Geometry Quotes - Page 7

• In geometric and physical applications, it always turns out that a quantity is characterized not only by its tensor order, but also by symmetry.

  Hermann Weyl

  Order, Physics, Symmetry

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• Let no-one ignorant of geometry enter. Said to have been inscribed above the door of Plato's Academy.

  Plato

  Plato, Ignorance, Science

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• I have an infamously low capacity for visualizing relationships, which made the study of geometry and all subjects derived from it impossible for me.

  Sigmund Freud

  Teacher, Impossible, Study

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• How many theorems in geometry which have seemed at first impracticable are in time successfully worked out!

  Archimedes

  Firsts, Theorems

  Archimedes (2007). “The Works of Archimedes”, p.151, Cosimo, Inc.

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• Emotions are far harder things to understand than algebra and geometry, yet we spend hours in elucidating mathematics and expect such a problem as that of human relationships to solve itself.

  Frances G. Wickes

  Feelings, Emotion, Problem

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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.

  John Stuart Mill

  Science, Names, Progress

  John Stuart Mill (1865). “An Examination of Sir William Hamilton's Philosophy and of the Principal Philosophical Questions Discussed in His Writings”, p.531

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• 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

  Life, Ideas, Orbit

  Ralph Waldo Emerson (1860). “The Conduct of Life”, p.1

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• I have spent much time in the study of the abstract sciences; but the paucity of persons with whom you can communicate on such subjects disgusted me with them. When I began to study man, I saw that these abstract sciences are not suited to him, and that in diving into them, I wandered farther from my real object than those who knew them not, and I forgave them for not having attended to these things. I expected then, however, that I should find some companions in the study of man, since it was so specifically a duty. I was in error. There are fewer students of man than of geometry.

  Blaise Pascal

  Real, Communication, Science

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• A science of all these possible kinds of space [the higher dimensional ones] would undoubtedly be the highest enterprise which a finite understanding could undertake in the field of geometry... If it is possible that there could be regions with other dimensions, it is very likely that God has somewhere brought them into being.

  Immanuel Kant

  Space, Understanding, Fields

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• eternity is a depth which no geometry can measure, no arithmetic calculate, no imagination conceive, no rhetoric describe.

  Hannah More

  Imagination, Depth, Eternity

  Hannah More (1840). “Miscellaneous Works: Tragedies. Miscellaneous poems. Hymns and ballads. Sacred Dramas. Coelebs. Practical piety. Moriana”, p.593

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• Euler calculated the force of the wheels necessary to raise the water in a reservoir ... My mill was carried out geometrically and could not raise a drop of water fifty yards from the reservoir. Vanity of vanities! Vanity of geometry!

  Frederick The Great

  Vanity, Water, Yards

  Letters of Voltaire and Frederick the Great. Letter 221, 1927.

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• When we teach a child to sing or play the flute, we teach her how to listen. When we teach her to draw, we teach her to see. When we teach a child to dance, we teach him about his body and about space, and when he acts on a stage, he learns about character and motivation. When we teach a child design, we reveal the geometry of the world. When we teach children about the folk and traditional arts and the great masterpieces of the world, we teach them to celebrate their roots and find their own place in history.

  Jane Alexander

  Art, Motivation, Children

  Jane Alexander (2007). “Command Performance: An Actress in the Theater of Politics”, p.322, Da Capo Press

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• Metrical geometry is thus a part of descriptive geometry, and descriptive geometry is all geometry.

  Arthur Cayley

  Science

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• The only royal road to elementary geometry is ingenuity.

  Eric Temple Bell

  Science, Royal, Ingenuity

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• 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.

  Benoit Mandelbrot

  Special, Shapes, Lines

  Source: bigthink.com

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• In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

  Jean-Victor Poncelet

  Success, Teaching, Science

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• I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.

  Benoit Mandelbrot

  Latin, Order, Names

  "Encyclopedia of World Biography" edited by Thomson Gale, 1997.

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• Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.

  Benoit Mandelbrot

  Circles, Shapes, Lines

  Source: bigthink.com

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• I got into animals by drawing hair follicles. I liked drawing hair, and from that I got into feathers and fur, then into images of animals. The patterning is the same, but the proportions of the body change from one animal to the next. A lot of it is just geometry and consciousness.

  Kiki Smith

  Animal, Hair, Drawing

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• 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

  Medicine, Heaven, Attention

  "De architectura". Book by Vitruvius. Book I, Chapter I, Section 3,

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• I am much occupied with the investigation of the physical causes [of motions in the Solar System]. My aim in this is to show that the celestial machine is to be likened not to a divine organism but rather to a clockwork ... insofar as nearly all the manifold movements are carried out by means of a single, quite simple magnetic force. This physical conception is to be presented through calculation and geometry.

  Johannes Kepler

  Mean, Science, Simple

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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.

  Hans Reichenbach

  Space, Structure, Theory

  Hans Reichenbach (1958). “Philosophie Der Raum-Zeit-Lehre”, p.100, Courier Corporation

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• Poetry is a subject as precise as geometry.

  Gustave Flaubert

  Poetry Is, Subjects, Precise

  Letter to Louise Colet, 14 August 1853

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• The Philosophy of Tea is not mere aestheticism ... for it expresses conjointly with ethics and religion our whole point of view about man and nature. It is hygiene, for it enforces cleanliness; it is economics, for it shows comfort in simplicity rather than in the complex and costly; it is moral geometry, inasmuch as it defines our sense of proportion to the universe.

  Okakura Kakuzo

  Philosophy, Men, Views

  Andrew Forbes, David Henley, Okakura Kakuzo “The Illustrated Book of Tea”

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• Geometry is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics the light in buildings can be drawn from fixed quarters of the sky. Difficult questions involving symmetry are solved by means of geometrical theories and methods.

  Marcus Vitruvius Pollio

  Mean, Squares, Light

  "De architectura". Book by Vitruvius. Book I, Chapter I, Section 4,

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