Quotes & Sayings About Geometry In Nature

Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated. — Benoit Mandelbrot

Relying on the face might be human nature - even babies prefer to look at attractive people. But, of course, judging someone based on the geometry of his features is, from a moral and legal standpoint, no better than judging him based on the color of his skin. — Paul Bloom

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

Why is geometry often described as 'cold' and 'dry?' One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line ... Nature exhibits not simply a higher degree but an altogether different level of complexity. — Benoit Mandelbrot

I regret that it has been necessary for me in this lecture to administer a large dose of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are. — Alfred North Whitehead

Rigid geometry forced in varied curves is "mother," / is "nature," is systematic violation." Muy Bueno. / This device is for you, the mutilated of no art. — Christian Peet

There is no need to express art in terms of nature. It can perfectly well be expressed in terms of geometry and the exact sciences. — Georges Vantongerloo

Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated. — Benoit Mandelbrot

I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid-a term used in this work to denote all of standard geometry-Nature exhibits not simply a higher degree but an altogether different level of complexity ... The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous." — Benoit Mandelbrot

Philosophy [nature] is written in that great book which ever is before our eyes
I mean the universe
but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. — Galileo Galilei

Of all the possible pathways of disorder, nature favors just a few. — James Gleick

The swirling lines of snow were composed of separate flakes, and each flake was a cluster of separate ice crystals--scientists had counted over a hundred of them in a single flake. Under the microscope each minuscule crystal, colorless and transparent, revealed a secret symmetry: six sides, the outward expression of an inward geometry of frozen molecules of water. But the real wonder was that no two crystals were precisely alike. In one of this father's camera magazines he had seen a stunning display of photomicrographs, and what was most amazing about the enlarged crystals was that each contained in its center a whole world of intricate six-sided designs, caused by microscopic air pockets. For no conceivable reason, Nature in a kind of exuberance created an inexhaustible outpouring of variations on a single form. A snowstorm was a fall of jewels, a delirium of hexagons--clearly the work of a master animator. — Steven Millhauser

Geometry, which should only obey Physics, when united with it sometimes commands it. If it happens that the question which we wish to examine is too complicated for all the elements to be able to enter into the analytical comparison we wish to make, we separate the more inconvenient [elements], we substitute others for them, less troublesome but also less real, and we are surprised to arrive, notwithstanding a painful labour, only at a result contradicted by nature; as if after having disguised it, cut it short or altered it, a purely mechanical combination could give it back to us. — Jean Le Rond D'Alembert

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

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

What he found was the geometry of the universe. Looking at the bubbles made by the Wego's propellers, he recalled his boarding school math teachers, who had taught him to measure a sphere's volume in terms of pi. He also remembered that pi was an irrational number, a decimal that never ended. He asked himself how nature could ever make bubbles in such circumstances. Did nature approximate? The rules his teachers had taught him must be mistaken. Spheres ought to be understood in terms of the forces that made them. At the age of twenty-one, Bucky determined that the universe had no objects. Geometry described forces. It was an insight bound to shape Bucky's entire worldview - informing every future invention - but — Jonathan Keats

Straight lines evidently belonged only to geometry, not to nature and life. — Hermann Hesse

Do you remember, Meir, that epigram quoted in the name of Rabbi Johanan ben Zaccai: 'There is no truth unless there be a faith on which it may rest'? Ironically enough the only sure principle I have achieved is this which I have known almost all my life. And it is so. For all truths rest ultimately on some act of faith, geometry on axioms, the sciences on the assumptions of the objective existence and orderliness of the world of nature. In every realm one must lay down postulates or he shall have nothing at all. So with morality and religion. Faith and reason are not antagonists. On the contrary, salvation is through the commingling of the two, the former to establish first premises, the latter to purify them of confusion and to draw the fullness of their implications. It is not certainty which one acquires so, only plausibility, but that is the best we can hope for. — Milton Steinberg

His way had therefore come full circle, or rather had taken the form of an ellipse or a spiral, following as ever no straight unbroken line, for the rectilinear belongs only to Geometry and not to Nature and Life. — Hermann Hesse

Truth is disputable; not taste: what exists in the nature of things is the standard of our judgement; what each man feels within himself is the standard of sentiment. Propositions in geometry may be proved, systems in physics may be controverted; but the harmony of verse, the tenderness of passion, the brilliancy of wit, must give immediate pleasure. No man reasons concerning another's beauty; but frequently concerning the justice or injustice of his actions. — David Hume

Every one who understands the subject will agree that even the basis on which the scientific explanation of nature rests is intelligible only to those who have learned at least the elements of the differential and integral calculus, as well as analytical geometry. — Felix Klein

And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought to be least neglected in Geometry. — Johannes Kepler

When the ancients discovered 'Phi', they were certain they had stumbled across God's building block for the world. — Dan Brown

I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit. — Benoit Mandelbrot

Perfect hexagonal tubes in a packed array. Bees are hard-wired to lay them down, but how does an insect know enough geometry to lay down a precise hexagon? It doesn't. It's programmed to chew up wax and spit it out while turning on its axis, and that generates a circle. Put a bunch of bees on the same surface, chewing side-by-side, and the circles abut against each other - deform each other into hexagons, which just happen to be more efficient for close packing anyway. — Peter Watts

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

Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world. — James Gleick

No very good sense can be given to the idea that the elements of Euclidean geometry may be found in nature because either everything is found in nature or nothing is. Euclidean geometry is a theory, and the elements of a theory may be interpreted only in terms demanded by the theory itself. Euclid's axioms are satisfied in the Euclidean plane. Nature has nothing to do with it. — David Berlinski

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

Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a "force" has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed. — Michio Kaku

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals. — Benoit Mandelbrot

Whenever we take the focus off ourselves and move it outward, we benefit. Life's most fortunate ironies are that what's best for the long run is best now, and selflessness serves our interests far better than selfishness. The wider our circle of considerations, the more stable we make the world - and the better the prospects for human experience and for all we might wish. The core message of each successive widening: we are one. The geometry of the human voyage is not linear; it's those ripples whose circles expand to encompass self, other, community, Life, and time. — Carl Safina

I am present at the sowing of the seed of the world. With a geometry of sunbeams, the soul lays the foundations of nature. — Ralph Waldo Emerson

Descriptive geometry has two objects: the first is to establish methods to represent on drawing paper which has only two dimensions,-namely, length and width,-all solids of nature which have three dimensions,-length, width, and depth,-provided, however, that these solids are capable of rigorous definition.
The second object is to furnish means to recognize accordingly an exact description of the forms of solids and to derive thereby all truths which result from their forms and their respective positions. — Gaspard Monge

The fractal structure nature has devised works so efficiently that, in most tissue, no cell is ever more than three or four cells away from a blood vessel. Yet the vessels and blood take up little space, no more than about five percent of the body. — James Gleick

A proposition of geometry does not compete with life; and a proposition of geometry is a fair and luminous parallel for a work of art. Both are reasonable, both untrue to the crude fact; both inhere in nature, neither represents it. — Robert Louis Stevenson

In geometry, as in nature, the circle is the archetypal shape of wholeness and inclusion. It is an effective shape for nonprofits or community-focused efforts. — Maggie Macnab

An American is a complex of occasions, themselves a geometry of spatial nature. — Charles Olson

For each successive class of phenomena, a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. — Henry John Stephen Smith