Tales of Impossibility (eBook)

The 2000-Year Quest to Solve the Mathematical Problems of Antiquity

David S. Richeson (Autor)

eBook Download: PDF

2019
456 Seiten
Princeton University Press (Verlag)
978-0-691-19423-3 (ISBN)

Infos

A comprehensive look at four of the most famous problems in mathematicsTales of Impossibility recounts the intriguing story of the renowned problems of antiquity, four of the most famous and studied questions in the history of mathematics. First posed by the ancient Greeks, these compass and straightedge problems-squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle-have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs-which demonstrated the impossibility of solving them using only a compass and straightedge-depended on and resulted in the growth of mathematics.Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Viete, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems.Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

Produkt-Details

• Erscheint lt. Verlag: 8.10.2019
• Zusatzinfo: 163 b/w illus. 5 tables.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geschichte der Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Mathematische Spiele und Unterhaltung
• Schlagworte: abstract algebra • Algebra • algebraic number • Angle trisection • Area of a circle • arithmetic • Axiom • Basel problem • bisection • Calculation • casus irreducibilis • circumference • coefficient • Compass-and-straightedge construction • complex number • Conchoid (mathematics) • conic section • conjecture • Constructible number • Coprime integers • Cube root • De Moivre's formula • DIAMETER • Dinostratus • Disquisitiones Arithmeticae • Divisibility rule • doubling the cube • Equation • equilateral triangle • Euclid's elements • Ferdinand von Lindemann • Fermat's Last Theorem • Gematria • Geometry • Georg Mohr • Gödel's Incompleteness Theorems • Halting Problem • Hippasus • Hypotenuse • Infinitesimal • Integer • irrational number • Isaac Barrow • Jacob Bernoulli • Liber Abaci • Line–line intersection • Line segment • Liouville number • mathematician • Mathematics • Menaechmus • Method of exhaustion • Michel Chasles • Muhammad ibn Musa al-Khwarizmi • Natural number • Neusis construction • Newton's method • Nonagon • Non-Euclidean geometry • Number Theory • On Spirals • On the Sphere and Cylinder • Parabola • Pierpont prime • Pierre Wantzel • Polygon • polynomial • Prime number • Probabilistic method • Proof of impossibility • Pure Mathematics • Pythagorean Theorem • Quadratic equation • Quadratic formula • quadratrix • Quantity • Rational number • real number • rectangle • regular polygon • result • Riemann hypothesis • Right triangle • Root of unity • Savilian Professor of Geometry • scientific notation • semicircle • Significant figures • Simon Stevin • square root • Squaring the circle • straightedge • Summation • Theorem • The Quadrature of the Parabola • Thomas Kuhn • transcendental number • Underwood Dudley • William Oughtred • Zero of a function
• ISBN-10: 0-691-19423-8 / 0691194238
• ISBN-13: 978-0-691-19423-3 / 9780691194233