Geometrical Quotes

Nobody since Newton has been able to use geometrical methods to the same extent for the like purposes; and as we read the Principia we feel as when we are in an ancient armoury where the weapons are of gigantic size; and as we look at them we marvel what manner of man he was who could use as a weapon what we can scarcely lift as a burden. ~ William Whewell

You are the mathematical and geometrical centre of all the universe, where the centre is you, and radius goes into the infinity. ~ Count Stefan Colonna Walewski

The essential point of view advanced here is this: the stability of every
living being, as of every structurally stable form, rests, in the last analysis, on a for-
mal structure - in fact, a geometrical object - whose biochemical realization is the
living being. ~ Rene Thom

The ancient Egyptian calendar is Precessionally Sexagesimal (Besides being theologically/decanally decimal). That means that the toggling between its "enhanced" Civil Calendar (i.e., 365 days yearly) and the geometrical Original Calendar (i.e., 360 days yearly) is based on the precession of the equinoxes (rather than being solely anchored in the solar system); where 148 squared over 365 equals to 60; and 148 multiples of 360 over 365 equals to the height of the Great Pyramid. ~ Ibrahim Ibrahim

Another means of silently lessening the inequality of property is to exempt all from taxation below a certain point, and to tax the higher portions or property in geometrical progression as they rise. Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. The earth is given as a common stock for man to labor and live on.
Letter to James Madison, October 28, 1785 ~ Thomas Jefferson

The theory of ramification is one of pure colligation, for it takes no account of magnitude or position; geometrical lines are used, but these have no more real bearing on the matter than those employed in genealogical tables have in explaining the laws of procreation. ~ James Joseph Sylvester

Then she understood that what she needed was the motion to a purpose, no matter how small or in what form, the sense of an activity going step by step to some chosen end across a span of time. The work of cooking a meal was like a closed circle, completed and gone, leading nowhere. But the work of building a path was a living sum, so that no day was left to die behind her, but each day contained all those that preceded it, each day acquired its immortality on every succeeding tomorrow. A circle, she thought, is the movement proper to physical nature, they say that there's nothing but circular motion in the inanimate universe around us, but the straight line is the badge of man, the straight line of a geometrical abstraction that makes roads, rails and bridges, the straight line that cuts the curving aimlessness of nature by a purposeful motion from a start to an end. The cooking of meals, she thought, is like the feeding of coal to an engine for the sake of a great run, but what would be the imbecile torture of coaling an engine that had no run to make? It is not proper for man's life to be a circle, she thought, or a string of circles dropping off like zeros behind him--man's life must be a straight line of motion from goal to farther goal, each leading to the next and to a single growing sum, like a journey down the track of a railroad, from station to station to--oh, stop it! ~ Ayn Rand

The personality and style of a photographer usually limits the type of subject with which he deals best. For example Cartier-Bresson is very interested in people and in travel; these things plus his precise feeling for geometrical relationships determine the type of pictures he takes best. What is of value is that a particular photographer sees the subject differently. A good picture must be a completely individual expression which intrigues the viewer and forces him to think. ~ Alexey Brodovitch

Large department stores, with their luxuriant abundance of canned goods, foods, and clothing, are like the primary landscape and the geometrical locus of affluence. Streets with overcrowded and glittering store windowsthe displays of delicacies, and all the scenes of alimentary and vestimentary festivity, stimulate a magical salivation. Accumulation is more than the sum of its products: the conspicuousness of surplus, the final and magical negation of scarcitymimic a new-found nature of prodigious fecundity. ~ Jean Baudrillard

I like to think that Einstein would look at string theory's journey and smile, enjoying the theory's remarkable geometrical features while feeling kinship with fellow travelers on the long and winding road toward unification. ~ Brian Greene

Within the holy circle of the stage, geometrical principles are used to organize physical energy so that the beauty of the human form reveals a web of drama and truth---that is the essence of dance as I have come to know it. ~ Gelsey Kirkland

Beauty cannot be defined by abscissas and ordinates; neither are circles and ellipses created by their geometrical formulas. ~ Carl Von Clausewitz

All conceptions in the game of chess have a geometrical basis. ~ Eugene Znosko-Borovsky

I felt as though the temple curtain had been drawn aside without warning and I, a goggle-eyed stranger somehow mistaken for an initiate, had been ushered into the sanctuary to witness the mystery of mysteries. I saw a phantasmagoria, a living tapestry of forms jeweled in minute detail. They danced together like guests at a rowdy wedding. They changed their shapes. Within themselves they juggled geometrical shards like the fragments in a kaleidoscope. They sent forth extensions of themselves like the flares of suns. Yet all their activity was obviously interrelated; each being's actions were in step with its neighbors'. They were like bees swarming: They obviously recognised each other and were communicating avidly, but it was impossible to know what they were saying. They enacted a pageant whose beauty awed me.

