Geometric Quotes & Sayings

...rich geometric experiences are the most important factor in the development of children's spatial thinking and reasoning. — John A. Van De Walle

We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways - even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols. — William Thurston

Modern man lives more and more in a preponderantly geometric order. All human creation mechanical or industrial is dependent upon geometric intentions. — Fernand Leger

They certainly aren't connected with the old geometric art. My work isn't geometric in that sense. — Donald Judd

To the untrained (human) eye, Thalassinia looks like an expanse of coral reefs and volcanic formations. There are no straight lines or geometric shapes to give away the fact that the structures are actually mermade. (Get it? Mermade. Like mermaid, but ... oh, never mind.) — Tera Lynn Childs

She is angle. I am
curve. Together, we are geometric
sculpture, and we make perfect sense. — Ellen Hopkins

This lingering hint of savagery isn't necessarily a strike against fire cooking, however. To the contrary, some believe a bloody slab of beefsteak augments the power of the eater. "Whoever partakes of it," Roland Barthes wrote in Mythologies, "assimilates a bull-like strength." By comparison, the braise or stew - and particularly the braise or stew of meat that's been cut into geometric cubes and rendered tender by long hours in the pot - represents a deeper sublimation, or forgetting, of the brutal reality of this particular transaction among species. Certainly — Michael Pollan

must reason your way through the problem. Using line only, draw one simple geometric shape, such as a square, triangle or circle. Without overlapping or intersecting, draw a different shape. Now, draw another. Choose your favorite. Make the other 2 like your favorite. Enlarge one of the shapes. Reduce one of them. Make one shape touch one edge of the page. Make the other — Paper Monument

As far as I could tell, the quickest way to a geeky guy's heart usually involved geometric shapes. — Angela N. Blount

The regular division of the plane into congruent figures evoking an association in the observer with a familiar natural object is one of these hobbies or problems ... I have embarked on this geometric problem again and again over the years, trying to throw light on different aspects each time. I cannot imagine what my life would be like if this problem had never occurred to me; one might say that I am head over heels in love with it, and I still don't know why. — M.C. Escher

A strong back is a big help but not even the strongest back was built for that treatment, and there combine not just at the kidneys, ad rill down the thighs and up the spine and athwart the shoulders, the ticklish weakness of gruel or water, and an aching that increases in geometric progression, and at length, in the small of the spine, a literal sensation of yielding, buckling, splintering, and breakage: and all of this, even though the mercy of nature has strengthened and hardened your flesh and anesthetized your nerves and your powers of reflection and imagination, reaches in time the brain and the more mirrorlike nerves, and thereby makes itself much worse than before. — James Agee

The feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely aesthetic feeling, which all mathematicians know — Henri Poincare

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to?
The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way. — Paul Lockhart

My work is always very geometric. — Bibhu Mohapatra

Chemists did it in their tubes and doctors did it with patience, but only a techie would do it in geometric progression. — Greg Bear

If a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic musical. — Ralph Waldo Emerson

ART VS. COMMERCE
he artist stood back to view the geometric precision of his latest creation.
"Beautiful," he murmured, "but will it sell?"
No time to examine the philosophic implications. Customers, buzzing with excitement, hovered near the piece. He wrapped up a deal quickly.
"This is business," the spider said with a vicious smile. "It ain't art. — Steve Moss

The effect is both domestic and wild, equal parts geometric and chaotic. It's the visual signature of small, diversified farms that creates the picture-postcard landscape here, along with its celebrated gastronomic one. Couldn't Americans learn to love landscapes like these around our cities, treasuring them not just gastronomically but aesthetically, instead of giving everything over to suburban development? Can we only love agriculture on postcards? — Barbara Kingsolver

Antarctic symphony has a geometric relationship to the landscape. It's saying that this landscape and the minimal kind of, you know I'm talking like seeing ice, is visually kind of eerily minimal. — DJ Spooky

