Geometry Quotes

Aldus Barnes, a structural engineer by training and member of the Advanced Geometry Unit (AGU) at Arup, has formed many successful collaborations and earned a prominent place for himself in architecture by adopting the language and skills of architects. "Talk in terms of texture and density, instead of torsion and shear. That way they don't think you are just another nerd," Barnes advises the young members of his team. ~ Yanni Alexander Loukissas

Projective geometry is all geometry. ~ Arthur Cayley

He was "a magician, a magician in the sense that he took what was given and simply forced the conclusions logically out of it, whether it was algebra, geometry, or whatever. He had some way of forcing out the results that made him different from the rest of the people." Israel Halperin about von Neumann ~ Robert Leonard

What's the matter?" said the old man. "Can't you make up your mind what kind you want?"
The kid laughed. "I want them all." He threw his hands out. "I'm learning everything!"
He opened one of the books. "Look ... geometry ... triangles ... ~ Jerry Spinelli

Geometry is the most complete science. ~ David Hilbert

A musical audience is at best uninspiring, at worst definitely drab ... Respectability hangs like a pall over the orchestra and the boxes; a sort of sterile sobriety ill-fitted to the passionate geometry of music. ~ Marya Mannes

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

Even today, I am in total awe of the following wondrous chain of ideas and interconnections. Guided throughout by principles of symmetry, Einstein first showed that acceleration and gravity are really two sides of the same coin. He then expanded the concept to demonstrate that gravity merely reflects the geometry of spacetime. The instruments he used to develop the theory were Riemann's non-Euclidean geometries-precisely the same geometries used by Felix Klein to show that geometry is in fact a manifestation of group theory (because every geometry is defined by its symmetries-the objects it leaves unchanged). Isn't this amazing? ~ Mario Livio

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

Music is the arithmetic of sounds as optics is the geometry of light. ~ Claude Debussy

I have no fault to find with those who teach geometry. That science is the only one which has not produced sects; it is founded on analysis and on synthesis and on the calculus; it does not occupy itself with the probable truth; moreover it has the same method in every country. ~ Frederick The Great

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason. ~ Nicholas Murray Butler

It has adopted the geometry most advantageous to the species or, in other words, the most convenient. ~ Henri Poincare

The geometer offers to the physicist a whole set of maps from which to choose. One map, perhaps, will fit the facts better than others, and then the geometry which provides that particular map will be the geometry most important for applied mathematics. ~ G.H. Hardy

In order to give meaning to the world, one has to feel oneself involved in what he frames. This attitude requires concentration, a discipline of mind, sensitivity, and a sense of geometry. ~ Henri Cartier-Bresson

Masonry, according to the general acceptation of the term, is an art founded on the principles of geometry, and devoted to the service and convenience of mankind. But Freemasonry, embracing a wider range and having a nobler object in view, namely, the cultivation and improvement of the human mind, may with more propriety be called a science, inasmuch as, availing itself of the terms of the former, it inculcates the principles of the purest morality, though its lessons are for the most part veiled in allegory and illustrated by symbols. ~ William Howard Taft

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

I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me. ~ Sigmund Freud

The science [geometry] is pursued for the sake of the knowledge of what eternally exists, and not of what comes for a moment into existence, and then perishes. ~ Plato

This king [Sesostris] divided the land among all Egyptians so as to give each one a quadrangle of equal size and to draw from each his revenues, by imposing a tax to be levied yearly. But everyone from whose part the river tore anything away, had to go to him to notify what had happened; he then sent overseers who had to measure out how much the land had become smaller, in order that the owner might pay on what was left, in proportion to the entire tax imposed. In this way, it appears to me, geometry originated, which passed thence to Hellas. ~ Herodotus

A science of all these possible kinds of space [the higher dimensional ones] would undoubtedly be the highest enterprise which a finite understanding could undertake in the field of geometry ... If it is possible that there could be regions with other dimensions, it is very likely that God has somewhere brought them into being. ~ Immanuel Kant