As the lights came back on, the auditorium seemed dull and unreal.I'd been watching various kinds of ordinary cells going about their daily business, as seen through a microscope and recorded by the latest time-lapse movie techniques. The filmmaker frankly admitted that neither he nor anyone else knew just what the cells were doing, or how and why they were doing it. We biologists, especially during our formative years in school, spent most of our time dissecting dead animals and studying preparations of dead cells stained to make their structures more easily visible - "painted tombstones," as someone once called them. Of course, we all knew that life was m ~ Robert O. Becker

I know death hath ten thousand several doors
For men to take their exits; and 'tis found
They go on such strange geometrical hinges,
You may open them both ways: any way, for heaven-sake ~ John Webster

Numbers are eternal while everything else is perishable; they are of the nature not of matter, but of mind; they permit mental operations of the most surprising and delightful kind without reference to the coarse external world of the senses-which is how the divine mind must be supposed to operate. The ecstatic contemplation of geometrical forms and mathematical laws is therefore the most effective means of purging the soul of earthly passion, and the principle link between man and divinity. ~ Arthur Koestler

Remembering ... that Eratosthenes of Cyrene, employing mathematical theories and geometrical methods, discovered from the course of the sun, the shadows cast by an equinoctial gnomon, and the inclination of the heaven that the circumference of the earth is two hundred and fifty-two thousand stadia, that is, thirty-one million five hundred thousand paces. ~ Marcus Vitruvius Pollio

The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth. This ~ Marcus Du Sautoy

String theorists have found special pairs of geometrical shapes for space that have completely different features when each is probed by unwrapped strings. They also have completely different features when each is probed by wrapped strings. But-and this is the punch line-when probed both ways, with wrapped and unwrapped strings, the shapes become indistinguishable. what the unwrapped strings see on one space, the wrapped strings see on the other, and vice versa, rendering identical the collective picture gleaned from the full physics of string theory. ~ Brian Greene

According to Thoth, because of the placement of the Great Pyramid on the Earth connecting into the Earth's huge geometrical field - specifically the octahedral field of the Earth, which is equivalent to our own fields - and because of the pyramid's mass and the geometries used in it, the white-light energy field spirals upward and becomes extremely strong, stretching all the way out to the center of the galaxy. The dark-light energy comes in from above, spirals through zero point and connects with the center of the Earth. In this way the Great Pyramid connects the center of the Earth to the center of our galaxy. ~ Drunvalo Melchizedek

Bees... by virtue of a certain geometrical forethought, knew that the hexagon is greater than the square and the triangle and will hold more honey for the same expenditure of material. ~ Pappus

Astronomy was the cradle of the natural sciences and the starting point of geometrical theories. ~ Cornelius Lanczos

An interesting question is whether symmetry with respect to translation, and indeed reflection and rotation too, is limited to the visual arts, or may be exhibited by other artistic forms, such as pieces of music. Evidently, if we refer to the sounds, rather than to the layout of the written musical score, we would have to define symmetry operations in terms other than purely geometrical, just as we did in the case of the palindromes. Once we do that, however, the answer to the question, Can we find translation-symmetric music? is a resounding yes. As Russian crystal physicist G. V. Wulff wrote in 1908: "The spirit of music is rhythm. It consists of the regular, periodic repetition of parts of the musical composition...the regular repetition of identical parts in the whole constitutes the essence of symmetry." Indeed, the recurring themes that are so common in musical composition are the temporal equivalents of Morris's designs and symmetry under translation. Even more generally, compositions are often based on a fundamental motif introduced at the beginning and then undergoing various metamorphoses. ~ Mario Livio

The effect was that of a Cyclopean city of no architecture known to man or to human imagination, with vast aggregations of night-black masonry embodying monstrous perversions of geometrical laws and attaining the most grotesque extremes of sinister bizarrerie. ~ H.P. Lovecraft

Ethics is not a
geometrical calculation; "others" are never very far from "us"; "they" and "we" are co-constituted and entangled through the very cuts "we" help to enact. Cuts cut "things" together and apart. Cuts are not enacted from the outside, nor are they ever enacted once and for all. ~ Karen Barad

