Geometry Quotes - Page 9

• ...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.

  Hans Reichenbach

  Space, Curves, Views

  Hans Reichenbach (1958). “Philosophie Der Raum-Zeit-Lehre”, p.83, Courier Corporation

  5 Copy quote

  Show source

• The concept of congruence in Euclidean geometry is not exactly the same as that in non-Euclidean geometry. ..."Congruent" means in Euclidean geometry the same as "determining parallelism," a meaning which it does not have in non-Euclidean geometry.

  Hans Reichenbach

  Mean, Doe, Congruence

  "The Philosophy of Space and Time". Book by Hans Reichenbach, 1957.

  10 Copy quote

  Show source

• Visual forms are not perceived differently from colors or brightness. They are sense qualities, and the visual character of geometry consists in these sense qualities.

  Hans Reichenbach

  Character, Color, Quality

  Hans Reichenbach (1958). “Philosophie Der Raum-Zeit-Lehre”, p.84, Courier Corporation

  8 Copy quote

  Show source

• Challenger was lost because NASA came to believe its own propaganda. The agency's deeply impacted cultural hubris had it that technology-engineering-would always triumph over random disaster if certain rules were followed. The engineers-turned-technocrats could not bring themselves to accept the psychology of machines with abandoning the core principle of their own faith: equations, geometry, and repetition-physical law, precision design, and testing-must defy chaos.

  William E. Burrows

  Believe, Technology, Agency

  William E. Burrows (2010). “This New Ocean: The Story of the First Space Age”, p.560, Modern Library

  4 Copy quote

  Show source

• Books, Manuals, Directives, Regulations. The geometries that circumscribe your working life draw norrower and norrower until nothing fits inside them anymore.

  Lord Byron

  Book, Regulation, Fit

  7 Copy quote

• Now, a 45-degree angle is not something we deal with in finance. It's something you see in a high school geometry class. Performance like that has never been recorded in human history.

  Harry Markopolos

  School, High School, Finance

  Source: www.gq.com

  4 Copy quote

  Show source

• The geometry reveals five development direction for applications (each with endless possibilities); dividing, dwelling, trestle, fenestration and artistic installation. I find these enabled designs so reflective of an ever-changing world where contextual factors and technological resources are shifting definitions of architecture, design, and the traditional boundaries between disciplines.

  Dror Benshetrit

  Dwelling, Discipline, Design

  Source: www.huffingtonpost.com

  4 Copy quote

  Show source

• Seriously, you don't have to know English. It'd be nice, a nice little plus. We don't want miracles. You don't have to know the country's language. But just some shapes, that's all. A square. A little geometry.

  David Spade

  Country, Nice, Squares

  "David Spade: Take the Hit". Documentary, Comedy, www.imdb.com. 1998.

  4 Copy quote

  Show source

• The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems -- the determination of the diagonal of a square and that of the circumference of a circle -- revealed the existence of new mathematical beings for which no place could be found within the rational domain.

  David van Dantzig

  Determination, Simple, Squares

  6 Copy quote

• The opinions of men should not be the object of any government. Our civil rights are no more dependent on our religious beliefs than they are dependent upon our thoughts about geometry or physics!

  Thomas Jefferson

  Religious, Men, Rights

  4 Copy quote

• Well, I do not mind telling you I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious. For instance, here is a portrait of a man at eight years old, another atfifteen, another at seventeen, another at twenty-three, and so on. All these are evidently sections, as it were, Three-Dimensional representations of his Four-Dimensioned being, which is a fixed and unalterable thing.

  H. G. Wells

  Time, Men, Eight

  H G Wells (2004). “The Time Machine (Sparklesoup Classics)”, p.6, Sparklesoup LLC

  4 Copy quote

  Show source

• A time will however come (as I believe) when physiology will invade and destroy mathematical physics, as the latter has destroyed geometry.

  John B. S. Haldane

  Time, Believe, Math

  7 Copy quote

• Time was when all the parts of the subject were dissevered, when algebra, geometry, and arithmetic either lived apart or kept up cold relations of acquaintance confined to occasional calls upon one another; but that is now at an end; they are drawn together and are constantly becoming more and more intimately related and connected by a thousand fresh ties, and we may confidently look forward to a time when they shall form but one body with one soul.