Scientists say every action initiates an equal and opposite reaction. I say that's just the start. I say every action initiates a most unequal and upredictable chain reaction, that every filament of living becomes part of a larger weave, while remaining identifiable. That every line of latitude requires several stripes of longitude to obtain meaning. That every universe is part of a bigger heaven, a heaven of rhythm and geometry, where a heartbeat is the apex of a triangle. ~ Ellen Hopkins

I call him truly learned who brings everything to bear on the truth, so that from geometry, music, grammar, and philosophy itself, culling what is usefule, he guards the faith against assault. ~ Clement Of Alexandria

Self-similarity is symmetry across scale. It implies recursion, pattern inside of pattern. ~ James Gleick

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

Wow. I'm twenty years old. Rene Descartes invented analytic geometry in his early twenties. Talk about pressure. ~ Anna Kay Akana

There are all sorts of things embodied in the LEGO brick - geometry and mathematics and truth and proportion and shape and colour ... It is a faintly spiritual activity that everybody connects with. ~ James May

Any one who has stood upon a lofty summit and gazed over an inchoate tangle of deep canyons and cragged mountains, of sunlit lakelets and black expanses of forest, has become aware of a certain giddy sensation that there are no distances, no measures, simply unrelated matter rising and falling without any analogy to the banal geometry of breadth, thickness, and height. ~ Bob Marshall

That's my big problem. That's it! Before the Arrival,guys like Evan Walker never looked twice at me, much less shot wild game for me and washed my hair. They never grabbed me by the back of the neck like the airbrushed model on his mother's paperback,abs a-clenching, pecs a-popping. My eyes have never been looked into, or my chin raised to bring my lips within an inch of theirs. I was the girl in the background, the just-friend,or -worse- the friend of a just-friend, the you-sit-next-to-her-in-geometry-but-can't-remember-her-name girl. ~ Rick Yancey

It is through geometry that one purifies the eye of the soul. ~ Plato

The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason. ~ Edward Gibbon

With this, in a powerful sense, our Question has been answered. The world, insofar as we speak of the world of Chemistry, biology, astrophysics, engineering, and everyday life, does embody beautiful ideas. The Core, which governs those domains, is profoundly rooted in concepts of symmetry and geometry, as we have seen. And it works its will, in quantum theory, through music-like rules. Symmetry really does determine structure. A pure and perfect Music of the Spheres really does animate the soul of reality. Plato and Pythagoras: We salute you! ~ Frank Wilczek

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

I came to find you last night," Lena says more quietly. "When I knew there was going to be a raid...I snuck out. I was there when - when the regulators came. I barely made it out. Alex helped me. We hid in a shed until they were gone..."
I close my eyes and reopen them. I remember wiggling into the damp earth, bumping my hip against the window. I remember standing, and seeing the dark forms of bodies lying like shadows in the grass, and the sharp geometry of a small she shed, nestled in the trees.
Lena was there. It was almost unimaginable.
"I can't believe that. I can't believe you snuck out during a raid - for me." My throat feels thick again, and I will myself not to start crying. For a moment I am overwhelmed by a feeling so huge and strange, I have no name for it: It surges over the guilt and the shock and the envy; it plunges a hand into the deepest part of myself and roots me to Lena. ~ Lauren Oliver

I can't stop biting my nails. It's a bad habit of mine. I like anything to do with math and numbers. I know a lot of people don't like geometry, but for me it's fun. ~ Khleo

Any day you had gym class was a weird school day. It started off normal. You had English, Social Studies, Geometry, then suddenly your in Lord of the Flies for 40 minutes. Your hanging from a rope, you have hardly any clothes on, teachers are yelling at you, kids are throwing dodge balls at you and snapping towels - you're trying to survive. And then it's Science,Language, and History. Now that is a weird day. ~ Jerry Seinfeld

Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler - such penetrating minds as Descartes and Pascal - were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime. ~ Charles Sanders Peirce

Elric: We are dreamers, shapers, singers, and makers. We study the mysteries of laser and circuit, crystal and scanner, holographic demons and invocation of equations. These are the tools we employ, and we know many things.