The existence of the terrible in every particle of the air. You breathe it in as part of something transparent; but within you it precipitates, hardens, acquires angular, geometrical forms in among your organs; for all the torments and horrors suffered at places of execution, in torture chambers, in madhouses, in operating theatres, under the arches of bridges in late autumn – all this is possessed of a tenacious permanence, all of it persists and, jealous of all that is, clings to its own frightful reality. People would prefer to be able to forget much of it; sleep files away gently at the grooves in the brain, but dreams drive it away and trace the lines anew. And they wake, panting, and dissolve the gleam of a candle in the dark, and drink in the half-lit solace as if it were sugared water. ~ Rainer Maria Rilke

The concentration and reciprocal effect of industry and agriculture conjoin in a growth of productive powers, which increases more in geometrical than in arithmetical proportion. ~ Friedrich List

I am intoxicated with a feeling of rightfulness, a psychological snapping together of mating parts, a lucid moment of geometrical perfection. A liberating bliss. ~ Andrew X Pham

In this science the illustrations and examples are not confined in their effect merely to the practice they afford in the analytical art, but [ ... ] they also store the mind with independent geometrical and physical knowledge. Besides, it should be considered, that the only effectual method of impressing abstract formulae and rules upon the memory, and, indeed, of making them fully and clearly apprehended by the understanding, is by examples of their practical application. ~ Dionysius Lardner

Pure geometrical regularity gives a certain pleasure to men troubled by the obscurity of outside appearance. The geometrical line is something absolutely distinct from the messiness, the confusion, and the accidental details of existing things. ~ T. E. Hulme

In the candle's flickering light, the library's thousands of books emerged from the shadows, and for a moment Nicholas could not help admiring them again. During free time he had almost never looked up from the pages he was reading, but now he saw the books anew, from without rather than from within, and was reminded of how beautiful they were simply as objects. The geometrical wonder of them all, each book on its own and all the books together, row upon row, the infinite patterns and possibilities they presented. They were truly lovely. ~ Trenton Lee Stewart

I review all I know, but can synthesize no meaning. When I doze, the Fact, the certain accomplished calamity, wakes me roughly like a brutal nurse. I see it crouching inflexibly in a corner of the ceiling. It comes down in geometrical diagonal like lightning.
It says, I remain, I AM, I shall never cease to be: your memory will grow a deathly glaze: you will forget, you will fade out, but I cannot be undone.
Thus every quarter hour it puts the taste of death in my mouth, and shows me, but not gently, how I go whoring after oblivion. ~ Elizabeth Smart

Population, when unchecked, goes on doubling itself every 25 years or increases in a geometrical ratio. ~ Thomas Malthus

At the Stourbridge Fair in 1663, at age twenty, he purchased a book on astrology, "out of a curiosity to see what there was in it." He read it until he came to an illustration which he could not understand, because he was ignorant of trigonometry. So he purchased a book on trigonometry but soon found himself unable to follow the geometrical arguments. So he found a copy of Euclid's Elements of Geometry, and began to read. Two years later he invented the differential calculus. ~ Carl Sagan

Being perpetually charmed by his familiar siren, that is, by his geometry, he neglected to eat and drink and took no care of his person; that he was often carried by force to the baths, and when there he would trace geometrical figures in the ashes of the fire, and with his finger draws lines upon his body when it was anointed with oil, being in a state of great ecstasy and divinely possessed by his science. ~ Plutarch

His brown eyes would roam around the various sentimental and artistic bric-a-brac present, and his own banal toiles (the conventionally primitive eyes, sliced guitars, blue nipples and geometrical designs of the day), and with a vague gesture toward a painted wooden bowl or veined vase, he would say "Prenez donc une des ces poires. La bonne dame d'en face m'en offre plus que je n'en peux savourer." Or: "Mississe Taille Lore vient de me donner ces dahlias, belles fleurs que j'exècre. ~ Vladimir Nabokov

The problem of the planetary orbits had been hopelessly bogged down in its purely geometrical frame of reference, and when Kepler realized that he could not get it unstuck, he tore it out of that frame and removed it into the field of physics. This operation of removing a problem from its traditional context and placing it into a new one, looking at it through glasses of of a different colour as it were, has always seemed to me of the very essence of the creative process. It leads not only to a reevaluation of the problem itself, but often to a synthesis of much wider consequences, brought about by a fusion of the two previously unrelated frames of reference. In our case, the orbit of Mars became the unifying link between the two formerly seperate realms of physics and cosmology. ~ Arthur Koestler

