Quotes & Sayings About Geometry

It [ non-Euclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight. — Ivor Grattan-Guinness

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

There is a mathematical underpinning that you must first acquire, mastery of each mathematical subdiscipline leading you to the threshold of the next. In turn you must learn arithmetic, Euclidian geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, certain special functions of mathematical physics, matrix algebra, and group theory. For most physics students, this might occupy them from, say, third grade to early graduate school - roughly 15 years. Such a course of study does not actually involve learning any quantum mechanics, but merely establishing the mathematical framework required to approach it deeply. — Carl Sagan

Fortunate are the nations that can build wooden houses. Because wood breathes, transforms, deteriorates, like us. It is also important to have flowers and plants where we live, because they breathe, too. Contemplating a flower for three seconds can be a captivating solitary journey back to original geometry, which is always revitalizing. — Henryk Skolimowski

[In comedy] you never want to leave the actors hanging out to dry. So you need to come up with funny individual stories for each character, and then you do this sort of comedy geometry, weaving them together. Once you've got a funny structure and you know why the scenes are funny, then you get super funny people to say your own lines, say their own lines, say things in their own way, and every scene is a live rewrite in front of the camera. — Jeff Schaffer

The Creator, the fountain of all wisdom, the approver of perpetual order, the eternal and superessential spring of geometry and harmonics. — Johannes Kepler

F a special geometry has to be invented in order to account for a falling apple, even Newton might be appalled at the complications which would ensue when really difficult problems are tackled. — Oliver Lodge

The study of geometry is a petty and idle exercise of the mind, if it is applied to no larger system than the starry one. Mathematics should be mixed not only with physics but with ethics; that is mixed mathematics. — Henry David Thoreau

The classical theorists resemble Euclidean geometers in a non-Euclidean world who, discovering that in experience straight lines apparently parallel often meet, rebuke the lines for not keeping straight as the only remedy for the unfortunate collisions which are occurring. Yet, in truth, there is no remedy except to throw over the axiom of parallels and to work out a non-Euclidean geometry. — John Maynard Keynes

Enchanting is not the word that would immediately spring to mind when describing a play that deals with fractal geometry, iterated algorithms, chaos theory and the second law of thermodynamics, but it is a perfect fit for Tom Stoppard's astonishing 1993 play, which is as beautiful as it is brilliant. This is one Stoppard drama that you don't have to be Einstein to understand
you can feel it as well as think it. ( ... ) Breathtaking, exhilarating and deeply satisfying. — Lyn Gardner

The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry. — Eric Bell

In geometry I find certain imperfections which I hold to be the reason why this science, apart from transition into analytics, can as yet make no advance from that state in which it came to us from Euclid.
As belonging to these imperfections, I consider the obscurity in the fundamental concepts of the geometrical magnitudes and in the manner and method of representing the measuring of these magnitudes, and finally the momentous gap in the theory of parallels, to fill which all efforts of mathematicians have so far been in vain. — Nikolai Lobachevsky

This love triangle had reached new heights, and as much as Matt loved geometry, this was not the sort of triangle he wanted anything to do with. — Jessica Park

Greek architecture is the flowering of geometry. — Ralph Waldo Emerson

Euclid, who was still, when I was young, the sole acknowledged text-book of geometry for boys, lived in Alexandria, about 300 B.C., a few years after the death of Alexander and Aristotle. — Anonymous

Geometry draws the soul towards truth. — Plato

Believe me, if Archimedes ever had the grand entrance of a girl as pretty as Gloria to look forward to, he would never have spent so much time calculating the value of Pi. He would have been baking her a Pie! If Euclid had ever beheld a vision of loveliness like the one I see walking into my anti-math class, he would have forgotten all the geometry of lines and planes, and concentrated on the sweet simplicity of soft curves. If Pythagoras had ever had a girl look at him the way Gloria's eyes fix in my direction, he would have given up his calculations on the hypotenuse of right triangles and run for the hills to pick a bouquet of wildflowers. — David Klass

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

The geometry of the place was all wrong. One could not be sure that the sea and the ground were horizontal, — H.P. Lovecraft

The only things that can ever be universal, in a sense, are scaling things. — James Gleick

I write rhymes with addition and algebra, mental geometry. — Ice-T

Sire, there is no royal road to geometry. — Euclid

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 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

