Mathematical Fallacies and Paradoxes

Author: Bryan Bunch

Publisher: Courier Corporation

ISBN: 0486137937

Category: Mathematics

Page: 240

View: 8621

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Stimulating, thought-provoking analysis of the most interesting intellectual inconsistencies in mathematics, physics, and language, including being led astray by algebra (De Morgan's paradox). 1982 edition.

Magnificent Mistakes in Mathematics

Author: Alfred S. Posamentier,Ingmar Lehmann

Publisher: Prometheus Books

ISBN: 1616147482

Category: Mathematics

Page: 296

View: 8284

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Two veteran math educators demonstrate how some "magnificent mistakes" had profound consequences for our understanding of mathematics' key concepts. In the nineteenth century, English mathematician William Shanks spent fifteen years calculating the value of pi, setting a record for the number of decimal places. Later, his calculation was reproduced using large wooden numerals to decorate the cupola of a hall in the Palais de la Découverte in Paris. However, in 1946, with the aid of a mechanical desk calculator that ran for seventy hours, it was discovered that there was a mistake in the 528th decimal place. Today, supercomputers have determined the value of pi to trillions of decimal places. This is just one of the amusing and intriguing stories about mistakes in mathematics in this layperson's guide to mathematical principles. In another example, the authors show that when we "prove" that every triangle is isosceles, we are violating a concept not even known to Euclid - that of "betweenness." And if we disregard the time-honored Pythagorean theorem, this is a misuse of the concept of infinity. Even using correct procedures can sometimes lead to absurd - but enlightening - results. Requiring no more than high-school-level math competency, this playful excursion through the nuances of math will give you a better grasp of this fundamental, all-important science. From the Hardcover edition.

Christmaths—A Creative Problem Solving Math Book

Author: Yan Kow Cheong

Publisher: MathPlus Publishing

ISBN: 9810876556

Category: Christmas

Page: 196

View: 8811

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A recreational-and-problem-solving math book, CHRISTmaths: A Creative Problem Solving Math Book attempts to bring together the joy (or spirit) of Christmas and the spirit (or joy) of mathematics. Looking at topics linking Mathematics and Christmas—what the queen of the sciences and the king of the public holidays have in common—CHRISTmaths will not only appeal to a Christmas or Christian audience, but also to any problem solvers who enjoy mathematics recreationally. CHRISTmaths should appeal to • creative problem solvers who are bored by drill-and-kill math titles, and who desire to get an intellectual kick out of solving non-routine questions; • mathletes who long for some creative mathematical problem solving to tickle their mathematical bones. CHRISTmaths hopes to give readers the opportunity to experience the Ah, Aha! and Ha Ha of Mathematics. Contents Preface Biodata of 25 B.C. and A.D. Are You Christmas-Literate? The 12 Puzzles of Christmas Santa’s Itinerary 12 Daffynitions of CHRISTMAS A CHRISTMAS Spell Guesstimation on Christmas Day 7 Beautiful Xmas Series 12 Challenges @ Christmastime A Mathematician’s Musings on Xmas Day Mathematical Graphiti I Xmas Philamath 12 Myths about Christ and Christmas Mathematical Graphiti II Mathematical Graphiti III 25 No-Frills Christmas Crackers Did You Know…. The Mathematics of Christmas 25 Mathematical Quickies & Trickies Was Pythagoras a pre-Christian Christian? A Formula for Christmas Day Q&A about Christmas Clausophobia and the Rest Mathematical Graphiti III Mathematical Graphiti IV Number of Zeros in 1 × 2 × 3 ×⋯× 24 × 25 25 Math Things You Can Do on Christmas 1 × 2 × 3 ×⋯× (n − 1) × n ends in 25 zeros Taking Up Your Cross Mathematicians Christened Number of Digits in 2525 Christmas Tangrams CHRISTMAS By Numbers What day Is Christmas in 2025? The Mathematical Fathers The Answer Is Not 25 Christmas Countdown A Christmas Potpourri CHRISTMAS Alphametics Mathematical Graphiti IV Celebrate Father Christmas Week 25 Illegal Things You May Want to Do on Xmas The Twelve Days of Christmas A Green Christmas Answers/Hints/Solutions Bibliography & References Type of e-book: Nonfiction, problem solving, recreational, Singapore math, trick questions Audiences: Suitable for Grades 5-10

Mathematical Physics

A Popular Introduction

Author: Francis Bitter

Publisher: Courier Corporation

ISBN: 0486435016

Category: Mathematics

Page: 188

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Reader-friendly guide offers illustrative examples of the rules of physical science and how they were formulated. Topics include the role of mathematics as the language of physics; nature of mechanical vibrations; harmonic motion and shapes; geometry of the laws of motion; more. 60 figures. 1963 edition.