I'd paint long strips of canvas and abandon them on the beach, or put bread out in geometric patterns for the pigeons downtown. I wanted people to find something nice and intriguing to puzzle over. Then I'd go back to see if the things were still there, or if anyone would notice. — Jenny Holzer

All man's desired geometric progressions, if a high rate of growth is chosen, at last come to grief on a finite earth. And the social system for man on earth is fair enough, eventually, that almost all massive cheating ends in disgrace. — Charlie Munger

Much of what I make is geometric, and has a kind of almost mathematical logic to the form. — Anish Kapoor

He couldn't understand how I could be so bright in my other classes and a total failure in his. I must not be trying hard enough, he told me. In truth, I didn't care, and I didn't want to care. Geometric shapes with their dangerously sharp angles seemed the mortal enemies of words, and formulas were written in a hostage-taking language that made me despair of ever freeing the words from their captors. The best I could do was to avoid the enemy and save myself. — Thom Satterlee

Mathematical solutions are selected by the subliminal self on the basis of "mathematical beauty," of the harmony of numbers and forms, of geometric elegance. — Robert M. Pirsig

The sea-lentils tied to giant serpentine string beans, sea-liquor brine, sea-lyme grass, sea-moss, sea-cucumbers. He never knew the sea had such a lavish garden - sea-plumes, sea-grapes, sea-lungs. [ ... ] The sky put on its own evanescent spectacles, a pivoting stage, fugitive curtains, decors for ballets, floating icebergs, unrolled bolts of chiffon, gold and pearl necklaces, marabous of oyster white, scarves of Indian saris, flying feathers, shorn lambs, geometric architecture in snows and cotton. His theater was the clouds, where no spectacle repeated itself. — Anais Nin

Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements. — Omar Khayyam

A.N. Kolmogorov and Yasha Sinai had worked out some illuminating mathematics for the way a system's "entropy per unite time" applies to the geometric pictures of surfaces stretching and folding in phase space. The conceptual core of the technique was a matter of drawing some arbitrarily small box around some set of initial conditions, as one might draw a small square on the side of a balloon, then calculating the effect of various expressions or twists on the box. It might stretch in one direction, for example, while remaining narrow in the other. The change in area corresponded to an introduction of uncertainty about the system's past, a gain or loss of information. — James Gleick

A circle is the only geometric shape defined by its centre. No chicken and egg about it, the centre came first, the circumference follows. The earth, by definition, has a centre. And only the fool that knows it can go wherever he pleases, knowing the centre will hold him down, stop him flying out of orbit. But when your sense of centre shifts, comes whizzing to the surface, the balance has gone. The balance has gone. The balance my baby has gone. — Sarah Kane

He closed his eyes and shook his head. "I am not one of those who believes that God made the world and walked away from it, that He has no further choices to make, no ongoing presence in the world. I believe that He is everywhere, making choices all the time." "But only because there are certain things you have not explained yet with geometric proofs. — Neal Stephenson

The old concept of chronological, orderly, symmetrical development of character died when it was discovered that the unconscious motivations are entirely at odds with fabricated conventions. Human beings do not grow in perfect symmetry. They oscillate, expand, contract, backtrack, arrest themselves, retrogress, mobilize, atrophy in part, proceed erratically according to experience and traumas. Some aspects of the personality mature, others do not. Some live in the past, some in the present. Some people are futuristic characters, some are cubistic, some are hard-edged, some geometric, some abstract, some impressionistic, some surrealistic! — Anais Nin

Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio. — Stephen M. Barr

If one were to refuse to have direct, geometric, intuitive insights, if one were reduced to pure logic, which does not permit a choice among every thing that is exact, one would hardly think of many questions, and certain notions ... would escape us completely. — Henri Lebesgue

But who shall parcel out His intellect by geometric rules, Split like a province into round and square? — William Wordsworth

Within the human consciousness is the unique ability to perceive the transparency between absolute, permanent relationships, contained in the insubstantial forms of a geometric order, and the transitory, changing forms of our actual world. The content of our experience results from an immaterial, abstract, geometric architecture which is composed of harmonic waves of energy, nodes of relationality, melodic forms springing forth from the eternal realm of geometric proportion. — Robert Lawlor

