the lack of change. — David Gemmell

Ladies and gentlemen, I don't know whether you fully understand that I have just been shot, but it takes more than that to kill a Bull Moose. — Theodore Roosevelt

This is about these particular candidates in this particular year. That's what motivates me. — David Dinkins

The golden ratio is a reminder of the relatedness of the created world to the perfection of its source and of its potential future evolution. — Robert Lawlor

Speaking generally, sociability stands in inverse ratio with age. A little child raises a piteous cry of fright if it is left alone for only a few minutes; and later on, to be shut up by itself is a great punishment. Young people soon get on very friendly terms with one another; it is only the few among them of any nobility of mind who are glad now and then to be alone; - but to spend the whole day thus would be disagreeable. A grown-up man can easily do it; it is little trouble to him to be much alone, and it becomes less and less trouble as he advances in years. An old man who has outlived all his friends, and is either indifferent or dead to the pleasures of life, is in his proper element in solitude; and in individual cases the special tendency to retirement and seclusion will always be in direct proportion to intellectual capacity. For — Arthur Schopenhauer

All natural results are spontaneous. The diamond sparkles without effort, and the flowers open impulsively beneath the summer rain. And true religion is a spontaneous thing,
as natural as it is to weep, to love, or to rejoice. — Edwin Hubbel Chapin