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

Projective geometry is all geometry. — Arthur Cayley

Geometry existed before the creation. It is co-eternal with the mind of God ... Geometry provided God with a model for the Creation ... — Johannes Kepler

Geometry is the noblest branch of physics. — William Fogg Osgood

Symmetry is only a property of dead things. Did you ever see a tree or a mountain that was symmetrical? It's fine for buildings, but if you ever see a symmetrical human face, you will have the impression that you ought to think it beautiful, but that in fact you find it cold. The human heart likes a little disorder in its geometry, Kyria Pelagia. Look at your face in a mirror, Signorina, and you will see that one eyebrow is a little higher than the other, that the set of the lid of your left eye is such that the eye is a fraction more open that the other. It is these things that make you both attractive and beautiful, whereas ... otherwise you would be a statue. Symmetry is for God, not for us. — Louis De Bernieres

Art has no immediate future because all art is collective and there is no more collective life(there are only dead collections of people), and also because of this breaking of the true pact between the body and the soul. Greek art coincided with the beginning of geometry and with athleticism, the art of the Middle Ages with the craftsmen's guilds, the art of the Renaissance with the beginning of mechanics, etc ... Since 1914 there has been a complete cut. Even comedy is almost impossible. There is only room for satire (when was it easier to understand Juvenal?). Art will never be reborn except from amidst a general anarchy - it will be epic no doubt, because affliction will have simplified a great many things ... It is therefore quite useless for you to envy Leonardo or Bach. Greatness in our times must take a different course. Moreover it can only be solitary, obscure and without an echo ... (but without an echo, no art). — Simone Weil

One of the great sources of employment for people with Ph.D.s in geometry is the animation industry. — Margaret Wertheim

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 the chemistry is right between star and photographer and the geometry of the pictures pleases the star, often the two people end up with a long-term professional friendship during which they continue to work together and to produce highly personal images. — Eve Arnold

Life is merely a fracas on an unmapped terrain, and the universe a geometry stricken with epilepsy. — Emile M. Cioran

It is hard to convince a high-school student that he will encounter a lot of problems more difficult than those of algebra and geometry. — E.W. Howe

The only logical meaning of necessity seems to be derived from implication. A proposition is more or less necessary according as the class of propositions for which it is a premiss is greater or smaller.* In this sense the propositions of logic have the greatest necessity, and those of geometry have a high degree of necessity. But this sense of necessity yields no valid argument from our inability to imagine holes in space to the conclusion that there cannot really be any space at all except in our imaginations. — Bertrand Russell

Either one or the other [analysis or synthesis] may be direct or indirect. The direct procedure is when the point of departure is known-direct synthesis in the elements of geometry. By combining at random simple truths with each other, more complicated ones are deduced from them. This is the method of discovery, the special method of inventions, contrary to popular opinion. — Andre-Marie Ampere

Geometry is a Deductive Science. — John Stuart Mill

Everything you invent is true: you can be sure of that. Poetry is a subject as precise as geometry. — Julian Barnes

You must follow me carefully. I shall have to controvert one or two ideas that are almost universally accepted. The geometry, for instance, they taught you at school is founded on a misconception. — H.G.Wells

If I died, would it get me out of my geometry test tomorrow? One could only hope. — Kristin Cast

I did not know then that this is what life is - just when you master the geometry of one world, it slips away, and suddenly again, you're swarmed by strange shapes and impossible angles. — Ta-Nehisi Coates

But then, Cap'n Crunch in a flake form would be suicidal madness; it would last about as long, when immersed in milk, as snowflakes sifting down into a deep fryer. No, the cereal engineers at General Mills had to find a shape that would minimize surface area, and, as some sort of compromise between the sphere that is dictated by Euclidean geometry and whatever sunken treasure related shapes that the cereal aestheticians were probably clamoring for, they came up with this hard -to-pin-down striated pillow formation. — Neal Stephenson

The radar directed flak intensifies. Like swarms of angry red-and-yellow-eyed snakes slithering up invisible ropes in the sky. The sky around them is a glittering maelstrom of light. The stars pale into insignificance. Down below the city is lit up in sections as shockwaves fan out in kaleidoscopic bursts. Shell smoke rising up from the ground. On his right a burst of flame and a thick guttering of black smoke lit up by the geometry of the searchlights. — Glenn Haybittle

It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery - Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry. — Alfred North Whitehead

Geometry in every proposition speaks a language which experience never dares to utter; and indeed of which she but halfway comprehends the meaning. — William Whewell