John Sheridan: Such as?

Elric: The true secrets, the important things. Fourteen words to make someone fall in love with you forever. Seven words to make them go without pain. How to say good-bye to a friend who is dying. How to be poor. How to be rich. How to rediscover dreams when the world has stolen them. That is why we are going away - to preserve that knowledge.

Sheridan: From what?

Elric: There is a storm coming, a black and terrible storm. We would not have our knowledge lost or used to ill purpose. From this place we will launch ourselves into the stars. With luck, you will never see our kind again in your lifetime. I know you have your orders, Captain. Detain us if you wish. But I cannot tell you where we are going. I can only ask you to trust us. ~ J. Michael Straczynski

Not that the propositions of geometry are only approximately true, but that they remain absolutely true in regard to that Euclidean space which has been so long regarded as being the physical space of our experience. ~ Arthur Cayley

There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry. ~ John Rawls

Einstein's gravitational theory, which is said to be the greatest single achievement of theoretical physics, resulted in beautiful relations connecting gravitational phenomena with the geometry of space; this was an exciting idea. ~ Richard P. Feynman

It is well known that geometry presupposes not only the concept of space but also the first fundamental notions for constructions in space as given in advance. It only gives nominal definitions for them, while the essential means of determining them appear in the form of axioms. The relationship of these presumptions is left in the dark; one sees neither whether and in how far their connection is necessary, nor a priori whether it is possible. From Euclid to Legendre, to name the most renowned of modern writers on geometry, this darkness has been lifted neither by the mathematicians nor the philosophers who have laboured upon it. ~ Bernhard Riemann

Archimedes to Eratosthenes greeting ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge. ~ Archimedes

I try to tell the teacher, you know. I don't give a fuck about geometry or English. Like I'm probably going to drive a truck or something when I get out of school. Join the army or something simple. I'm sure in the army they're all going to be wondering what an acute angle is. I'm sure I'll make lots of friends driving my truck because I can diagram some lousy goddamn sentence. And then after school I'm free, right? What's that mean? I go down to the bowling alley or the shopping mall with my friends. We scope the grils, smoke a little doobidge, maybe a tab of acid every now and then. But that's not really living, is it? I mean, if that's living, then excuse me right now. I'll go out and put a bullet in the old brainpan. But if that's not all there is, right, well, maybe there's something I could do a little less radical, like, you know. I don't mind life or anything--I'm perfectly willing to give it a try. So what the hell, I figured. I'm sick of school, drugs, this goddamn oppressive house of Ethel's and all. Maybe it's time I experimented a little more with my life, took a few more chances. So that's when I decided to become a warlock. To master the satanic arts of black magic. Devil worshiping, for you laymen. I want to master what they call the black arts. ~ Scott Bradfield

Pyramids, cathedrals, and rockets exist not because of geometry, theories of structures, or thermodynamics, but because they were first a picture- literally a vision-in the minds of those who built them. Society is where it is today because people had the perception; the images and the imagination; the creativity that the Arts provide, to make the world the place we live in today. ~ Eugene S. Ferguson

[Computer science] is not really about computers and it's not about computers in the same sense that physics is not really about particle accelerators, and biology is not about microscopes and Petri dishes ... and geometry isn't really about using surveying instruments. ~ Hal Abelson

Books. More books than I had ever seen in my life. I gasped and crawled to my knees. I couldn't breathe. Books galore. Music books, philosophy books. Math books. Geometry. Opera scores, logic. I sobbed and cradled the books. I hugged them to my naked chest and I cried. I smelled them and touched their spines. I remember how violently my fingers shook. I buried my nose in their pages and wept. Never had I ever held so many books in my life. And they were mine. All my very own. The orgasm still riddled my body. It had barely begun to fade. One orgasm ended, but the euphoria was just beginning. ~ Angela B. Chrysler

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

Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane ... I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane. ~ Augustus De Morgan