I do not believe you can have infinite population or economic growth in a finite world. We are living on the shoulders of some awesome geometric curves. — Richard Lamm

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth. - Galileo Galilei, The Assayer, 1623 — Max Tegmark

People conceptualize conditioning in different ways," he said. "Some think it's a ladder straight up. Others see plateaus, blockages, ceilings. I see it as a geometric spiraling upward, with each spin of the circle taking you a different distance upward. Some spins may even take you downward, just gathering momentum for the next upswing. Sometimes you will work your fanny off and see very little gain; other times you will amaze yourself and not really know why. — John L. Parker Jr.

About Archimedes one remembers that he did strange things: he ran around naked shouting Heureka!, plunged crowns into water, drew geometric figures as he was about to be killed, and so on ... One ends up forgetting he was a scientist of whom we still have many writings. — Lucio Russo

All my work comes from perceiving. I kept seeing things that were brooding in me. I'm not a geometric artist. — Ellsworth Kelly

We have a company, Geometric Software, which is into engineering services software. We have a company called Nature's Basket, which is into gourmet retailing. Both are specialized companies. — Adi Godrej

Most [Shetland patterns] are fairly small and simple, as textile patterns go. Almost all are symmetrical, with eight smaller parts. As a result, most are geometric rather than representational. ...
One last feature, less easy to define but easy enough to recognise ... is the liking for little motifs and for a pattern to be 'finished'. — Sheila McGregor

It snowed right before Jack stopped talking to Hazel, fluffy white flakes big enough to show their crystal architecture, like perfect geometric poems. — Anne Ursu

In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry. — Hermann Weyl

Red, orange and green geometric designs painted its body as well as the flimsy collar around its neck. The creature flicked its tail and blinked its deep-set eyes, apparently oblivious to their presence.
"That's a yraglian lizards," Deven whispered. "We need to stay back. They smell really bad if you upset them. I mean, really, really bad."
Dirck nodded, unsurprised that the first native creature he encountered on Cyraria represented it so well. — Marcha A. Fox

I had, over the years, collected things, small things, as people do, and I had put them all together and showed them in what became a building in the form of the Geometric Mouse. — Claes Oldenburg

He simply went from vertical to horizontal in one marvelous geometric sweep. — Terry Pratchett

It struck me recently, that one should really consider the sequence of a protein molecule about to fold into a precise geometric form as a line of melody written in a canon form & so designed by Nature to fold back into itself, creating harmonic chords of interaction consistent with biological function — Christian B. Anfinsen

For me, madness was definitely not a condition of illness; I did not believe that I was ill. It was rather a country, opposed to Reality, where reigned an implacable light, blinding, leaving no place for shadow; an immense space without boundary, limitless, flat; a mineral, lunar country, cold as the wastes of the North Pole. In this stretching emptiness, all is unchangeable, immobile, congealed, crystallised. Objects are stage trappings, placed here and there, geometric cubes without meaning.
People turn weirdly about, they make gestures, movements without sense; they are phantoms whirling on an infinite plain, crushed by the pitiless electric light. And I - I am lost in it, isolated, cold, stripped purposeless under the light. — Marguerite Sechehaye

Outside the moon had come out. It was full, a disk of bright silver. I saw a large, dramatic spider web on my back porch that must have been made while I was in the house with my mind in turmoil; the spider was just finishing the outer circle of it. The moon illuminated the strands of the big taut web so that it seemed to be made of pure light. It was dazzling, geometric and mysterious, and it calmed me just to stop and look at it, at the elaboration and power of life that could make such a design. — Walter Tevis

Geometry exist everywhere.It is necessary, however, to have eyes to see it, intelligence to understand it , and spirit to wonder at it.The wild Bedouin sees geometric forms but doesn't understand them ; the Sunni understands them but does not admire them; the artist, finally, perceives the perfection of figures, understands beauty, and admires order and harmony.God was the Great Geometer.He geometrized heaven and earth. — Malba Tahan