A geometry implies the heterogeneity of locus, namely that there is a locus of the Other. Regarding this locus of the Other, of one sex as Other, as absolute Other, what does the most recent development in topology allow us to posit? — Jacques Lacan

Two possibilities present themselves for the analytical treatment of metrical geometry. — Hermann Weyl

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

Psychoanalysis and Zen, in my private psychic geometry, are equal to nicotine. They are anti-existential. Nicotine quarantines one out of existence. — Norman Mailer

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

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. It would have been better if some middle-aged collector of Star Wars action figures had found me in that snowbank. — Rick Yancey

I call it sacred geometry. When everything's just right and it feels really balanced, so that when it unfolds to the next part, you feel totally familiar and at ease within the song. — Jason Mraz

We are, all four of us, blood relatives, and we speak a kind of esoteric, family language, a sort of semantic geometry in which the shortest distance between any two points is a fullish circle. — J.D. Salinger

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

Architects should be educated, skillful with the pencil, instructed in geometry, know much history, have followed the philosophers with attention, understand music, have some knowledge of medicine, know the opinions of the jurists, and be acquainted with astronomy and the theory of the heavens — Marcus Vitruvius Pollio

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 smiled. Mom laughed, shaking her head. "That's the punchline? Why is that even funny?" "It's the Pythagorean theorem," said Lauren. "It's a math formula for . . . something." "Right triangles," I said, and looked pointedly at Margaret. "I told you I'd already done geometry. — Dan Wells

But Miss Ferguson preferred science over penmanship. Philosophy over etiquette. And, dear heavens preserve them all, mathematics over everything. Not simply numbering that could see a wife through her household accounts. Algebra. Geometry. Indecipherable equations made up of unrecognizable symbols that meant nothing to anyone but the chit herself. It was enough to give Miss Chase hives.

The girl wasn't even saved by having any proper feminine skills. She could not tat or sing or draw. Her needlework was execrable, and her Italian worse. In fact, her only skills were completely unacceptable, as no one wanted a wife who could speak German, discuss physics, or bring down more pheasant than her husband. — Eileen Dreyer

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

Now the reason that we think computer science is about computers is pretty much the same reason that the Egyptians thought geometry was about surveying instruments: when some field is just getting started and you don't really understand it very well, it's very easy to confuse the essence of what you're doing with the tools that you use. — Hal Abelson

The pattern appears so ethereally, that it is hard to remember that the shape is an attractor. It is not just any trajectory of a dynamical system. It is the trajectory toward which all other trajectories converge. — James Gleick

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

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

Perhaps you have seen me. I know well, my purpose was merely that of a symbol, 'equals', 'times' ... ; but what is said, for all that, was identity-less: a kind of live geometry. — Albert Goldbarth

Mustardseed grinned at Bertie. "I was never any good at geometry, but you're stuck in a love triangle, aren't you?"
"Shut up," she ordered even as Moth asked, "But what if there were four of them?"
"That's a love rectangle, and five people would be a love pentagon."
"And what are six people in love?" Cobweb demanded.
Mustardseed thought it over a moment. "Manslaughter, I suppose. — Lisa Mantchev

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. — Mario Livio

Best Witchcraft is Geometry
To the magician's mind -
His ordinary acts are feats
To thinking of mankind. — Emily Dickinson

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

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

In creating the world, God used arithmetic, geometry, and likewise astronomy. — Nicholas Of Cusa

the difficulty of a sentence depends not just on its word count but on its geometry. Good writers often use very long sentences, and they garnish them with words that are, strictly speaking, needless. But they get away with it by arranging the words so that a reader can absorb them a phrase at a time, each phrase conveying a chunk of conceptual structure. — Steven Pinker

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

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

It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to his mind. Yet, when he stated the fifth postulate, he stood at the parting of the ways. His subconscious prescience is astounding. There is nothing comperable to it in the whole history of science. — George Sarton

The world of shapes, lines, curves, and solids is as varied as the world of numbers, and it is only our long-satisfied possession of Euclidean geometry that offers us the impression, or the illusion, that it has, that world, already been encompassed in a manageable intellectual structure. The lineaments of that structure are well known: as in the rest of life, something is given and something is gotten; but the logic behind those lineaments is apt to pass unnoticed, and it is the logic that controls the system. — David Berlinski