Andrew's kissing Amanda again, her back pinned against the door frame, his hands working through a geometry problem where the goal is to find the point of intersection where two legs bisect. People would like math so much more if it involved real life like that. ~ Julia Kent

Where there is matter, there is geometry. ~ Johannes Kepler

Speed is simply the rite that initiates us into
emptiness: a nostalgic desire for forms to revert to immobility, concealed beneath the very intensification of their mobility. Akin to the nostalgia for living forms that haunts geometry. ~ Jean Baudrillard

Everybody at the party is a many sided polygon ... Nonagon! ~ They Might Be Giants

Euler calculated the force of the wheels necessary to raise the water in a reservoir ... My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry! ~ Frederick The Great

It struck me as an operational way to define free will, in a way that allowed you to reconcile free will with determinism. The system is deterministic, but you can't say what it's going to do next. ~ James Gleick

Americans have all these classes that mean they just know odd things, so engineers know about William Blake and poets know about analytical geometry. She probably took one on Aristotle and the politics of gender. ~ Deborah Meyler

Gregorian chant, Romanesque architecture, the Iliad , the invention of geometry were not, for the people through whom they were brought into being and made available to us, occasions for the manifestation of personality. ~ Simone Weil

She wanted to run her hands over him as he whispered the impassioned corollaries of non-Euclidean geometry. ~ Sherry Thomas

They asked for Plato's assistance. He told them: "You hated wisdom and ran away from geometry, therefore God has afflicted you a punishment, for wisdom and philosophical knowledge have a high rank with God." ... The plague was lifted and they ceased to defame the branches of theoretical knowledge. ~ Mulla Sadra

This, dear Phaedrus, is the most important point: no geometry without the word. Without it, figures are accidents, and neither make manifest nor serve the power of the mind. ~ Paul Valery

It was in Alexandria that the circumference of the earth was first measured, the sun fixed at the center of the solar system, the workings of the brain and the pulse illuminated, the foundations of anatomy and physiology established, the definitive editions of Homer produced. It was in Alexandria that Euclid had codified geometry. ~ Stacy Schiff

For it is the duty of an astronomer to compose the history of the celestial motions through careful and expert study. ~ Nicolaus Copernicus

The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn. ~ Isaac Newton

They say the silence is the language of God, but so is music. This is why we dance, we become loud in our silence. ~ Aleksandra Ninkovic

In an agential realist account, agency is cut loose from its traditional humanist orbit. Agency is not aligned with human intentionality or subjectivity. Nor does it merely entail resignification or other specific kinds of moves within a social geometry ofantihumanism. The space of agency is not only substantially larger than that allowed for in Butler's performative account,
for example, but also, perhaps rather surprisingly, larger than what liberal humanism proposes. Significantly, matter is an agentive factor in its iterative materialization. ~ Karen Barad

Seriously, you don't have to know English. It'd be nice, a nice little plus. We don't want miracles. You don't have to know the country's language. But just some shapes, that's all. A square. A little geometry. ~ David Spade

I hope you theorists know what you're doing.' 'I can assure you that we don't. The geometry is still beyond us. All I learnt in the void was that our best guess so far is certainly wrong. ~ Greg Egan

In physics, theories are made of math. We don't use math because we want to scare away those not familiar with differential geometry and graded Lie algebras; we use it because we are fools. Math keeps us honest - it prevents us from lying to ourselves and to each other. You can be wrong with math, but you can't lie. ~ Sabine Hossenfelder

Preliminary accounting, banking and surveying (known as arithmetic, algebra and geometry). ~ Alan Watts

Me, and thousands of others in this country like me, are half-baked, because we were never allowed to complete our schooling. Open our skulls, look in with a penlight, and you'll find an odd museum of ideas: sentences of history or mathematics remembered from school textbooks (no boy remembers his schooling like the one who was taken out of school, let me assure you), sentences about politics read in a newspaper while waiting for someone to come to an office, triangles and pyramids seen on the torn pages of the old geometry textbooks which every tea shop in this country uses to wrap its snacks in, bits of All India Radio news bulletins, things that drop into your mind, like lizards from the ceiling, in the half hour before falling asleep
all these ideas, half formed and half digested and half correct, mix up with other half-cooked ideas in your head, and I guess these half-formed ideas bugger one another, and make more half-formed ideas, and this is what you act on and live with. ~ Aravind Adiga

