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Mathematics and the Imagination Dover Publications
Książki / Literatura obcojęzyczna
Introduction I. NEW NAMES FOR OLD Easy words for hard ideas Transcendental Non-simple curve Simple curve Simple group Bolsheviks and giraffes Turbines Turns and slides Circles and cycles Patho-circles Clocks Hexagons and parhexagons "Radicals, hyperradicals, and ultraradicals (nonpolitical)" New numbers for the nursery Googol and googolplex Miracle of the rising book The mathescope II. BEYOND THE GOOGOL Counting?the language of number "Counting, matching, and "Going to Jerusalem" Cardinal numbers Cosmic chess and googols The sand reckoner Mathematical induction The infinite and its progeny Zeno Puzzles and quarrels Bolzano Galileo's puzzle Cantor Measuring the measuring rod The whole is no greater than some of its parts The first transfinite?Alepho Arithmetic for morons Common sense hits a snag Cardinality madman The tortoise unmasked Motionless motion Private life of a number The house that Cantor built III. "Pie, i, e (PIE)" Chinamen and chandeliers Twilight of common sense "Pie, i, e" Squaring the circle and its cousins Mathematical impossibility "Silk purse, sow's ear, ruler and compass" Rigor mortis Algebraic equations and transcendental numbers Galois and Greek epidemics Cube duplicators and angle trisectors Biography of pie "Infancy: Archimedes, the Bible, the Egyptians" "Adolescence: Vieta, Van Ceulen" "Maturity: Wallis, Newton, Leibniz" "Old Age: Dase, Richter, Shanks" Victim of schizophrenia Boon to insurance companies (e) Logarithms or tricks of the trade Mr. Briggs is surprised Mr. Napier explains "Biography of e; or e, the banker's boon" Pituitary gland of mathematics: the exponential function (i) "Humpty Dumpty, Doctor or Semantics" Imaginary numbers "The v-1, or "Where am I?" " "Biography of i, the self-made amphibian" "Omar Khayyám, Cardan, Bombelli, and Gauss" i and Soviet Russia Program music of mathematics "Breakfast in bed; or, How to become a great mathematician" Analytic geometry Geometric representation of i Complex plane "A famous formula, faith, and humility" IV. ASSORTED GEOMETRIES?PLANE AND FANCY The talking fish and St. Augustine A new alphabet High priests and mumbo jumbo Pure and applied mathematics Euclid and Texas Mathematical tailors Geometry?a game "Ghosts, table-tipping, and the land of the dead" Fourth-dimension flounders Henry More to the rescue Fourth-dimension?a new gusher A cure for arthritis Syntax suffers a setback The physicist's delight Dimensions and manifolds Distance formulae Scaling blank walls Four-dimensional geometry defined Moles and tesseracts A four-dimensional fancy Romance of flatland Three-dimensional cats and two-dimensional kings Gallant Gulliver and the gloves Beguiling voices and strange footprints Non-Euclidean geometry Space credos and millinery Private and public space Rewriting our textbooks The prince and the Boethians The flexible fifth The mathematicians unite?nothing to lose but their chains Lobachevsky breaks a link Riemann breaks another Checks and double checks in mathematics The tractrix and the pseudosphere Great circles and bears The skeptic persists?and is stepped on Geodesics Seventh Day Adventists Curvature Lobachevskian Eiffel Towers and Riemannian Holland Tunnels V. PASTIMES OF PAST AND PRESENT TIMES Puzzle acorns and mathematical oaks Charlemagne and crossword puzzles "Mark Twain and the "farmer's daughter" The syntax of puzzles Carolyn Flaubert and the cabin boy "A wolf, a goat, and a head of cabbage" Brides and cuckolds I'll be switched "Poisson, the misfit" "High finance; or, The international beer wolf" Lions and poker players The decimal system Casting out nines "Buddha, God, and the binary scale" "The march of culture; or, Russia, the home of the binary system" The Chinese rings The tower of Hanoi "The ritual of Benares: or, Charley horse in the Orient" "Nim, Sissa Ben Dahir, and Josephus" Bismarck plays the boss The 15 puzzle plague The spider and the fly A nightmare of relatives The magic square Take a number from 1 to 10 Fermat's last theorem Mathematics' lost legacy VI. PARADOX LOST AND PARADOX REGAINED Great paradoxes and distant relatives Three species of paradox Paradoxes strange but true Wheels that move faster on top than on bottom The cycloid family "The curse of transportation; or, How locomotives can't make up their minds" Reformation of geometry Ensuing troubles Point sets?the Arabian Nights of mathematics Hausdorff spins a tall tale Messrs. Banach and Tarski rub the magic lamp Baron Munchhausen is stymied by a pea Mathematical fallacies "Trouble from a bubble; or, Dividing by zero" The infinite?troublemaker par excellence Geometrical fallacies Logical paradoxes?the folk tales of mathematics Deluding dialectics of the poacher and the prince; of the introspective barber; of the number 111777; of this book and Confucius; of the Hon. Bertrand Russell "Scylla and Charybdis; or, What shall poor mathematics d "Twits Napoleon, who does" The Marquis de Condorcet has high hopes M. le Marquis omits a factor and loses his head Fourier of the Old Guard Dr. Darwin of the New The syllogism scraps a standby Mr. Socrates may not die "Ring out the old logic, ring in the new" VIII. RUBBER-SHEET