The people who see the population explosion in the Malthusian way - as a geometric progression - forget that population growth is not a biological issue. People are not increasing in numbers out of stupidity and ignorance. Population growth is an ecological phenomenon linked very intimately to other issues, such as the usurpation of the resources which allow people to live. — Vandana Shiva

In Degas's compositions with several dancers, their steps, postures and gestures often resemble the almost geometric, formal letters of an alphabet, whereas their bodies and heads are recalcitrant, sinuous and individual. — John Berger

Basic geometric shapes communicate universal qualities common to all cultures. Practical design integrates them appropriately. — Maggie Macnab

Destruction is creation. Become as a little child. Language as space, a kind of mathematical notation, geometric locations in the lab of memory. Reading. Maps. Codes, substitutions, the secret names of things. The glorious inrush of a word. The joy of chatter. Every color's wavelength, by number. — Kim Stanley Robinson

In every story I'd read about dragons, they dwelled in caves far away from civilization. They didn't live in the upper heights of ritzy Gangnam with a view of the Han River shimmering in the moonlight. And they certainly didn't live in a villa that looked like a geometric cube with windows that changed color based on the time. — Heather Heffner

For nine years I worked to change what was hairdressing then into a geometric art form with color, perm without setting which had never been done before. — Vidal Sassoon

But is it not already an insult to call chess anything so narrow as a game? Is it not also a science, an art, hovering between these categories like Muhammad's coffin between heaven and earth, a unique yoking of opposites, ancient and yet eternally new, mechanically constituted and yet an activity of the imagination alone, limited to a fixed geometric area but unlimited in its permutations, constantly evolving and yet sterile, a cogitation producing nothing, a mathematics calculating nothing, an art without an artwork, an architecture without substance and yet demonstrably more durable in its essence and actual form than all books and works, the only game that belongs to all peoples and all eras, while no one knows what god put it on earth to deaden boredom, sharpen the mind, and fortify the spirit? — Stefan Zweig

I guess a sock is also a geometric shape - technically - but I don't know what you'd call it. A socktagon? — Stephen King

On the geometric level, we see certain physical elements repeated endlessly, combined in an almost endless variety of combinations ... It is puzzling to realize that the elements, which seem like elementary building blocks, keep varying, and are different every time that they occur ... If the elements are different every time that they occur, evidently then, it cannot be the elements themselves which are repeating in a building or town; these so-called elements cannot be the ultimate "atomic" constituents of space. — Christopher Alexander

Organic planning does not begin with a preconceived goal; it moves from need to need, from opportunity to opportunity, in a series of adaptations that themselves become increasingly coherent and purposeful, so that they generate a complex final design, hardly less unified than a pre-formed geometric pattern. — Lewis Mumford

I exist, I think, I feel pain. Is all this as certain as a geometric truth? Yes. Why? It is because these truths are proved by the same principle that a thing cannot be and not be at the same thime. I cannot at the same time exist and not exist, feel and not feel. A triangle cannot at the same time have and not have 180 degrees, which is the sum of two right angles. — Voltaire

It is the invaluable merit of the great Basle mathematician Leonard Euler, to have freed the analytical calculus from all geometric bounds, and thus to have established analysis as an independent science, which from his time on has maintained an unchallenged leadership in the field of mathematics. — Thomas Reid

So it's not an architectural masterpiece. When Da5id and Hiro and the other hackers wrote The Black Sun, they didn't have enough money to hire architects or designers, so they just went in for simple geometric shapes. The avatars milling around the entrance don't seem to care. — Neal Stephenson

Extraordinary success is sequential, not simultaneous. What starts out linear becomes geometric. You do the right thing and then you do the next right thing. Over time it adds up, and the geometric potential of success is unleashed. The domino effect applies to the big picture, like your work or your business, and it applies to the smallest moment in each day when you're trying to decide what to do next. — Gary Keller