I am conscious that an equal division of property is impracticable. But the consequences of this enormous inequality [in Europe] producing so much misery to the bulk of mankind, legislators cannot invent too many devices for subdividing property, ... [One] means of silently lessening the inequality of property is to exempt all from taxation below a certain point, and to tax the higher portions of property in geometrical progression as they rise. ~ Thomas Jefferson

Deep down, it's all baseball, no matter what kind of geometrical shape you play it with. ~ Vernon D. Burns

The couturier should be a geometrician, for the human body makes
geometrical figures to which the materials should correspond. ~ Madeleine Vionnet

I think the Greeks first took astrology to India and took from the Hindus the science of astronomy and carried it back with them from Europe. Because in India you will find old altars made according to a certain geometrical plan, and certain things had to be done when the stars were in certain positions, therefore I think the Greeks gave the Hindus astrology, and the Hindus gave them astronomy. ~ Swami Vivekananda

A planar geometrical figure with more than three vertices can be decomposed into a set of triangles, and it can be reconstructed from a set of triangles. ~ Vladimir Prelog

In learning general relativity, and then in teaching it to classes at Berkeley and MIT, I became dissatisfied with what seemed to be the usual approach to the subject. I found that in most textbooks geometric ideas were given a starring role, so that a student...would come away with an impression that this had something to do with the fact that space-time is a Riemannian [curved] manifold. Of course, this was Einstein's point of view, and his preeminent genius necessarily shapes our understanding of the theory he created. However, I believe that the geometrical approach has driven a wedge between general relativity and [Quantum Field Theory]. As long as it could be hoped, as Einstein did hope, that matter would eventually be understood in geometrical terms, it made sense to give Riemannian geometry a primary role in describing the theory of gravitation. But now the passage of time has taught us not to expect that the strong, weak, and electromagnetic interactions can be understood in geometrical terms, and too great an emphasis on geometry can only obscuret he deep connections between gravitation and the rest of physics...[My] book sets out the theory of gravitation according to what I think is its inner logic as a branch of physics, and not according to its historical development. It is certainly a historical fact that when Albert Einstein was working out general relativity, there was at hand a preexisting mathematical formalism, that of Riemannian geometry, that he could an ~ Steven Weinberg

Jean-Pierre Marquis, From a Geometrical Point of View: A Study of the History and Philosophy of Category Theory, Springer Science & Business Media, 2008. ~ Roger Scruton

We can ... treat only the geometrical aspects of mathematics and shall be satisfied in having shown that there is no problem of the truth of geometrical axioms and that no special geometrical visualization exists in mathematics. ~ Hans Reichenbach

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

Faith--in the sense of an unreserved commitment which is never completely justified-enters the picture as soon as we leave the realm of pure geometrical ideas and have to deal
with the existing world. Each of our perceptions is an act of faith in
that it affirms more than we strictly know, since objects are inexhaustibJe and our information limited. ~ Maurice Merleau Ponty

What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men. ~ G.H. Hardy

In One Dimensions, did not a moving Point produce a Line with two terminal points?
In two Dimensions, did not a moving Line produce a Square wit four terminal points?
In Three Dimensions, did not a moving Square produce - did not the eyes of mine behold it - that blessed being, a Cube, with eight terminal points?
And in Four Dimensions, shall not a moving Cube - alas, for Analogy, and alas for the Progress of Truth if it be not so - shall not, I say the motion of a divine Cube result in a still more divine organization with sixteen terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this - if I might qupte my Lord's own words - "Strictly according to Analogy"?
Again, was I not taught by my Lord that as in a Line there are two bonding points, and in a Square there are four bounding Lines, so in a Cube there must be six bounding Squares? Behold once more the confirming Series: 2, 4, 6: is not this an Arithmetical Progression? And consequently does it not of necessity follow that the more divine offspring of the divine Cube in the Land of Four Dimensions, must have eight bounding Cubes: and is not this also, as my Lord has taught me to believe, "strictly according to analogy"? ~ Edwin A. Abbott

