Geometry Quotes

There are certain conceptual powers in this project, like the relationship of glass to sand, and the idea of putting glass back into the earth, which is where it comes from, which are related to the whole concept of I Am. So there's that one below-surface idea, and then there's these other practical and more pragmatic ideas about how the light functions and the geometry and mathematics behind the reverberation of light from the surface outward.

Descartes constructed as noble a road of science, from the point at which he found geometry to that to which he carried it, as Newton himself did after him. ... He carried this spirit of geometry and invention into optics, which under him became a completely new art.

Geometry is the art of correct reasoning from incorrectly drawn figures.

In the physical world, one cannot increase the size or quantity of anything without changing its quality. Similar figures exist only in pure geometry.

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

The early study of Euclid made me a hater of geometry.

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

All the standard equations of mathematical physics can be separated and solved in Kerr geometry.

[On Archimedes mathematical results:] It is not possible to find in all geometry more difficult and intricate questions, or more simple and lucid explanation... No investigation of yours would succeed in attaining the proof, and yet, once seen you immediately believe you would have discovered it.

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

I've got a real sense of three-dimensional geometry. I can look at a flat piece of fabric and know that if I put a slit in it and make some fabric travel around a square, then when you lift it up it will drape in a certain way, and I can feel how that will happen.

Experience proves that anyone who has studied geometry is infinitely quicker to grasp difficult subjects than one who has not.

Common to the two geometries is only the general property of one-to-one correspondence, and the rule that this correspondence determines straight lines as shortest lines as well as their relations of intersection.

Having been the discoverer of many splendid things, he is said to have asked his friends and relations that, after his death, they should place on his tomb a cylinder enclosing a sphere, writing on it the proportion of the containing solid to that which is contained.

Or maybe it is only that we are so habitually inattentive that when some rare but simple geometry grabs us by the shoulders and shakes us into consciousness, we call our response sacred.

Flowers construct the most charming geometries: circles like the sun, ovals, cones, curlicues and a variety of triangular eccentricities, which when viewed with the eye of a magnifying glass seem a Lilliputian frieze of psychedelic silhouettes.

I keep looking for ultimate answers, but maybe there aren't any or maybe I'm not looking in the right places, because in the section marked ANSWERS in the back of my geometry book, there's only a bunch of numbers, and all I can find to stare at in the refrigerator is five carrots and a jar of no-fat mayonnaise.

We admit, in geometry, not only infinite magnitudes, that is to say, magnitudes greater than any assignable magnitude, but infinite magnitudes infinitely greater, the one than the other. This astonishes our dimension of brains, which is only about six inches long, five broad, and six in depth, in the largest heads.

Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.

'Tis a short sight to limit our faith in laws to those of gravity, of chemistry, of botany, and so forth. Those laws do not stop where our eyes lose them, but push the same geometry and chemistry up into the invisible plane of social and rational life, so that, look where we will, in a boy's game, or in the strifes of races, a perfect reaction, a perpetual judgment keeps watch and ward.

Since geometry is co-eternal with the divine mind before the birth of things, God himself served as his own model in creating the world (for what is there in God which is not God?), and he with his own image reached down to humanity.

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

If we concentrate our attention on trying to solve a problem of geometry, and if at the end of an hour we are no nearer to doing so than at the beginning, we have nevertheless been making progress each minute of that hour in another more mysterious dimension. Without knowing or feeling it, this apparent barren affort has brought more light into the soul.

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.

[Professor Bragg asserts that] In sodium chloride there appear to be no molecules represented by NaCl. The equality in number of sodium and chlorine atoms is arrived at by a chess-board pattern of these atoms; it is a result of geometry and not of a pairing-off of the atoms.

Human knowledge is dark and uncertain; philosophy is dark, astrology is dark, and geometry is dark.

Our model of the cosmos must be as inexhaustible as the cosmos. A complexity that includes not only duration but creation, not only being but becoming, not only geometry but ethics. It is not the answer we are after, but only how to ask the question.

At the Egyptian city of Naucratis there was a famous old god whose name was Theuth; the bird which is called the Ibis was sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters.

In creating the world, God used arithmetic, geometry, and likewise astronomy.

Crystals grew inside rock like arithmetic flowers. They lengthened and spread, added plane to plane in an awed and perfect obedience to an absolute geometry that even stones - maybe only the stones - understood.

I am coming more and more to the conviction that the necessity of our geometry cannot be demonstrated, at least neither by, nor for, the human intellect. . . Geometry should be ranked, not with arithmetic, which is purely aprioristic, but with mechanics.

No employment can be managed without arithmetic, no mechanical invention without geometry.

In things to be seen at once, much variety makes confusion, another vice of beauty. In things that are not seen at once, and have no respect one to another, great variety is commendable, provided this variety transgress not the rules of optics and geometry.

When Moses was alive, these pyramids were a thousand years old. Here began the history of architecture. Here people learned to measure time by a calendar, to plot the stars by astronomy and chart the earth by geometry. And here they developed that most awesome of all ideas - the idea of eternity.

Geometry is the archetype of the beauty of the world.

The importance of infinite processes for the practical exigencies of technical life can hardly be overemphasized. Practically all applications of arithmetic to geometry, mechanics, physics and even statistics involve these processes directly and indirectly.

The geometry reveals five development direction for applications (each with endless possibilities); dividing, dwelling, trestle, fenestration and artistic installation. I find these enabled designs so reflective of an ever-changing world where contextual factors and technological resources are shifting definitions of architecture, design, and the traditional boundaries between disciplines.

Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

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

That, if a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.

In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle.

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.

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.

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

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?

Music is the arithmetic of sounds as optics is the geometry of light.

Not only in geometry, but to a still more astonishing degree in physics, has it become more and more evident that as soon as we have succeeded in unraveling fully the natural laws which govern reality, we find them to be expressible by mathematical relations of surprising simplicity and architectonic perfection. It seems to me to be one of the chief objects of mathematical instruction to develop the faculty of perceiving this simplicity and harmony.

Ruy-Sanchez's works of fiction are always amazing: adventure, poetry and intelligence in a new geometry of words... His writing has nerve and agility, his intelligence is sharp without being cruel, his mood is sympathetic without complicity.

Fashion is not just about what we wear, but...fashion is also a business. It is an art, it's a career that involves science, engineering, accounting and so much more. People can learn about the math behind Charles James' designs, and think, 'Maybe I should pay closer attention to geometry this semester'

Algebraic geometry seems to have acquired the reputation of being esoteric, exclusive, and very abstract, with adherents who are secretly plotting to take over all the rest of mathematics. In one respect this last point is accurate.