I got to draw shapes. I really like to draw funky, geometric shapes. And I got to use just different fonts and make a joke of how feminine it was, but it didn't even have people in it. To me, it was so exciting and interesting to do that for a while. — David Rees

The moth settled onto the curtain and sat still. It was an astonishing creature, with black and white wings patterned in geometric shapes, scarlet underwings, and a fat white body with black spots running down it like a snowman's coal buttons. No human eye had looked at this moth before; no one would see its friends. So much detail goes unnoticed in the world. — Barbara Kingsolver

In 1929 the discovery of the wonders of the geometric series struck Wall Street with a force comparable to the invention of the wheel. — John Kenneth Galbraith

looked around, trying to imagine what it'd be like to work there. The furniture was trendy but functional, and plants gave the area a personal touch. The walls were painted a warm off-white, and they were decorated with framed ads that Elle recognized immediately. Geometric-patterned rugs covered much of the floor. Taken individually, none of it was really her — Cleo Peitsche

It was not a great presence but a great absence, a geometric ocean of darkness that seemed to swallow heaven itself. — Laura Hillenbrand

Architecture is the triumph of human imagination over materials, methods, and men, to put man into possession of his own Earth. It is at least the geometric pattern of things, of life, of the human and social world. It is at best that magic framework of reality that we sometimes touch upon when we use the word order. — Frank Lloyd Wright

So all night long the storm roared on:
The morning broke without a sun;
In tiny spherule traced with lines
Of Nature's geometric signs,
In starry flake, and pellicle,
All day the hoary meteor fell;
And, when the second morning shone,
We looked upon a world unknown,
On nothing we could call our own.
Around the glistening wonder bent
The blue walls of the firmament,
No cloud above, no earth below,
A universe of sky and snow! — John Greenleaf Whittier

String theory, therefore, is rich enough to explain all the fundamental laws of nature. Starting from a simple theory of a vibrating string, one can extract the theory of Einstein, Kaluza-Klein theory, supergravity, the Standard Model, and even GUT theory. It seems nothing less than a miracle that, starting from some purely geometric arguments from a string, one is able to rederive the entire progress of physics for the past 2 milleninia. All the theories so far discussed in this book are automatically included in string theory. — Michio Kaku

Ensor sees with his imagination, but his vision is perfectly accurate, of an almost geometric precision. He is one of the very few who can really see. Like you, he has an obsession with masks; he is a seer as you and I are. The common herd, of course thinks that he is mad.
*****************
You shall see what sort of man Ensor is, and what a marvellous insight he has into the invisible realm where our vices are created ... those vices for which our faces make masks. — Jean Lorrain

Some songs seem to achieve the quality of a geometric object - a ball, box, or cone - and I don't mess with 'em. — Peter Blegvad

Rosemary and Guy Woodhouse had signed a lease on a five-room apartment in a geometric white house on First Avenue when they received word, from a woman named Mrs. Cortez, that a four-room apartment in the Bramford had become available. — Ira Levin

A game of chess is a visual and plastic thing, and if it isn't geometric in the static sense of the word, it is mechanical, since it moves. It's a drawing; it's a mechanical reality. — Marcel Duchamp

Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define. — Giuseppe Peano

In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance. — Martin Gardner

The five elements are energies, not things. In Hinduism, they are known as the five tattvas. Psychic people can see them and their geometric forms. — Stefan Emunds

Geometric shapes hold an energy pattern, and scientists did some experiments which say certain geometric shapes can affect matter around them. It's simply because when a human looks at a shape, they instantly receive energy from their brain. — Tom DeLonge

Now ... the basic principle of modern mathematics is to achieve a complete fusion [of] 'geometric' and 'analytic' ideas. — Jean Dieudonne

I don't see how it's doing society any good to have so many members walking around with vague memories of algebraic formulas and geometric diagrams and clear memories of hating them. — Paul Lockhart

That's a geometric figure, that bird, he don't exist without an angle. — Donald E. Westlake