It had had a fragrant element, reminding him of a regular childhood experience, a memory that reverberated like the chimes of a prayer bell inside his head. For a few moments, he pictured the old Orthodox church that had dominated his remote Russian village. The bearded priest was swinging the elaborate incense-burner, suspended from gold-plated chains. It had been the same odour. Hadn't it? He blinked, shook his head. He couldn't make sense of that.
He decided, with an odd lack of enthusiasm, that he'd imagined it. The effects of the war played tricks of the mind, of the senses. Looking over his shoulder, he counted all seven of his men as they emerged from the remnants of the four-storey civic office building.
A few muddied documents were scattered on the ground, stamped with the official Nazi Party eagle, its head turned to the left, and an emblem he failed to recognize, but which looked to him like a decorative wheel, with a geometrical design of squares at its centre. Even a blackened flag had survived the bomb damage. Hanging beneath a crumbling windowsill, the swastika flapped against the bullet-ridden façade, the movement both panicky and defiant, Pavel thought.
His men were conscripts. A few still wore their padded khaki jackets and mustard-yellow blouses. Most, their green field tunics and forage caps. All the clothing was lice-ridden and smeared with soft ash. Months of exposure to frozen winds had darkened their skins and narrowed their eyes. They'd ~ Gary Haynes

Philosophy is written in this all-encompassing book that is constantly open to our eyes, that is the universe; but it cannot be understood unless one first learns to understand the language and knows the characters in which it is written. It is written in mathematical language, and its characters are triangles, circles, and other geometrical figures; without these it is humanly impossible to understand a word of it, and one wanders in a dark labyrinth. ~ Galileo Galilei

Whether we like it or not, if we are to pursue a career in science, eventually we have to learn the "language of nature": mathematics. Without mathematics, we can only be passive observers to the dance of nature rather than active participants. As Einstein once said, "Pure mathematics is, in its way, the poetry of logical ideas." Let me offer an analogy. One may love French civilization and literature, but to truly understand the French mind, one must learn the French language and how to conjugate French verbs. The same is true of science and mathematics. Galileo once wrote, "[The universe] cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to understand a single word. ~ Michio Kaku

The mathematical thermology created by Fourier may tempt us to hope that, as he has estimated the temperature of the space in which we move, me may in time ascertain the mean temperature of the heavenly bodies: but I regard this order of facts as for ever excluded from our recognition. We can never learn their internal constitution, nor, in regard to some of them, how heat is absorbed by their atmosphere. We may therefore define Astronomy as the science by which we discover the laws of the geometrical and mechanical phenomena presented by the heavenly bodies. ~ Auguste Comte

Frederick consistently used his central position to concentrate against one fraction of the enemy, and he always employed tactics of indirect approach. Thereby he gained many victories. But his tactical indirect approach was geometrical rather than psychological-unprepared by the subtler forms of surprise favoured by Scipio-and for all their executive skill, these manoeuvres were narrow. The opponent might be unable to meet the following blow, owing to the inflexibility of his mind or his formations, but the blow itself did not fall unexpectedly. ~ B.H. Liddell Hart

It is impossible to anticipate all of the misdeeds engendered by the universal conflict of human passions. They multiply at a compound rate with the growth in population and the interlacing of particular interests that cannot be directed with geometrical precision towards the public utility. ~ Cesare Beccaria

I hate this plan!" the surveyor was shouting. "The road was perfectly straight. This is a pimple in the face of my road!"
"Get out your equipment and mark us a perfect semicircle," said Arnando, cool as morning dew. "Make the best of it, you geometrical tyrant. ~ Rachel Hartman

Many transition states have a well-defined preferred geometrical requirement. ~ Derek Harold Richard Barton

For the same reason, he insisted on treating the sun as the centre of his system not only in the physical but in the geometrical sense, by making the distances and positions of the planets relative to the sun (and not relative to the earth or the centre C) the basis of his computations. The shift of emphasis, which was more instinctive than logical, became a major factor in his success. ~ Arthur Koestler

Both a priori reasoning and experience teach us that as as these funds grow larger the geometrical rate of growth by compound interest ultimately defeats itself. ~ Benjamin Graham

I quickly learned that reading is cumulative and proceeds by geometrical progression: each new reading builds upon whatever the reader has read before. ~ Alberto Manguel

Because it is occasionally possible, just for brief moments, to find the words that will unlock the doors of all those many mansions inside the head and express something - perhaps not much, just something - of the crush of information that presses in on us from the way a crow flies over and the way a man walks and the look of a street and from what we did one day a dozen years ago. Words that will express something of the deep complexity that makes us precisely the way we are, from the momentary effect of the barometer to the force that created men distinct from trees. Something of the inaudible music that moves us along in our bodies from moment to moment like water in a river. Something of the spirit of the snowflake in the water of the river. Something of the duplicity and the relativity and the merely fleeting quality of all this. Something of the almighty importance of it and something of the utter meaninglessness. And when words can manage something of this, and manage it in a moment, of time, and in that same moment, make out of it all the vital signature of a human being - not of an atom, or of a geometrical diagram, or of a heap of lenses - but a human being, we call it poetry. ~ Ted Hughes

