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Geometry Quotes

Browse 359 quotes about Geometry.

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Geometry Quotes

“He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.”

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Book:The Thin Red Line
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“The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church, which had been maintained through the Middle Ages, had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science 'more geometrico.”

MindMatterTruthScienceBeliefSpacePowerInspireSimplicityIntellectAstronomyThoughtCertaintySkepticismMathematicianPhysicistMiddle AgesGeometryDespotismAntiquityScepticismGreeksAncient GreeksInstitute For Advanced Study
Author:Hermann Weyl
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“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.”

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Book:Il Saggiatore
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“In the heaven of the great god Indra is said to be a vast and shimmering net, finer than a spider’s web, stretching to the outermost reaches of space. Strung at the each intersection of its diaphanous threads is a reflecting pearl. Since the net is infinite in extent, the pearls are infinite in number. In the glistening surface of each pearl are reflected all the other pearls, even those in the furthest corners of the heavens. In each reflection, again are reflected all the infinitely many other pearls, so that by this process, reflections of reflections continue without end.”

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Author:David Mumford, Caroline Series, David Wright
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“Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.”

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Book:Lectures and Essays by the Late William Kingdon Clifford, F.R.S.
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“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.”

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

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Author:Bernhard Riemann
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“Wir Theoso­phen wollen die andern gern verstehen; und wir können war­ten, bis sie uns Gleiches mit Gleichem vergelten werden. Sollte ich mein mathematisch-nüchternes Denken, und meine Spinoza-Verehrung verleugnen müssen, weil ich Theosoph bin, wahrlich ich wäre es in einer Stunde nicht mehr. Da ich aber Theosoph geworden bin, weil ich einstmals zwischen den Vorlesungen über «Integration linearer Differentialglei­chungen», synthetischer Geometrie und deskriptiver Geome­trie wirklich habe mathematisch denken gelernt und damit auch den Zugang zum spirituellen Forschen im Sinne Platos er­langt habe, so wird mir wohl—nichts passieren.”

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Author:Rudolf Steiner
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“The Golden Ratio defines the squaring of a circle. Stated in mathematical terms, this says: Given a square of known perimeter, create a circle of equal circumference. According to some, in ancient Egypt, this mathematical mystery was encoded in the measurements of the Great Pyramid of Giza.”

MathematicsGeometryAncient EgyptGolden RatioHistory Of MathematicsSacred GeometrySquaring The Circle
Book:Whole Elephant Revealed: Insights into the Existence and Operation of Universal Laws and the Golden Ratio
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“In the pentagram, the Pythagoreans found all proportions well-known in antiquity: arithmetic, geometric, harmonic, and also the well-known golden proportion, or the golden ratio. ... Probably owing to the perfect form and the wealth of mathematical forms, the pentagram was chosen by the Pythagoreans as their secret symbol and a symbol of health. - Alexander Voloshinov [As quoted in Stakhov]”

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Book:MATHEMATICS OF HARMONY: FROM EUCLID TO CONTEMPORARY MATHEMATICS AND COMPUTER SCIENCE
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“In terms of systems design, shapes are important. Rectangles are not common in nature. That's probably because from a systems design perspective, rectangles often degrade efficiency instead of contributing to efficiency. Yet humans have designed an entire supply chain system based on rectangles, squares and straight lines. If we want to be more efficient, we should replace those rectangles, squares and straight lines with ovals, circles and hexagons. And maybe some other nature inspired geometries.”

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Author:Hendrith Vanlon Smith Jr, CEO of Mayflower-Plymouth
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“... I left Caen, where I was living, to go on a geological excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.”

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Author:Henri Poincaré
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“Everything is fields, and a particle is just a smaller version of a field. There is a harmonic relationship involved. Disturbing ideas like those of Einstein in 1905 and Feynman Pocono Conference in 1948. Here we go; 1) The universe is ringing like a bell. Neil Turok's Public Lecture: The Astonishing Simplicity of Everything. 2) The stuff of the universe is waves or fields. 3) Scale is relative, not fixed because all of these waves are ratios of one another. 4) The geometry is fractal. This could be physical or computational. 5) If the geometry is computational then, there is no point in speaking about the relationship of the pixels on the display.”