Solve this

Math Activities for Students and Clubs

Author: James Stuart Tanton

Publisher: Cambridge University Press

ISBN: 9780883857175

Category: Mathematics

Page: 218

View: 2010

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This is a collection of intriguing mathematical problems and activities arising from our everyday experience.

Language and the Ineffable

A Developmental Perspective and Its Applications

Author: Louis S. Berger

Publisher: Lexington Books

ISBN: 0739147137

Category: Language Arts & Disciplines

Page: 147

View: 2014

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The prevailing conception of language is often called 'the received view.' Though ubiquitous, Louis S. Berger demonstrates its flaws and the difficulties it raises for other disciplines, such as philosophy and physics. In Language and the Ineffable, Berger develops an unconventional model of human development: ontogenesis. A radical and generative feature of the model is the premise that the neonate's world is holistic, boundary-less, unimaginable, and impossible to describe; in other words, ineffable. This study unsettles the foundations of sacrosanct beliefs about language and a host of other disciplines in the process.

Mathematics, Magic and Mystery

Author: Martin Gardner

Publisher: Courier Corporation

ISBN: 0486801179

Category: Games & Activities

Page: 208

View: 2887

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Famed puzzle expert explains math behind a multitude of mystifying tricks: card tricks, stage "mind reading," coin and match tricks, counting out games, geometric dissections, etc. More than 400 tricks. 135 illustrations.

More Joy of Mathematics

Exploring Mathematics All Around You

Author: Theoni Pappas

Publisher: Wide World Pub Tetra


Category: Mathematics

Page: 294

View: 1956

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Includes puzzles, games, ideas, and more, that have to do with mathematics

Analysis I

Author: Christiane Tretter

Publisher: Springer-Verlag

ISBN: 3034803494

Category: Mathematics

Page: 157

View: 2545

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Das Lehrbuch ist der erste von zwei einführenden Bänden in die Analysis. Es zeichnet sich dadurch aus, dass alle klassischen Themen der Analysis des ersten Semesters kompakt zusammengefasst sind und dennoch auf typische Anfängerprobleme eingegangen wird. Neben einer Einführung in die formale Sprache und die wichtigsten Beweistechniken der Mathematik bietet der Band eingängige Erläuterungen zu abstrakten Begriffen. Alle prüfungsrelevanten Inhalte sind abgedeckt und können anhand von Beispielen, Gegenbeispielen und Aufgaben nachvollzogen werden.

The History of Science and Technology

A Browser's Guide to the Great Discoveries, Inventions, and the People Who Made Them from the Dawn of Time to Today

Author: Bryan Bunch

Publisher: Houghton Mifflin Harcourt


Category: Science

Page: 784

View: 562

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In this age of genetic engineering and global warming, it is more important than ever to understand the history and current trends of science and technology. With so much information out there, though, it’s hard to know where to start. That’s where The History of Science and Technology — the most comprehensive and up-to-date chronology of its kind -- comes in. From the first stone tools to the first robot surgery, this easy-to-read, handy reference book offers more than seven thousand concise entries organized within ten major historical periods and categorized by subject, such as archaeology, biology, computers, food and agriculture, medicine and health, materials, and transportation. You can follow the world’s scientific and technological feats forward or backward, year by year, and subject by subject. Under 8400 BCE Construction, you will discover that the oldest known wall was built in Jericho. Jump to 1454 Communication and you will learn about Johann Gutenberg’s invention of movable type. Take an even larger leap to 2002 Computers and find out about the invention of the Earth Simulator, a Japanese supercomputer. The History of Science and Technology answers all the what, when, why, and how questions about our world’s greatest discoveries and inventions: How are bridges built? When were bifocal eyeglasses invented and by whom? What medical discovery led to the introduction of sterilization, vaccines, and antibiotics? What is the PCR (polymerase chain reaction) process, and why is it one of the pillars of the biotechnology revolution? Not only can you discover how our world came to be and how it works, but with cross-referenced entries you can also trace many intricate and exciting connections across time. Highly browsable yet richly detailed, expertly researched and indexed, The History of Science and Technology is the perfect desktop reference for both the science novice and the technologically advanced reader alike. From School Library Journal Grade 9 Up–Based on the authors' The Timetables of Science(1988; o.p.) and The Timetables of Technology(1993, both S & S),this hefty volume is divided into 10 periods, each beginning with an overview of major advances, many of which caused controversy in political, social, and religious arenas. The introductions are followed by yearly chronicles of specific accomplishments ranging from the time when hominoids used pebble tools through 2003. In all there are more than 7000 brief entries under such broad headings as "Tools," "Construction," "Astronomy," "Food & Agriculture," "Physics," and "Mathematics." Nearly 200 feature essays are interspersed, including "The Manhattan Project," "How did the Egyptians build the pyramids?," "Early surgery," "Time shifting," "The canal age," and "The size of the universe." These are best accessed from the table of contents, as the index doesn't differentiate essays from text references. Biographies appear as boxed insets with information on career highlights and a small portrait. While informative, the black-and-white photographs and illustrations found throughout are of mediocre quality. An affordable one-volume reference.–Vicki Reutter, Cazenovia High School, NY Copyright © Reed Business Information, a division of Reed Elsevier Inc. All rights reserved.

