Geometry Quotes - Page 12

• There are infinitely many variations of the initial situation and therefore no doubt indefinitely many theorems of moral geometry.

  John Rawls

  Doubt, Variation, Moral

  "A Theory of Justice". Book by John Rawls, 1971.

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• Those arts which are, to be sure, not finite, as geometry and arithmetic, do not suffer adornment; others, contrarily, are rather subject to division and embellishment, such as astronomy and jurisprudence.

  Gerolamo Cardano

  Art, Suffering, Jurisprudence

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• It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible.

  Bertrand Russell

  Kings, Plato, Teaching

  Bertrand Russell (2013). “History of Western Philosophy: Collectors Edition”, p.95, Routledge

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• Why waste words? Geometry existed before the Creation, is co-eternal with the mind of God, is God himself (what exists in God that is not God himself?): geometry provided God with a model for the Creation and was implanted into man, together with God's own likeness - and not merely conveyed to his mind through the eyes.

  Johannes Kepler

  Eye, Men, History

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• Now, the reason that we think computer science is about computers is pretty much the same reason that the Egyptians thought geometry was about surveying instruments. And that is, when some field is just getting started and you don't really understand it very well, it's very easy to confuse the essence of what you're doing with the tools that you use.

  Hal Abelson

  Thinking, Essence, Tools

  "Overview and Introduction to Lisp". Introduction of video of lectures on the "Structure and Interpretation of Computer Programs", ocw.mit.edu. 1986.

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• Geometry is moribund. I want a lilt and joy to art.

  Ellsworth Kelly

  Art, Joy, Want

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• Geometry alone is not enough to portray human desires, expressions, aspirations, joys. We need more.

  Akira Yoshizawa

  Expression, Joy, Desire

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• Perhaps you have seen me. I know well, my purpose was merely that of a symbol, 'equals', 'times'... ; but what is said, for all that, was identity-less: a kind of live geometry.

  Albert Goldbarth

  Science, Identity, Purpose

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• Now, a good education is about so much more than just learning geometry or memorizing dates in history. All of that is important, but an education is also about exploring new things -- discovering what makes you come alive, and then being your best at whatever you choose

  Michelle Obama

  Education, Important, Alive

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• ... geometry became a symbol for human relations, except that it was better, because in geometry things never go bad. If certain things occur, if certain lines meet, an angle is born. You cannot fail. It's not going to fail; it is eternal. I found in rules of mathematics a peace and a trust that I could not place in human beings. This sublimation was total and remained total. Thus, I'm able to avoid or manipulate or process pain.

  Louise Bourgeois

  Pain, Lines, Able

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• It would be foolish to give credit to Euclid for pangeometrical conceptions; the idea of geometry deifferent from the common-sense one never occurred to his mind. Yet, when he stated the fifth postulate, he stood at the parting of the ways. His subconscious prescience is astounding. There is nothing comperable to it in the whole history of science.

  George Sarton

  Ideas, Common Sense, Giving

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• My old geometry teacher called me and he was like yo man you need to start wearing a shirt. You're ruining my marriage.

  Drew Chadwick

  Teacher, Men, Needs

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• [Computer science] is not really about computers and it's not about computers in the same sense that physics is not really about particle accelerators, and biology is not about microscopes and Petri dishes... and geometry isn't really about using surveying instruments.

  Hal Abelson

  Computer, Physics, Biology

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• I entered an omnibus to go to some place or other. At that 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 non-Euclidean geometry.

  Henri Poincare

  Ideas, Feet, Steps

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• The method of Fluxions is the general key by help whereof the modern mathematicians unlock the secrets of Geometry, and consequently of Nature.

  George Berkeley

  Keys, Secret, Helping

  George Berkeley (2016). “The Analyst: A Discourse Addressed to an Infidel Mathematician”, p.3, Library of Alexandria

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• Archimedes to Eratosthenes greeting. ... certain things first became clear to me by a mechanical method, although they had to be demonstrated by geometry afterwards because their investigation by the said method did not furnish an actual demonstration. But it is of course easier, when we have previously acquired by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

  Archimedes

  Firsts, Easier, Investigation

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• Aspiring to these wide generalizations, the analysis of quadratic functions soars to a pitch from whence it may look proudly down on the feeble and vain attempts of geometry proper to rise to its level or to emulate it in its flights.

  James Joseph Sylvester

  Analysis, Looks, Levels

  James Joseph Sylvester (2005). “The Collected Mathematical Papers of James Joseph Sylvester”, p.150, American Mathematical Soc.

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• We learned to put discipline in the haircuts by using actual geometry, actual architectural shapes and bone structure. The cut had to be perfect and layered beautifully, so that when a woman shook it, it just fell back in.

  Vidal Sassoon

  Cutting, Discipline, Perfect

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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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• 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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• 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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• What we do may be small, but it has a certain character of permanence; and to have produced anything of the slightest permanent interest, whether it be a copy of verses or a geometrical theorem, is to have done something utterly beyond the powers of the vast majority of men.

  G. H. Hardy

  Character, Science, Men

  G. H. Hardy (2012). “A Mathematician's Apology”, p.76, Cambridge University Press

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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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• Abstraction didn't have to be limited to a kind of rectilinear geometry or even a simple curve geometry. It could have a geometry that had a narrative impact. In other words, you could tell a story with the shapes. It wouldn't be a literal story, but the shapes and the interaction of the shapes and colors would give you a narrative sense. You could have a sense of an abstract piece flowing along and being part of an action or activity. That sort of turned me on.

  Frank Stella

  Simple, Impact, Curves

  Source: www.interviewmagazine.com

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