Golden Ratio Quotes

Quotes tagged as "golden-ratio" Showing 1-30 of 48
“When we are locked up between a mood of 'transparency' and a feel of 'discretion,' we must clear up our mental muddle, until we find the "golden ratio," and recognize the peak of 'candor.' By hitting the point of recognition and enlightenment, we can make a correct choice and follow the right track ("Unfulfilled meeting")”
Erik Pevernagie

Guy Murchie
“The Fibonacci Sequence turns out to be the key to understanding how nature designs... and is... a part of the same ubiquitous music of the spheres that builds harmony into atoms, molecules, crystals, shells, suns and galaxies and makes the Universe sing.”
Guy Murchie, The Seven Mysteries of Life: An Exploration of Science and Philosophy

John Michell
“The water beneath the Temple was both actual and metaphorical, existing as springs and streams, as spiritual energy, and as a symbol of the receptive or lunar aspect of nature.

The meaning of that principle is too wide and elusive for it to be given any one name, so in the terminology of ancient science it was given a number, 1,080. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666.

These two numbers, which have an approximate golden-section relationship of 1:1.62, were at the root of the alchemical formula that expressed the supreme purpose of the Temple. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666. Not merely was it used to generate energy from fusion of atmospheric and terrestrial currents, but it also served to combine in harmony all the correspondences of those forces on every level of creation.”
John Michell, The Dimensions of Paradise: Sacred Geometry, Ancient Science, and the Heavenly Order on Earth

R.A. Schwaller de Lubicz
“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, Nature Word

“Thus nature provides a system for proportioning the growth of plants that satisfies the three canons of architecture. All modules are isotropic and they are related to the whole structure of the plant through self-similar spirals proportioned by the golden mean.”
Jay Kappraff, Connections: The Geometric Bridge Between Art and Science

“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, Mathematics of Harmony

“The Ark of the Covenant is a Golden Rectangle because its rectangular shape is in the proportions of the Golden Ratio.”
Donald Frazer, Hieroglyphs and Arithmetic of the Ancient Egyptian Scribes: Version 1

John Anthony West
“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, Serpent in the Sky: The High Wisdom of Ancient Egypt

“Buckminster Fuller explained to me once that because our world is constructed from geometric relations like the Golden Ratio or the Fibonacci Series, by thinking about geometry all the time, you could organize and harmonize your life with the structure of the world.”
Einar Thorsteinn

Peter Tompkins
“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, Secrets of the Great Pyramid: Two Thousand Years of Adventures & Discoveries Surrounding the Mysteries of the Great Pyramid of Cheops

“The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series.”
Schwaller de Lubicz

“Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio.”
Stephen M. Barr, Modern Physics and Ancient Faith

“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, Beginnings: The Sacred Design

Jonathan  Black
“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, Mark Booth

“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 Divine Proportion

“The pyramid that can be constructed on the diameters of earth and moon bears the precise proportions of the Great Pyramid”
Bonnie Gaunt, Stonehenge and the Great Pyramid

Carl Johan Calleman
“While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is defined by the [golden] ratio ....”
Carl Johan Calleman, The Purposeful Universe: How Quantum Theory and Mayan Cosmology Explain the Origin and Evolution of Life

“Petrie found nothing that disproved the pyramidologist's assumption that the Great Pyramid had been built according to a master plan. Indeed, he describes the Pyramid's architecture as being filled with extraordinary mathematical harmonies and concordances: those same strange symmetries that had so haunted the pyramidologist.

Petrie not only noted, for example, that the proportions of the reconstructed pyramid approximated to pi - which others have since elaborated to include those twin delights of Renaissance and pyramidological mathematicians, the Golden Section and the Fibonacci Series ...”
John Romer, The Great Pyramid: Ancient Egypt Revisited

“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, Numbers: Their History and Meaning

“In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.”
Alexey Stakhov, "Golden" Non-Euclidean Geometry, The: Hilbert's Fourth Problem, "Golden" Dynamical Systems, and the Fine-Structure Constant

“It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms.”
Richard A. Dunlap, The Golden Ratio and Fibonacci Numbers

“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, The Sphinx Mystery: The Forgotten Origins of the Sanctuary of Anubis

“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 , Matrix of Creation: Sacred Geometry in the Realm of the Planets

“The Golden Mean was considered a fundamental constant by the Egyptians and the fundamental division of the whole into two parts.”
Richard Heath, Sacred Number and the Origins of Civilization: The Unfolding of History through the Mystery of Number

“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, Harmonic Proportion and Form in Nature, Art and Architecture

“In a way, the Phi Triangle of the Golden Mean could be compared to the path of light sent forth from the great All-Seeing Eye of God in the beginning, and which paved the way for the creation of the Universe.”
William Eisen, The English Cabalah Volume 2, The Mysteries of Phi

“The Great Pyramid, that monument to spirituality that the Agashan Teachers hold in such high esteem, is built according to the principles of Pi and Phi.”
William Eisen, The English Cabalah Volume 2, The Mysteries of Phi

“The golden ratio is the key to universal physics.

-- Sir Edward Victor Appleton, Nobel Laureate in physics (1947)”
Sir Edward Victor Appleton

Peter Tompkins
“Plato considered the golden section proportion the most binding of all mathematical relations, making it the key to the physics of the cosmos.”
Peter Tompkins , Secrets of the Great Pyramid: Two Thousand Years of Adventures & Discoveries Surrounding the Mysteries of the Great Pyramid of Cheops

“The golden section was discovered by the Egyptians, and has been used in art and architecture, most commonly, during the classical ages of Egypt and Greece.”
Steven L. Griffing, The Golden Section:An Ancient Egyptian and Grecian Proportion

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