Mathematik und Plausibles Schließen

Band 2: Typen und Strukturen plausibler Folgerung

Author: G. Polya

Publisher: Birkhäuser

ISBN: 9783764307158

Category: Science

Page: 326

View: 3063

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10 in denen meine Beobachtungen meine Schlusse zu stutzen scheinen. Aber ich achte das Urteil des Lesers und will ihn nicht zwingen oder auf irgendeine unsaubere Weise dazu bringen, meine Schlusse anzu nehmen. Naturlich erheben die hier gebotenen Ansichten keinen Anspruch auf Endgultigkeit. Ich konnte in der Tat eine Reihe von Stellen ange ben, wo ich klar empfinde, dass eine grossere oder kleinere Verbesse rung am Platz ware. Ich glaube jedoch, dass die Hauptrichtung richtig ist, und ich hoffe, dass die Ausfuhrungen und vor allem die Beispiele in diesem Werk dazu beitragen mogen, die -Doppelnatun und die -komplementaren Aspekte) plausiblen, insbesondere induktiven Schliessens, zu erhellen, das zuweilen als -objektiv) und zuweilen als -subjektiv) erscheint. Stanford University Georg P6lya Mai 1953 VORWORT ZUR ZWEITEN AUFLAGE Die vorliegende zweite Auflage wurde erweitert durch einen An hang. Dieser enthalt einen Aufsatz -Heuristische Schlussweisen in der Zahlentheorie), entnommen dem American Mathematical Monthly mit der Genehmigung des herausgebenden Vereins, und zusatzliche Bemerkungen und Aufgaben zu verschiedenen Kapiteln. Herzlichen Dank Fraulein Dr. A. Roth fur die gewissenhafte Uber setzung und Frau H. Bretscher fur freundliche Hilfe."

Alice im Quantenland

Author: Robert Gilmore

Publisher: Springer-Verlag

ISBN: 3322850099

Category: Technology & Engineering

Page: 239

View: 5479

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Alice sitzt gelangweilt vor dem Fernseher; da fällt ihr Blick auf "Alice im Wunderland", das sie kürzlich gelesen hat. Sie sehnt sich danach, vergleichbare Abenteuer zu erleben, stürzt und fällt in Ohnmacht. In ihrem Traum fällt sie durch den Bildschirm hindurch, wo sie - verkleinert - auf die Elektronen trifft, die als Strahl den Bildschirm zum Leuchten bringen. Das ist erst der Anfang der Geschichte, in der Alice nach und nach die Besonderheiten der Quantenwelt kennenlernt. Sie begegnet Menschen wie Niels Bohr, die sie unter ihre Fittiche nehmen, und steht mit Elektronen und Quarks auf du und du. In dieser neuen Form der Geschichte von Alice beschreibt Robert Gilmore - selbst angesehener Physiker - kenntnisreich und amüsant, welche Besonderheiten uns die Welt der Elektronen und Quarks bietet. Schließlich wird Alice (und damit den Lesern) klargemacht, daß nach 70 Jahren der Forschung auf diesem Gebiet ungelöste Fragen an die Grundlagen der Quantentheorie übriggeblieben sind, die vielleicht nie gelöst werden können. Rezension erschienen in: junge wissenschaft Ausgabe / Band 12Jg., Heft 45, S. 60f Feb. 97 (...) ist es dem Autor in hervorragender Weise gelungen, eine didaktisch äußerst wertvolle Darstellung der Quantenmechanik zu präsentieren(...) (...)erreicht damit einen wesentlich größerenLeserkreis(...) (...)sehr abgerundetes Bild der Quantenphysik(...) (...)in sehr geschickter Weise(...) (...)in sehr prägnanter Form, jedoch in fachlicher Hinsicht völlig korrekt(...) (...)Als besonders gelungen darf man die Übersetzung aus dem englischen Original bezeichnen(...) (...)Sehr lobenswert erwähnt werden muß wohl auch die vom deutschen Übersetzer vorgenommene Aktualisierung beim inzwischen gelungenen Nachweis des top-Quark am Fermilab(...) (...)Der rezensent ist davon überzeugt, daß auch der versierte Physiker dieses Buch mit großem Genuß lesen muß(...)