The passive stiffness of a joint reflects properties of the muscle tissue, joint capsule, tendons, skin and geometry of the joint. — Leon Chaitow

In his ... 'Geometrical peculiarities of the Pyramids', Ballard shows the relationship between the equal area theory and the golden number. After checking Herodotus' statement via dimensions Ballard concludes: 'I have therefore the authority of Herodotus to support the theory which I shall subsequently set forth, that this pyramid was the exponent of lines divided in mean and extreme ratio. — Roger Herz-Fischler

Really, universally, relations stop nowhere, and the exquisite problem of the artist is eternally but to draw, by a geometry of his own, the circle within which they shall happily appear to do so. — Henry James

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

Here I beg you to observe in passing that the scruples that prevented ancient writers from using arithmetical terms in geometry, and which can only be a consequence of their inability to perceive clearly the relation between these two subjects, introduced much obscurity and confusion into their explanations. — Rene Descartes

The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry ... Congruent means in Euclidean geometry the same as determining parallelism, a meaning which it does not have in non-Euclidean geometry. — Hans Reichenbach

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

Geometry is knowledge that appears to be produced by human beings, yet whose meaning is totally independent of them. — Rudolf Steiner

The thing about reason is that there's a geometry to it. It travels in a straight line, so that slightly different beginnings can lead you to wildly divergent endpoints. — Rachel Hartman

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

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

At George Mason University I saw Hoppe present a lecture in which he claimed that Ludwig von Mises had set the intellectual foundation for not only economics, but for ethics, geometry, and optics, as well. This bizarre claim turned a serious scholar and profound thinker into a comical cult figure, a sort of Euro Kim Il Sung. — Tom G. Palmer

It's not only the myths surrounding chess. Chess itself is a myth, you know? A game of hierarchy, of war. It's a story that people have been using to explain complex concepts for eons. Mathematics, yes. Geometry. Business. Philosophy. Even love. — Skye Warren

The geometry of landscape and situation seems to create its own systems of time, the sense of a dynamic element which is cinematizing the events of the canvas, translating a posture or ceremony into dynamic terms. The greatest movie of the 20th century is the Mona Lisa, just as the greatest novel is Gray's Anatomy. — J.G. Ballard

Why did math matter so much? Some reasons were practical: More and more jobs required familiarity with probability, statistics, and geometry. The other reason was that math was not just math. Math is a language of logic. It is a disciplined, organized way of thinking. There is a right answer; there are rules that must be followed. More than any other subject, math is rigor distilled. Mastering the language of logic helps to embed higher-order habits in kids' minds: the ability to reason, for example, to detect patterns and to make informed guesses. Those kinds of skills had rising value in a — Amanda Ripley

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

Geometry is moribund. I want a lilt and joy to art. — Ellsworth Kelly

How physical beauty turns out to be chemistry and geometry and anatomy. Art is really science. Discovering why people like something is so you can replicate it. Copy it. It's a paradox, "creating" a real smile. Rehearsing again and again a spontaneous moment of horror. All the sweat and boring effort that goes into creating what looks easy and instant. — Chuck Palahniuk

As to writing another book on geometry [to replace Euclid] the middle ages would have as soon thought of composing another New Testament. — Augustus De Morgan

I would say, if you like, that the party is like an out-moded mathematics ... that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline. — Alain Badiou

To me, however, the question of the times resolved itself into a practical question of the conduct of life. How shall I live? We are incompetent to solve the times. Our geometry cannot span the huge orbits of the prevailing ideas, behold their return, and reconcile their opposition. We can only obey our own polarity. — Ralph Waldo Emerson

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems
the determination of the diagonal of a square and that of the circumference of a circle
revealed the existence of new mathematical beings for which no place could be found within the rational domain. — David Van Dantzig

The object of geometry in all its measuring and computing, is to ascertain with exactness the plan of the great Geometer, to penetrate the veil of material forms, and disclose the thoughts which lie beneath them? When our researches are successful, and when a generous and heaven-eyed inspiration has elevated us above humanity, and raised us triumphantly into the very presence, as it were, of the divine intellect, how instantly and entirely are human pride and vanity repressed, and, by a single glance at the glories of the infinite mind, are we humbled to the dust. — Benjamin Peirce

Now, a good education is about so much more than just learning geometry or memorizing dates in history. All of that is important, but an education is also about exploring new things
discovering what makes you come alive, and then being your best at whatever you choose — Michelle Obama