  James Joseph Sylvester

  Life, Math, Ties

  James Joseph Sylvester (1870). “The Laws of Verse: Or Principles of Versification Exemplified in Metrical Translations, Together with an Annotated Reprint of the Inaugural Presidential Address to the Mathematical and Physical Section of the British Association at Exeter”, p.124

  7 Copy quote

  Show source

• The purely formal language of geometry describes adequately the reality of space. We might say, in this sense, that geometry is successful magic. I should like to state a converse: is not all magic, to the extent that it is successful, geometry?

  Rene Thom

  Successful, Reality, Space

  16 Copy quote

• If we concentrate our attention on trying to solve a problem of geometry, and if at the end of an hour we are no nearer to doing so than at the beginning, we have nevertheless been making progress each minute of that hour in another more mysterious dimension. Without knowing or feeling it, this apparent barren affort has brought more light into the soul.

  Simone Weil

  Light, Knowing, Soul

  Simone Weil (2009). “Waiting on God (Routledge Revivals)”, p.32, Routledge

  4 Copy quote

  Show source

• No one fully understands spinors. Their algebra is formally understood but their general significance is mysterious. In some sense they describe the 'square root' of geometry and, just as understanding the square root of -1 took centuries, the same might be true of spinors.

  Michael Atiyah

  Squares, Roots, Understanding

  19 Copy quote

• Logic was to cognition as geometry was to landscape

  Kim Stanley

  Landscape, Cognition, Logic

  6 Copy quote

• ...to characterize the import of pure geometry, we might use the standard form of a movie-disclaimer: No portrayal of the characteristics of geometrical figures or of the spatial properties of relationships of actual bodies is intended, and any similarities between the primitive concepts and their customary geometrical connotations are purely coincidental.

  Carl Gustav Hempel

  Math, Might Use, Body

  Carl Gustav Hempel (2001). “The Philosophy of Carl G. Hempel: Studies in Science, Explanation, and Rationality”, p.24, Oxford University Press on Demand

  9 Copy quote

  Show source

• The prime ideal is a princess of the world of ideals. Her father is the prince 'Point' in the world of geometry. Her mother is the princess 'Prime Numbers' in the world of numbers. She inherits the purity from her parents.

  Kato

  Mother, Father, Princess

  4 Copy quote

• I write rhymes with addition and algebra, mental geometry.

  Ice T

  Education, Writing, Mathematics

  Song: Mind Over Matter, Album: O.G. Original Gangster

  4 Copy quote

  Show source

• Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).

  Gian-Carlo Rota

  Writing, Two, Three

  7 Copy quote

• Here I beg you to observe in passing that the scruples that prevented ancient writers from using arithmetical terms in geometry, and which can only be a consequence of their inability to perceive clearly the relation between these two subjects, introduced much obscurity and confusion into their explanations.

  Rene Descartes

  Two, Confusion, Experience

  10 Copy quote

• Enchanting is not the word that would immediately spring to mind when describing a play that deals with fractal geometry, iterated algorithms, chaos theory and the second law of thermodynamics, but it is a perfect fit for Tom Stoppard's astonishing 1993 play, which is as beautiful as it is brilliant. This is one Stoppard drama that you don't have to be Einstein to understand -- you can feel it as well as think it. (...) Breathtaking, exhilarating and deeply satisfying.

  Lyn Gardner

  Beautiful, Drama, Spring

  5 Copy quote

• Psychoanalysis and Zen, in my private psychic geometry, are equal to nicotine. They are anti-existential. Nicotine quarantines one out of existence.

  Norman Mailer

  Psychics, Quarantine, Existential

  Norman Mailer, Michael Lennon (1988). “Conversations with Norman Mailer”, p.45, Univ. Press of Mississippi

  18 Copy quote

  Show source

• And in between the two, in between the sky and the sea, were all the winds. And there were all the nights and all the moons. To be a castaway is to be a point perpetually at the centre of a circle. However much things may appear to change-the sea may shift from whisper to rage, the sky might go from fresh blue to blinding white to darkest black-the geometry never changes. Your gaze is always a radius. The circumference is ever great. In fact, the circles multiply. To be a castaway is to be caught in a harrowing ballet of circles.

  Yann Martel

  Moon, Night, Blue

  7 Copy quote