GEOMETRY Seven bridges over a stein of beer Euler shivers Is warmed by news from home Invents topology Dissolves the dilemma of Sunday strollers Babies' cribs and Pythagoreans Talismen and queer figures Position is everything in topology Da Vinci and Dali Invariants Transformations The immutable derby "Competition for the caliph's cup; or, Sifting out the suitors by science" Mr. Jordan's theorem Only seems idiotic Deformed circles Old facts concerning Times Square and a balloonist's head Eccentric deportment of several distinguished gentlemen at Princeton Their passion for pretzels Their delving in doughnuts Enforced modesty of readers and authors The ring Lachrymose recital around a Paris pissoir "Who staggered how many times around the walls of what?" In and out the doughnut Gastric surgery?from doughnut to sausage in a single cut N-dimensional pretzels The Möbius strip Just as black as it is painted Foments industrial discontent Never takes sides Bane of painter and paintpot alike The iron rings "Mathematical cotillion; or, How on earth do I get rid of my partner?" "Topology?the pinnacle of perversity; or, Removing your vest without your coat" Down to earth?map coloring Four-color problem Euler's theorem The simplest universal law Brouwer's puzzle The search for invariants IX. CHANGE AND CHANGEABILITY The calculus and cement Meaning of change and rate of change Zeno and the movies "Flying Arrow" local?stops at all points" Geometry and genetics The arithmetic men dig pits Lamentable analogue of the boomerang History of the calculus Kepler Fermat Story of the great rectangle Newton and Leibniz Archimedes and the limit "Shrinking and swelling; or, "Will the circle go the limit?" Brief dictionary of mathematics and physics "Military idyll; or, The speed of the falling bomb" The calculus at work The derivative Higher derivatives and radius of curvature Laudable scholarship of automobile engineers The third derivative as a shock absorber The derivative finds its mate Integration Kepler and the bungholes "Measuring lengths; or, The yawning regress" Methods of approximation Measuring areas under curves Method of rectangular strips The definite Indefinite On the inverse of the other "The outline of history and the descent of man: or, y=ex" Sickly curves and orchidaceous ones The snowflake Infinite perimeters and postage stamps Anti-snowflake Super-colossal pathological specimen?the curve that fills space The unbelievable crisscross EPILOGUE. MATHEMATICS AND THE IMAGINATION
Immanuel Kant, Vol. 1 of 2 Forgotten Books
Książki / Literatura obcojęzyczna
Excerpt from Immanuel Kant, Vol. 1 of 2: A Study and a Comparison With Goethe, Leonardo Da Vinci, Bruno, Plato and Descartes If there be one defect more peculiarly English than another it is the tendency to sneer at everything foreign, at everything that is not familiar, everything outside the daily experience of our narrow life. Talking the other day with a man of acknowledged ability and great public worth, I happened to mention the name of Kant. "Of one thing I can assure you," said my friend, "I am too old to have anything to do with German philosophy." Coming from such a man these words set me wondering. Does there, after all, exist such a thing as German philosophy? Surely philosophy is the common possession of all mankind, not the monopoly of any one race or language. There can be few men in the world, whatever their nationality may be, who do not sometimes "think about thought." The famous misunderstood "Cogito ergo sum" of Descartes, concerning which Chamberlain has much to say, must often come into the least thoughtful minds. Why am I? What am I? What are the relations between me and the world? The investigation of the laws of human thought, its objects, methods, and results, belong to all humanity, otherwise it is nothing. And in the case of Kant, that great Lord of Thought, how far can he be called German? Have we Britons, too, not some small heredity share in the legacy which he has left to the world? About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
My Father Il Duce Kales Press
Książki / Literatura obcojęzyczna
In this historical, revisionist memoir, Romano Mussolini (September 26, 1927-February 3, 2006), the last surviving child of dictator Benito Mussolini, contributes his unique perspective to the growing body of work that portrays Il Duce's era. Through Romano's portrait of never before publicly shared memories and feelings, My Father Il Duce brings alive the domestic scenes of his childhood particularly when they intersected with his father's public role. He also relates in detail the memories of his mother, Donna Rachele, who lived until 1979 and often spoke with Romano about his father. Romano's memories, sorted by chapter, but not presented chronologically, shift between his own recollections of time spent with his father to the years after Mussolini's death in 1945. The prose lingers and then artistically moves forward, melancholy to fierce to vulnerable, like the notes of the jazz music played by Romano during his acclaimed musical career. Mussolini is presented here as a man who was supremely convinced that he was the master of his life: "'Everything happening around me, '" my father used to say, "'leaves me