Conic Sections Quotes

We've searched our database for all the quotes and captions related to Conic Sections. Here they are! All 10 of them:

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets
Mortimer J. Adler (How to Read a Book: The Classic Guide to Intelligent Reading)
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 (Collected Papers of Charles Sanders Peirce, Volumes V and VI, Pragmatism and Pragmaticism and Scientific Metaphysics)
After Us, the Salamanders!, The Future belongs to the Newts, Newts Mean Cultural Revolution. Even if they don't have their own art (they explained) at least they are not burdened with idiotic ideals, dried up traditions and all the rigid and boring things taught in schools and given the name of poetry, music, architecture, philosophy and culture in any of its forms. The word culture is senile and it makes us sick. Human art has been with us for too long and is worn-out and if the newts have never fallen for it we will make a new art for them. We, the young, will blaze the path for a new world of salamandrism: we wish to be the first newts, we are the salamanders of tomorrow! And so the young poetic movement of salamandrism was born, triton - or tritone - music was composed and pelagic painting, inspired by the shape world of jellyfish, fish and corals, made its appearance. There were also the water regulating structures made by the newts themselves which were discovered as a new source of beauty and dignity. We've had enough of nature, the slogans went; bring on the smooth, concrete shores instead of the old and ragged cliffs! Romanticism is dead; the continents of the future will be outlined with clean straight lines and re-shaped into conic sections and rhombuses; the old geological must be replaced with a world of geometry. In short, there was once again a new trend that was to be the thing of the future, a new aesthetic sensation and new cultural manifestoes; anyone who failed to join in with the rise of salamandrism before it was too late felt bitterly that he had missed his time, and he would take his revenge by making calls for the purity of mankind, a return to the values of the people and nature and other reactionary slogans. A concert of tritone music was booed off the stage in Vienna, at the Salon des Indépendents in Paris a pelagic painting called Capriccio en Bleu was slashed by an unidentified perpetrator; salamandrism was simply victorious, and its rise was unstoppable.
Karel Čapek (War with the Newts)
Strangely enough, without names they were still things. He could see them and think about them in terms of shapes, or numbers. Formula of description. Various combinations of conic sections and the six surfaces of revolution symmetrical around an axis, the plane, the sphere, the cylinder, the catenoid, the unduloid, and the nodoid; shapes without the names, but the shapes alone were like names. Spatializing language.
Kim Stanley Robinson (Green Mars (Mars Trilogy, #2))
Joining the world of shapes to the world of numbers in this way represented a break with the past. New geometries always begin when someone changes a fundamental rule. Suppose space can be curved instead of flat, a geometer says, and the result is a weird curved parody of Euclid that provides precisely the right framework for the general theory of relativity. Suppose space can have four dimensions, or five, or six. Suppose the number expressing dimension can be a fraction. Suppose shapes can be twisted, stretched, knotted. Or, now, suppose shapes are defined, not by solving an equation once, but by iterating it in a feedback loop. Julia, Fatou, Hubbard, Barnsley, Mandelbrot-these mathematicians changed the rules about how to make geometrical shapes. The Euclidean and Cartesian methods of turning equations into curves are familiar to anyone who has studied high school geometry or found a point on a map using two coordinates. Standard geometry takes an equation and asks for the set of numbers that satisfy it. The solutions to an equation like x^2 + y^2 = 1, then, form a shape, in this case a circle. Other simple equations produce other pictures, the ellipses, parabolas, and hyperbolas of conic sections or even the more complicated shapes produced by differential equations in phase space. But when a geometer iterates an equation instead of solving it, the equation becomes a process instead of a description, dynamic instead of static. When a number goes into the equation, a new number comes out; the new number goes in, and so on, points hopping from place to place. A point is plotted not when it satisfies the equation but when it produces a certain kind of behavior. One behavior might be a steady state. Another might be a convergence to a periodic repetition of states. Another might be an out-of-control race to infinity.
James Gleick (Chaos: Making a New Science)
My colleague Michael Harris, a distinguished number theorist at the Institut de Mathematiques de Jussieu in Paris, has a theory that three of Thomas Pynchon's major novels are governed by the three conic sections: Gravity's Rainbow is about paraboloas (all those rockets, launching, dropping!), Mason & Dixon about ellipses, and Against the Day about hyperbolas. This seems as good to me as any other organizing theory of these novels I've encountered; certainly Pynchon, a former physics major who likes to drop references to Mobius strips and the quaternions in his novels, knows very well what the conic sections are.
Jordan Ellenberg (How Not to Be Wrong: The Power of Mathematical Thinking)
He saw how the virginal circles of Eudoxus had led to a more coherent astronomy, how the conic sections of Apollonius had prefigured the spirit of universal gravitation. The world had its uses, yes; ideas could be rotated to expedient planes. It wasn’t his method to test the disposition of the physical universe but this didn’t “mean he reacted skeptically to those who drove hooks into nature. He considered the case of Archimedes, son of astronomer, floating body, lever adept, nude runner, catapulter, weigher of parabolas, tactician of solar power, sketcher of equations in sand and with fingernail on own body anointed in after-bath olive oil, killed by dreamless Romans.
Don DeLillo (Ratner's Star)
ferryman’s hefty Africans pace short reciprocating arcs on the deck, sweeping and shoveling the black water of the Charles Basin with long stanchion-mounted oars, minting systems of vortices that fall to aft, flailing about one another, tracing out fading and flattening conic sections that Sir Isaac could probably work out in his head. The Hypothesis of Vortices is pressed with many difficulties. The sky’s a matted reticule of taut jute and spokeshaved tree-trunks. Gusts make the anchored ships start and jostle like nervous horses hearing distant guns.
Neal Stephenson (Quicksilver (The Baroque Cycle #1))
Most of the general considerations in the chapter on 'The Evolution of Ideas' equally apply to the evolution of art. In both fields the truly original geniuses are rare compared with the enormous number of talented practitioners; the former acting as spearheads, opening up new territories, which the latter will then diligently cultivate. In both fields there are periods of crisis, of 'creative anarchy', leading to a break-through to new frontiers-followed by decades, or centuries of consolidation, orthodoxy, stagnation, and decadence-until a new crisis arises, a holy discontent, which starts the cycle again. Other parallels could be drawn: 'multiple discoveries' -the simultaneous emergence of a new style, for which the time is ripe, independently in several places; 'collective discoveries' originating in a closely knit group, clique, school, or team; 'rediscoveries'- the periodic revivals of past and forgotten forms of art; lastly 'cross-fertilizations' between seemingly distant provinces of science and art. To quote a single example: the rediscovery of the treatise on conic sections by Apollonius of Perga, dating from the fourth century B.C., gave the ellipse to Kepler who built on it a new astronomy-and to Guarini, who introduced new vistas into architecture.
Arthur Koestler (The Act of Creation)
Coat of Arms for Cuba since April 24, 1906. It was created by Miguel Teurbe Tolón and consists of a shield, crowned by a soft conical cap known as a Phrygian Cap, signifying freedom and the pursuit of liberty. The star in the middle of the cap denotes Cuba’s Independence. The same symbol is used on the seal of the United States Senate and the United States Department of the Army. The shield, supported by oak leaves on one side and laurel leaves on the other, is divided into three sections. At the top of the shield is the sun rising over Cuba, the key to the Gulf of Mexico and the Caribbean Sea. The diagonal blue and white stripes represent the Cuban flag, and the royal palm, with the Sierra Maestra Mountains looming in the background, represents the country’s abundance.
Hank Bracker