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Author:Rick Delmonico
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“The diameter divides into the circumference, you know. It ought to be three times. You'd think so, wouldn't you? But does it? No. Three point one four one and lots of other figures. There's no end to the buggers. Do you know how pissed off that makes me?" "I expect it makes you extremely pissed off," said Teppic politely. "Right. It tells me that the Creator used the wrong kind of circles. It's not even a proper number! I mean, three point five, you could respect. Or three point three. That'd look *right*." He stared morosely at the pie.”

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Book:Pyramids
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“Geometry of Guilt. Later, when the studio was deserted, Dr Nathan saw Talbert standing on the roof of the maze, surveying the contours of the sloping basin below. His dark-skinned face resembled that of a pensive architect. Once again Karen Novotny had died, Talbert’s fears and obsessions mimetized in her alternate death. Dr Nathan decided not to speak to him. His own identity would seem little more than a summary of postures, the geometry of an accusation. Exposed Placenta. The following week, when Dr Nathan returned, Talbert had not moved. He sat on the edge of the water-filled basin, staring into the lucid depths of that exposed placenta. His emaciated figure was by now little more than a collection of tatters. After watching him for half an hour Dr Nathan walked back to his car.”

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Book:The Atrocity Exhibition
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“In Euclid's Elements we meet the concept which later plays a significant role in the development of science. The concept is called the "division of a line in extreme and mean ratio" (DEMR). ...the concept occurs in two forms. The first is formulated in Proposition 11 of Book II. ...why did Euclid introduce different forms... which we can find in Books II, VI and XIII? ...Only three types of regular polygons can be faces of the Platonic solids: the equilateral triangle... the square... and the regular pentagon. In order to construct the Platonic solids... we must build the two-dimensional faces... It is for this purpose that Euclid introduced the golden ratio... (Proposition II.11)... By using the "golden" isosceles triangle...we can construct the regular pentagon... Then only one step remains to construct the dodecahedron... which for Plato is one of the most important regular polyhedra symbolizing the universal harmony in his cosmology.”

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Book:"GOLDEN" NON-EUCLIDEAN GEOMETRY, THE: HILBERT'S FOURTH PROBLEM, "GOLDEN" DYNAMICAL SYSTEMS, AND THE FINE-STRUCTURE CONSTANT
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“If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.”

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

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Book:Breaking the Idols of Ignorance: Admonition of the Soi Disant Sufi
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“Burak Cem Coşkun’s Pumpkin Dessert with Tahini in the Cloud Chamber is a strikingly unique addition to contemporary literature that successfully merges the precision of theoretical physics with the lyrical soul of Anatolian philosophy. As the fourth volume in his *Science and Poetry* series, the work functions less like a traditional poetry collection and more like a "meta-text" where the author, a physicist by training, uses concepts like de-Sitter space, neutrinos, and topological solution spaces to explore deeply human themes of memory, existence, and nature. The structure is intellectually ambitious, moving from the "Fine Tuning" of cosmic scales to "Transcendental" reflections that feel rooted in the Ionian tradition of natural philosophers like Thales and Anaximander. What makes the reading experience so natural is how the author anchors these abstract scientific metaphors in physical locations—from the "glacial austerity of Stockholm" to the "mist-veiled nights of Tartu"—and ends with a fascinating philosophical "postulate" regarding Randomly Organized Structural Entities (ROSE) that attempts to unify biophysics with astrophysics through a geometry-centered framework. It is an evocative read for anyone interested in the intersection of mythos and logos, successfully arguing that the language of the universe is not just mathematical, but inherently poetic.”

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Book:Pumpkin Dessert with Tahini in the Cloud Chamber - Without Walnuts & Neutrinoless: Science & Poetry, Volume IV
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“The new painters do not propose, any more than did their predecessors, to be geometers. But it may be said that geometry is to the plastic arts what grammar is to the art of the writer. Today, scholars no longer limit themselves to the three dimensions of Euclid. The painters have been lead quite naturally, one might say by intuition, to preoccupy themselves with the new possibilities of spatial measurement which, in the language of the modern studios, are designated by the term fourth dimension.”

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Author:Guillaume Apollinaire
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