Hiro's father, who was stationed in Japan for many years, was obsessed with cameras. He kept bringing them back from his stints in the Far East, encased in many protective layers, so that when he took them out to show Hiro, it was like watching an exquisite striptease as they emerged from all that black leather and nylon, zippers and straps. And once the lens was finally exposed, pure geometric equation made real, so powerful and vulnerable at once, Hiro could only think it was like nuzzling through skirts and lingerie and outer labia and inner labia ... It made him feel naked and weak and brave. — Neal Stephenson

The issues are by some geometric number - 100 or 200 or 500 - times more complicated today than we appreciated them to be when Franklin Roosevelt was around. — Gaylord Nelson

The design is a really flat primary color with all sorts of abstract geometric shapes, just implying something. And then you'd have your characters running from something with guns. It was very expressionistic. — Don Hertzfeldt

As you know, Bergson pointed out that there is no such thing as disorder but rather two sorts of order, geometric and living. — Jean Piaget

predecessor of Isaac Newton at Cambridge University, maintained that irrational numbers have no meaning independent of geometric lengths. — Morris Kline

New York ... is a city of geometric heights, a petrified desert of grids and lattices, an inferno of greenish abstraction under a flat sky, a real Metropolis from which man is absent by his very accumulation. — Roland Barthes

I feel more and more as if time did not exist at all ... only various spaces interlocking according to the rules of a higher form of stereometry[the geometric measurement of solid bodies], between which the living and the dead can move back and forth as they like, and the longer I think about it the more it seems to me that we who are still alive are unreal in the eyes of the dead. — W.G. Sebald

Viewed as a geometric figure, the ant's path is irregular, complex, and hard to describe. — Herbert A. Simon

In a way, composing on the melodic level is an expression of a melodic truth, almost like a geometric truth. If it has clarity, other people will recognize it. There's no way of isolating it in a gallery on a white wall and saying, "This is a work of art. This is a mathematical proof." — Eyvind Kang

The great commander can certainly move fast and strike like lightning, but his art of war consists first and foremost in moderation, measured geometric order, carefully weighed-up knowledge of circumstances and rules, a tranquil 'thinking things over'; without this there is little use in being acquainted with that 'infinity of situations' in which a soldier finds himself. — Claudio Magris

What does it mean when you hook up your work to that of a late modernist giant working in a reductive vein - Ad Reinhardt, Agnes Martin, Robert Ryman, Ellsworth Kelly, Frank Stella, or Donald Judd, for example - like a caboose? I am not talking about engaging directly with another artist's work or ideas, but of perpetuating a look or, in the case of Wade Guyton, the various monochromatic, striped and geometric surfaces we associate with Minimalism. — John Yau

I think when a man first discovers that two and two is four, there is 'beauty' in that; and we can see why. But if people stand and look at the moon and one says 'I think it's just beautiful tonight' and the other says 'The moon makes me feel awful' we are both 'clear'. A geometric shape - we know why we like it; and an unreasonable shape; it has a certain mystery that we recognize as real; but it is difficult to put these things in an objective way. — William Baziotes

My forms are geometric, but they don't interact in a geometric sense. They're just forms that exist everywhere, even if you don't see them. — Ellsworth Kelly

You existed. You existed now as a fractal.
Definition:
A fractal is generally a rough or fragmented geometric shape that can be broken into parts, each of which is (at least approximately) a reduced-size copy of the whole.
Maybe I was a fractal. Maybe the photographer was a fractal.
Maybe we were all fractals. — David Levithan

I started collecting aerial photographs of Native American and South Pacific architecture; only the African ones were fractal. And if you think about it, all these different societies have different geometric design themes that they use. So Native Americans use a combination of circular symmetry and fourfold symmetry. — Ron Eglash

The effectiveness of work increases according to geometric progression if there are no interruptions. — Andre Maurois

During the late afternoon and early evening there is a specific dimension that interconnects with our physical world. This particular dimension can be visualized as series of horizontally shaped geometric planes that extent out into infinity. — Frederick Lenz