indifferent. I consciously choose 'Live dangerously' as my life's motto. As an old soldier, I say, 'If I advance, follow me. If I retreat, kill me. If they kill me, vindicate me.'" He saw his existence in scenes of high drama, envisioning in the end, Romano tells us, that he would be placed in front of throngs at New York City's Madison Square Garden and then executed in a macabre spectacle. In this memoir, Romano does not truly ponder the consequences of his father's alliances and dictatorship, though with at least one notable exception that he gave considerable thought to his personal anger toward Hitler for "stabbing my father in the back at his darkest hour." Instead, he seeks to render concrete the memories that he held silent over a lifetime before they were lost to history. The fascist order that Mussolini created and imposed upon Italy is one that Italians and students of history the world over are still interpreting. Indeed, his legacy was centerstage in the May 2006 Italian national elections, and one of the deputies in the Italian parliament today who represents his alliances is Alessandra Mussolini, Romano's daughter and defender of her infamous grandfather. As the trend of historical revisionism in Italy continues, in particular regarding the role of fascism, some of this kinder, gentler Mussolini is already widely accepted. Thus, My Father Il Duce (in Italian Il Duce Mio Padre) was published to great attention and controversy in Italy in 2004 and quickly became a bestseller. Romano often appeared on Italian national television and in newspaper interviews. In part, this illuminates that fascist supporters are alive and well, while also confirms even among non-supporters, the ongoing attraction to the cult of personality Mussolini masterminded. In Italy, this public discourse about Mussolini is common. However, for others it is important to establish a context for Romano's memoir. This is accomplished here through an accompanying masterful twenty-one page introductory essay by one of the world's foremost authorities on Italian political culture, Alexander Stille: writing the introductory essay to My Father Il Duce is a bit like writing the warning label on a powerful drug that has its uses but must be taken with care and knowledge of its possible side effects. Romano reached his goal of living to see the first publication of his memoir in Italian. As for this English-language edition, he earlier expressed approval of the front cover design. On January 1, 2006, he received the translated English language manuscript of his writing. During the last month of his life, he approved it. Romano Mussolini died on February 3, 2006, at age seventy-nine in a Rome hospital soon after heart surgery. Romano's death made international news. The New York Times obituary reported: "In the 1950's and 60's he was in the vanguard of Italian jazz with his group the Romano Mussolini All Stars, and he played with American greats like Dizzy Gillespie, Duke Ellington and Chet Baker. Mr. Mussolini gained even greater international fame with his first marriage, to Anna Maria Scicolone, the sister of the actress Sophia Loren....Despite his own scrupulous avoidance of politics, politicians from Italy's right wing-parties widely lauded Mr. Mussolini and his family name in statements they released: 'Romano knew how to make us love him for his humanity, his art, but also for the dignity and coherence with which he defended his family from attacks and demonizations.'" Through Romano's worldwide celebrity and well-regarded nature, his words in defense of Il Duce, albeit ones he no doubt wrote as a son who loved his father, offer a rare insider's perspective that can help us better understand, and therefore more readily defeat tyranny. This memoir's account of history further reminds us of the continuing need for our vigilance in the pursuit of truth.
If Only We Could Know! Ivan R Dee, Inc
Książki / Literatura obcojęzyczna
It will soon be a hundred years since the death of Anton Chekhov. He was apt to remark that immortality is rubbish, but what has happened to his creative legacy in the last century matches all of man's metaphors that express the idea of immortality. And the process continues, overcoming boundaries of time and space, and taking different form in different countries. In this luminous book of criticism, Chekhov's foremost Russian interpreter offers to Western readers a remarkably clear and commanding appraisal of the master's work. Vladimir Kataev concerns himself chiefly with Chekhov's unique treatment of a wide range of diverse themes, motifs, and situations. With ringing authority and critical common sense, he examines Chekhov's major tales, stories, and plays, pointing out patterns of development in Chekhov's approach to characters and themes, and tracing the roots of Chekhov's ideas as expressed through his plots. The hallmark of Mr. Kataev's interpretations is their clarity. No one who has endured tortuous explanations of Chekhov will fail to welcome his lucid criticism. With his careful arguments, he quietly undermines many conventional (and persistent) approaches to Chekhov, Western as well as Russian, and establishes a radically new position of his own.
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