The mathematical difficulties of the theory of rotation arise chiefly from the want of geometrical illustrations and sensible images, by which we might fix the results of analysis in our minds. ~ James Clerk Maxwell

If they would, for Example, praise the Beauty of a Woman, or any other Animal, they describe it by Rhombs, Circles, Parallelograms, Ellipses, and other geometrical terms ... ~ Jonathan Swift

It is to geometry that we owe in some sort the source of this discovery [of beryllium]; it is that [science] that furnished the first idea of it, and we may say that without it the knowledge of this new earth would not have been acquired for a long time, since according to the analysis of the emerald by M. Klaproth and that of the beryl by M. Bindheim one would not have thought it possible to recommence this work without the strong analogies or even almost perfect identity that Citizen Haüy found for the geometrical properties between these two stony fossils. ~ Antoine-François Fourcroy

The more we progress the more we tend to progress. We advance not in arithmetical but in geometrical progression. We draw compound interest on the whole capital of knowledge and virtue which has been accumulated since the dawning of time. ~ Arthur Conan Doyle

I sit in my chair, the wreath on the ceiling floating above my head, like a frozen halo, a zero. A hole in space where a star exploded. A ring, on water, where a stone's been thrown. All things white and circular. I wait for the day to unroll, for the earth to turn, according to the round face of the implacable clock. The geometrical days, which go around and around, smoothly and oiled. Sweat already on my upper lip, I wait, for the arrival of the inevitable egg, which will be lukewarm like the room and will have a green film on the yolk and will taste faintly of sulphur. Today, ~ Margaret Atwood

No Roman ever died in contemplation over a geometrical diagram. ~ Alfred North Whitehead

The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician's "blank form of a universe" without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition. Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems. ~ Lawrence Joseph Henderson

With the exception of the geometrical series, there does not exist in all of mathematics a single infinite series the sum of which has been rigorously determined. In other words, the things which are the most important in mathematics are also those which have the least foundation. ~ Niels Henrik Abel

Boldwood looked at her - not slily, critically, or understandingly, but blankly at gaze, in the way a reaper looks up at a passing train - as something foreign to his element, and but dimly understood. To Boldwood women had been remote phenomena rather than necessary complements - comets of such uncertain aspect, movement, and permanence, that whether their orbits were as geometrical, unchangeable, and as subject to laws as his own, or as absolutely erratic as they superficially appeared, he had not deemed it his duty to consider. He ~ Thomas Hardy

To pray is to pay attention to something or someone other than oneself. Whenever a man so concentrates his attention - on a landscape, a poem, a geometrical problem, an idol, or the True God - that he completely forgets his own ego and desires, he is praying. The primary task of the schoolteacher is to teach children, in a secular context, the technique of prayer. ~ W. H. Auden

Legislators cannot invent too many devices for subdividing property ... Another means of silently lessening the inequality of property is to exempt all from taxation below a certain point, and to tax the higher portions or property in geometrical progression as they rise. Whenever there are in any country uncultivated lands and unemployed poor, it is clear that the laws of property have been so far extended as to violate natural right. ~ Thomas Jefferson

General relativity is the cornerstone of cosmology and astrophysics. It has also provided the conceptual basis for string theory and other attempts to unify all the forces of nature in terms of geometrical structures. ~ Paul Davies

The universe will finally become a ball of radiation, becoming more and more rarified and passing into longer and longer wave-lengths. The longest waves of radiation are Hertzian waves of the kind used in broadcasting. About every 1500 million years this ball of radio waves will double in diameter; and it will go on expanding in geometrical progression for ever. Perhaps then I may describe the end of the physical world as-one stupendous broadcast. ~ Arthur Eddington

CHAPTER VII Geometrical Details. - Calculation of the Capacity of the Balloon. - The Double Receptacle. - The Covering. - The Car. - The Mysterious Apparatus. - The Provisions and Stores. - The Final Summing up. ~ Jules Verne

Next comes the realist phase ("After all, from a purely geometrical point of view a cat is only a tube with a door at the top."). ~ Terry Pratchett