I believe that all centers that appear in space - whether they originate in biology, in physical forces, in pure geometry, in color - are alike simply in that they all animate space. It is this animated space that has its functional effect upon the world, that determines the way things work, that governs the presence of harmony and life. ~ Christopher Alexander

A maze is a puzzle to be solved, with twists and turns and dead ends. It requires logical, analytical thinking and usually has a different way out than the way in. The maze could be a metaphor of struggling through life, going one way and then another until the exit takes your by surprise.

A maze signifies entrapment, while the labyrinth, with its unicursal path leading into the center and out again the same way, provides enlightenment. It's the process, the journey into your deepest self, your soul, the part where God abides. It's a passive path, a surrender even, to an order and design repeated through creation. A sacred geometry. ~ Kristen Heitzmann

As to the need of improvement there can be no question whilst the reign of Euclid continues. My own idea of a useful course is to begin with arithmetic, and then not Euclid but algebra. Next, not Euclid, but practical geometry, solid as well as plane; not demonstration, but to make acquaintance. Then not Euclid, but elementary vectors, conjoined with algebra, and applied to geometry. Addition first; then the scalar product. Elementary calculus should go on simultaneously, and come into vector algebraic geometry after a bit. Euclid might be an extra course for learned men, like Homer ... ~ Oliver Heaviside

Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing. ~ H.G.Wells

Of the two alternatives - a curved manifold in a Euclidean space of ten dimensions or a manifold with non-Euclidean geometry and no extra dimensions - which is right? I would rather not attempt a direct answer, because I fear I should get lost in a fog of metaphysics. But I may say at once that I do not take the ten dimensions seriously; whereas I take the non-Euclidean geometry of the world very seriously, and I do not regard it as a thing which needs explaining away. ~ Arthur Stanley Eddington

He deals the cards to find the answer
The sacred geometry of chance
The hidden law of a probable outcome
The numbers lead a dance
I know that the spades
Are the swords of a soldier
I know that the clubs are weapons of war
I know that diamonds
Mean money for this art
But that's not the shape of my heart ~ Sting

The detailed geometry of the coenzyme molecule as a whole is fascinating in its complexity. ~ Dorothy Hodgkin

By refraining from reducing multiplication to addition we are enabled through these axioms to banish continuity, which is so difficult to fix precisely, from the logical structure of geometry. ~ Hermann Weyl

It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible. ~ Bertrand Russell

As long as algebra and geometry have been separated, their progress have been slow and their uses limited; but when these two sciences have been united, they have lent each mutual forces, and have marched together towards perfection. ~ Joseph-Louis Lagrange

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

The geometry of a peacock's tail is more aerial: The eyes in a peacock's spread tail are situated at the intersecting point of a double cluster of spirals, that are apparently Archimedean spirals. ~ Gaston Bachelard

A philosophical thought is not supposed to be impervious to all criticism; this is the error Whitehead describes of turning philosophy into geometry, and it is useful primarily as a way of gaining short-term triumphs in personal arguments that no one else cares (or even knows) about anyway. A good philosophical thought will always be subject to criticisms (as Heidegger's or Whitehead's best insights all are) but they are of such elegance and depth that they change the terms of debate, and function as a sort of "obligatory passage point" (Latour's term) in the discussions that follow.
Or in other words, the reason Being and Time is still such a classic, with hundreds of thousands or millions of readers almost a century later, is not because Heidegger made "fewer mistakes" than others of his generation. Mistakes need to be cleaned up, but that is not the primary engine of personal or collective intellectual progress. ~ Graham Harman

If someone gave you the rules to the game you have been playing right away, you would miss the most exciting part – the details. Sometimes it's all about the details, they make the whole more meaningful. ~ Iva Kenaz

