Discover the most popular and inspiring quotes and sayings on the topic of Geometrizes. Share them with your friends on social media platforms like Facebook, Twitter, or your personal blogs, and let the world be inspired by their powerful messages. Here are the Top 100 Geometrizes Quotes And Sayings by 79 Authors including Ralph Waldo Emerson,Hans Reichenbach,Akira Yoshizawa,Plato,Euripides for you to enjoy and share.

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If a man is at once acquainted with the geometric foundation of things and with their festal splendor, his poetry is exact and his arithmetic musical.
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We must ... maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.
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Geometry alone is not enough to portray human desires, expressions, aspirations, joys. We need more.
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The knowledge of which geometry aims is the knowledge of the eternal.
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Mighty is geometry; joined with art, resistless.
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The present author confesses that, to him, geometry is nothing at all, if not a branch of art ...
A Treatise on Algebraic Plane Curves
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Geometry existed before the creation. It is co-eternal with the mind of God ... Geometry provided God with a model for the Creation ...
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We must here follow the first course so as to be able to pass on later to generalisations which extend beyond the limits of Euclidean geometry.
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But we must not underestimate the potency of the mathematical process of abstraction. A surprising variety of things happen to have both magnitude and direction and to combine according to the parallelogram law; and many of them are not at all reminiscent of journeys.
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Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.
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Let no one destitute of Geometry enter my doors.
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The fools think I am writing algebra but what I am really writing is geometry.
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Gravity is a response to geometry.
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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.
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Geometric calculus consists in a system of operations analogous to those of algebraic calculus, but in which the entities on which the calculations are carried out, instead of being numbers, are geometric entities which we shall define.
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God is a geometrician.
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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.
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The composer opens the cage door for arithmetic, the draftsman gives geometry its freedom.
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... if geometry were as much opposed to our passions and present interests as is ethics, we should contest it and violate I but little less, notwithstanding all the demonstrations of Euclid and Archimedes ...
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Space creates shape; Shape creates space.
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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.
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As astronomy is the daughter of idleness, geometry is the daughter of property.
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Two possibilities present themselves for the analytical treatment of metrical geometry.
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The circle is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form and in equilibrium. Of the three primary forms, it points most clearly to the fourth dimension.
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Projective geometry is all geometry.
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Experience proves that anyone who has studied geometry is infinitely quicker to grasp difficult subjects than one who has not.
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There is geometry in the humming of the strings. There is music in the spacing of the spheres.
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Geometry is the noblest branch of physics.
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The only royal road to elementary geometry is ingenuity.
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Modern man lives more and more in a preponderantly geometric order. All human creation mechanical or industrial is dependent upon geometric intentions.
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Geometry is the most complete science.
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Algebra is nothing more than geometry, in words;
geometry is nothing more than algebra, in pictures.
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The application of algebra to geometry ... has immortalized the name of Descartes, and constitutes the greatest single step ever made in the progress of the exact sciences.
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A triangle with four points is what Euclid rides into hell.
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Projective geometry has opened up for us with the greatest facility new territories in our science, and has rightly been called the royal road to our particular field of knowledge.
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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.
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Geometry is beautifully logical, and it teaches you how to think and prove that things are so, step by step by step. Proofs are excellent lessons in reasoning. Without logic and reasoning, you are dependent on jumping to conclusions or - worse - having empty opinions.
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All modern work on unification may be said to represent a program of geometrization that resembles Einstein's earlier attempts, although the manifold subject to geometrization is larger than he anticipated and the quantum framework of the program would not have been to his liking.
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Height, width, and depth are the three phenomena which I must transfer into one plane to form the abstract surface of the picture, and thus to protect myself from the infinity of space.
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No employment can be managed without arithmetic, no mechanical invention without geometry.
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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.
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Greek architecture is the flowering of geometry.
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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.
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A few rules include all that is necessary for the perfection of the definitions, the axioms, and the demonstrations, and consequently of the entire method of the geometrical proofs of the
art of persuading.
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How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!
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connoisseurs of geologic form,
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When a king asked Euclid, the mathematician, whether he could not explain his art to him in a more compendious manner? he was answered, that there was no royal way to geometry.
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Fire, air, earth, and water are bodies and therefore solids, and solids are contained in planes, and plane rectilinear figures are made up of triangles.
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There is no Royal Road to Geometry.
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About the fearful sphere which we inhabit, whose centre may be calculated and whose circumference is physically established, there spin metaphors whose centre is everywhere and whose circumference shows itself only through holes in the dark.
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Writing is the geometry of the soul.
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Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth.
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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.
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The differential element of non-Euclidean spaces is Euclidean. This fact, however, is analogous to the relations between a straight line and a curve, and cannot lead to an epistemological priority of Euclidean geometry, in contrast to the views of certain authors.
