Geometry Quotes - Page 13

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

  Johannes Kepler

  Spring, Order, Fountain

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• A multitude of bees can tell the time of day, calculate the geometry of the sun's position, argue about the best location for the next swarm. Bees do a lot of close observing of other bees; maybe they know what follows stinging and do it anyway.

  Lewis Thomas

  Next, Location, Sun

  Lewis Thomas (1984). “Late Night Thoughts on Listening to Mahler's Ninth Symphony”, Bantam

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• Certainly it is permitted to anyone to put forward whatever hypotheses he wishes, and to develop the logical consequences contained in those hypotheses. But in order that this work merit the name of Geometry, it is necessary that these hypotheses or postulates express the result of the more simple and elementary observations of physical figures.

  Giuseppe Peano

  Simple, Order, Names

  "The Mathematical Philosophy of Giuseppe Peano". Philosophy of Science Vol. 30, No. 3, July 1963.

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• Pickover's lively, provocative travel guide takes readers into the fascinating realm of mystic math, from perfectly strange numbers to fractured geometries and other curious nooks and crannies of ancient worlds and modern times.

  Ivars Peterson

  Math, Numbers, World

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• Kepler's discovery would not have been possible without the doctrine of conics. Now contemporaries of Kepler-such penetrating minds as Descartes and Pascal-were abandoning the study of geometry ... because they said it was so UTTERLY USELESS. There was the future of the human race almost trembling in the balance; for had not the geometry of conic sections already been worked out in large measure, and had their opinion that only sciences apparently useful ought to be pursued, the nineteenth century would have had none of those characters which distinguish it from the ancien régime.

  Charles Sanders Peirce

  Character, Science, Race

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• One of the great sources of employment for people with Ph.D.s in geometry is the animation industry.

  Margaret Wertheim

  People, Employment, Source

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• It is impossible not to feel stirred at the thought of the emotions of man at certain historic moments of adventure and discovery - Columbus when he first saw the Western shore, Pizarro when he stared at the Pacific Ocean, Franklin when the electric spark came from the string of his kite, Galileo when he first turned his telescope to the heavens. Such moments are also granted to students in the abstract regions of thought, and high among them must be placed the morning when Descartes lay in bed and invented the method of co-ordinate geometry.

  Alfred North Whitehead

  Morning, Ocean, Adventure

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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.

  Felix Klein

  Territory, Fields, Royal

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• It isn't a circle--it is simply a long line--as in geometry, you know, one that reaches into infinity. And because we cannot see the end--we also cannot see how it changes. And it is very odd by those who see the changes--who dream, who will not give up--are called idealists...and those who see only the circle we call them the "realists"!

  Lorraine Hansberry

  Dream, Giving Up, Circles

  Lorraine Hansberry (2011). “A Raisin in the Sun”, p.116, Vintage

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• The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason.

  Edward Gibbon

  Art, Sight, Hands

  Edward Gibbon (2015). “Delphi Complete Works of Edward Gibbon (Illustrated)”, p.594, Delphi Classics

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• The lock-step approach of algebra, geometry, and then more algebra (but rarely any statistics) is still dominant in U. S. schools, but hardly anywhere else. This fragmented approach yields effective mathematics education not for the many but for the few primarily those who are independently motivated and who will learn under any conditions.

  Lynn Steen

  Teaching, School, Math

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• 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.

  Octavio Paz

  Writing, Adventure, Nerves

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• At that stage of my youth, death remained as abstract a concept as non-Euclidean geometry or marriage. I didn't yet appreciate its terrible finality or the havoc it could wreak on those who'd entrusted the deceased with their hearts.

  Jon Krakauer

  Heart, Appreciate, Youth

  Jon Krakauer (2011). “Into the Wild”, p.154, Pan Macmillan

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• Analytical geometry has never existed. There are only people who do linear geometry badly, by taking coordinates, and they call this analytical geometry. Out with them!

  Jean Dieudonne

  People, Linear, Coordinates

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• If the chemistry is right between star and photographer and the geometry of the pictures pleases the star, often the two people end up with a long-term professional friendship during which they continue to work together and to produce highly personal images.

  Eve Arnold

  Stars, Two, Long

  Eve Arnold (2002). “Film Journal”, p.8, A&C Black

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• Considerable obstacles generally present themselves to the beginner, in studying the elements of Solid Geometry, from the practice which has hitherto uniformly prevailed in this country, of never submitting to the eye of the student, the figures on whose properties he is reasoning, but of drawing perspective representations of them upon a plane. ...I hope that I shall never be obliged to have recourse to a perspective drawing of any figure whose parts are not in the same plane.

  Augustus De Morgan

  Country, Eye, Science

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• The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

  Nicholas Murray Butler

  Philosophy, Tools, Records

  NICHOLAS MURRAY BUTLER (1898). “THE MEANING OF EDUCATION AND OTHERS ESSAYS AND ADDRESSES”

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• 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.

  Euclid

  Science, Squares, Triangles

  Euclid, Phillips (1826). “Elements of Geometry, Containing the First Six Books of Euclid”, p.41

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• Did you measure to attain your height? Did you use geometry to radiate your limb? Did you lament storm-torn branches? Did you inventory your leaves for the sun? You did none of these things, yet man in his cleverness Cannot match your perfection.

  Ming-Dao Deng

  Men, Perfection, Tree

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• 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.

  David Mumford

  Math, Lasts, Esoteric

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• Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all.

  Albert Einstein

  Science, Discovery, Two

  Letter to J.S. Switzer on April 23, 1953. "The Scientific Revolution: A Historiographical Inquiry". Book by H. Floris Cohen, p. 234, 1994.

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• Masonry, according to the general acceptation of the term, is an art founded on the principles of geometry, and devoted to the service and convenience of mankind. But Freemasonry, embracing a wider range and having a nobler object in view, namely, the cultivation and improvement of the human mind, may with more propriety be called a science, inasmuch as, availing itself of the terms of the former, it inculcates the principles of the purest morality, though its lessons are for the most part veiled in allegory and illustrated by symbols.

  William Howard Taft

  Art, Views, Mind

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• I believe that all centers that appear in space - whether they originate in biology, in physical forces, in pure geometry, in color - are alike simply in that they all animate space. It is this animated space that has its functional effect upon the world, that determines the way things work, that governs the presence of harmony and life.

  Christopher Alexander

  Believe, Origin Of Life, Color

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• No story is a straight line. The geometry of a human life is too imperfect and complex, too distorted by the laughter of time and the bewildering intricacies of fate to admit the straight line into its system of laws.

  Pat Conroy

  Laughter, Fate, Law

  Pat Conroy (2012). “Beach Music”, p.115, Random House

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• Greek architecture is the flowering of geometry.

  Ralph Waldo Emerson

  Greek, Architecture, Flowering

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