. . .biographers tend to regard as character those elements of personality that remain constant, or nearly so, throughout. . .Like practitioners of fractal geometry, biographers seek patterns that persist as one moves from micro- to macro-levels of analysis, and back again.
. . .
It follows from this that the scale across which we seek similarity need not be chronological. Consider the following incidents in the life of Stalin between 1929 and 1940, arranged not by dates but in terms of ascending horror. Start with the parrot he kept in a cage in his Kremlin apartment. The dictator had the habit of pacing up and down for long periods of time, smoking his pipe, brooding, and occasionally spitting on the floor. One day the parrot tried to mimic Stalin's spitting. He immediately reached into the cage with his pipe and crushed the parrot's head. A very micro-level event, you might well say, so what?

But then you learn that Stalin, while on vacation in the Crimea, was once kept awake by a barking dog. It turned out to be a seeing-eye dog that belonged to a blind peasant. The dog wound up being shot, and the peasant wound up in the Gulag. And then you learn that Stalin drove his independently minded second wife, who tried to talk back to him, into committing suicide. And that he arranged for Trotsky, who also talked back, to be assassinated halfway around the world. And that he arranged as well the deaths of as many of Trotsky's associates that he could reach, ~ John Lewis Gaddis

Once, I went to the roof of a project and saw a hawk perched on the rail; always, you see the city in the near distance, its towers and spires studded with lights, both stately and slapdash, like the crazy geometry of rock crystal. There were many days when you felt sorry for people who worked inside. ~ Edward Conlon

It was a hundred years later that Einstein gave a theory (general relativity) which said that the geometry of the universe is determined by its content of matter, so that no one geometry is intrinsic to space itself. Thus to the question, "Which geometry is true?" nature gives an ambiguous answer not only in mathematics, but also in physics ~ Douglas R. Hofstadter

I presume that to the uninitiated the formulae will appear cold and cheerless; but let it be remembered that, like other mathematical formulae, they find their origin in the divine source of all geometry. Whether I shall have the satisfaction of taking part in their exposition, or whether that will remain for some more profound expositor, will be seen in the future. ~ Benjamin Peirce

I'd been doing projects outdoors for the public. I made pigeons eat geometry by putting bread out in rhomboids and triangles. I don't know if this activity made sense, but the work was available. ~ Jenny Holzer

Fain would I turn back the clock and devote to French or some other language the hours I spent upon algebra, geometry, and trigonometry, of which not one principle remains with me. Stay! There is one theorem painfully drummed into my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it? ~ Jessie Belle Rittenhouse

Geometry is the science of correct reasoning on incorrect figures. ~ George Polya

If the human mind can understand the universe, it means the human mind is fundamentally of the same order as the divine mind. If the human mind is of the same order as the divine mind, then everything that appeared rational to God as he constructed the universe, it's "geometry," can also be made to appear rational to the human understanding, and so if we search and think hard enough, we can find a rational explanation and underpinning for everything. This is the fundamental proposition of science. ~ Robert Zubrin

The ballet makes us look at those bodies, it makes us listen to that music, it makes us wonder at the geometry, of the way they come together. The way that extraordinary space is controlled and given such emotional force. ~ John Guare

Merkabah is translated as either meaning the throne of god or chariot. Both definitions imply a means of spiritual ascension, not a physical one. They only have it partly right. ~ L.Z.Marie

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism. ~ Edwin A. Abbott

This was the missing piece in the puzzle. The secret of wood that bound matter together was the Yang-Mills filed, not the geometry of Einstein. It appeared as though this, and not geometry, was the central lesson of physics. ~ Michio Kaku

the problem is then to develop a theory of invariance with respect to arbitrary linear transformations, in which, however, in contra-distinction to the case of affine geometry, we have a definite invariant quadratic form, viz. the metrical groundform once and for all as an absolute datum. ~ Hermann Weyl

The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom. ~ Jean Cocteau

Geometry is the rules of all mental investigation ~ Mikhail Lomonosov