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And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought to be least neglected in Geometry.
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Thus God himself was too kind to remain idle and began to play the game of signatures signing his likeness unto the world: therefore I chance to think that all nature and the graceful sky are symbolized in the art of Geometria.
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Self-similarity is a dull subject because you are used to very familiar shapes. But that is not the case. Now many shapes which are self-similar again, the same seen from close by and far away, and which are far from being straight or plane or solid.
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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.
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We find in the history of ideas mutations which do not seem to correspond to any obvious need, and at first sight appear as mere playful whimsies such as Apollonius' work on conic sections, or the non-Euclidean geometries, whose practical value became apparent only later.
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A tree nowhere offers a straight line or a regular curve, but who doubts that root, trunk, boughs, and leaves embody geometry?
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We are only geometricians of matter; the Greeks were, first of all, geometricians in the apprenticeship to virtue.
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But who shall parcel out His intellect by geometric rules, Split like a province into round and square?
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Algebra is but written geometry and geometry is but figured algebra.
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Since the age of six I have had the habit of sketching forms of objects. Although from about fifty I have often published my pictorial works, before the seventieth year none is worthy.
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We are perpetually moralists, but we are geometricians only by chance. Our intercourse with intellectual nature is necessary; our speculations upon matter are voluntary, and at leisure.
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Simple shapes are inhuman. They fail to resonate with the way nature organizes itself or with the way human perception sees the world.
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Circles and right lines limit and close all bodies, and the mortal right-lined circle must conclude and shut up all.
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...words so precisely placed that in combination with other words, also precisely placed, they carve out a shape in space and time.
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While the expressive possibilities of Neoplasticism are limited to two dimensions (the plane), Elementarism realizes the possibility of plasticism in four dimensions, in the field of time-space.
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A work of morality, politics, criticism will be more elegant, other things being equal, if it is shaped by the hand of geometry.
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When the whole and the parts are seen at once, as mutually producing and explaining each other, as unity in multeity, there results shapeliness.
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Bodies are real entities. Surfaces and lines are but fictitious entities. A surface without depth, a line without thickness, was never seen by any man; no; nor can any conception be seriously formed of its existence.
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A given circle cannot be so true that a truer one cannot be found; and the movement of a sphere at one moment is never precisely equal to its movement at another, nor does it ever describe two circles similar and equal, even if from appearances the opposite may seem true.
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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.
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I ran into Isosceles. He had a great idea for a new triangle!
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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.
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One can understand nature only when one has learned the language and the signs in which it speaks to us; but this language is mathematics and these signs are methematical figures.
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In creating the world, God used arithmetic, geometry, and likewise astronomy.
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Hence it is that the shape of something is especially meaningful.
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Geometry is moribund. I want a lilt and joy to art.
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Everything is made up of shapes and spaces.
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Light and the rational forms are locked in combat; light sets them into motion, bends what is straight, makes parallels oval, inscribes circles in the intervals, makes the intervals active.
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In many cases a dull proof can be supplemented by a geometric analogue so simple and beautiful that the truth of a theorem is almost seen at a glance.
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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.
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...rich geometric experiences are the most important factor in the development of children's spatial thinking and reasoning.
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Frontiers are physical as well as symbolic constructions
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triangle of my mons,
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The geometry of the things around us creates coincidences, intersections.
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Maps, contour maps and all maps, intrigue us for the metaphors that they are: tools to give us a sense of something whose truth is far richer but without which we would perceive nothing and never find our bearings.
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Near that a dusty paint-box, some odd hooks, A half-burnt match, an ivory block, three books, Where conic sections, spherics, logarithms, To great Laplace, from Saunderson and Sims, Lie heaped in their harmonious disarray Of figures,-disentangle them who may.
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The greatest mathematics has the simplicity and inevitableness of supreme poetry and music, standing on the borderland of all that is wonderful in Science, and all that is beautiful in Art.
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As lines, so loves oblique, may well Themselves in every angle greet; But ours, so truly parallel, Though infinite, can never meet.
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Geography is the art of the mappable.
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Treat nature by the cylinder, the sphere, the cone, everything in proper perspective so that each side of an object or a plane is directed towards a central point.
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A circle may be small, yet it may be as mathematically beautiful and perfect as a large one.
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There are no sects in geometry.
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We may climb into the thin and cold realm of pure geometry and lifeless science, or sink into that of sensation. Between these extremes is the equator of life, of thought, or spirit, or poetry,
a narrow belt.
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The landlady of a boarding-house is a parallelogram - that is, an oblong angular figure, which cannot be described, but which is equal to anything.
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The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth.
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.