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Title details for Magnificent Mistakes in Mathematics by Alfred S. Posamentier - Available

Magnificent Mistakes in Mathematics

by Alfred S. Posamentier
Ingmar Lehmann
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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 Decouverte 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.

  • Creators

  • Publisher

  • Release date

    June 28, 2019

  • Formats

    • Kindle Book

    • OverDrive Read

      • ISBN: 9781616147488

    • EPUB ebook

      • ISBN: 9781616147488
      • File size: 5467 KB

  • Languages

    • English

  • Reviews

    • Library Journal

      August 1, 2013

      Posamentier (mathematics education, Mercy Coll.) and Lehmann (formerly, mathematics, Humboldt Univ., Berlin), coauthors of several math books, present a compendium of mathematical errors, arranged by topic into five chapters. Only the first, on errors made by eminent mathematicians, has much narrative. Here, we see number-theoretic conjectures that were based upon a few examples and a lot of wishful thinking. In Chapter Two, the authors address errors in arithmetic based mostly upon misunderstandings of notations. Chapter Three deals with algebraic errors primarily caused by inadvertent division by zero or the introduction of extraneous roots. In Chapter Four we have errors in geometric proofs, mostly arising from deliberately misleading diagrams. The final chapter deals with probability, showing mistakes made by confusing the concepts of conditionality, independence, and mutual exclusivity of events. Many of the errors are clever and instructive, some are repetitive and uninteresting; only a few should be designated as "magnificent." VERDICT This volume could be useful to a teacher of mathematics as a source of examples that can hammer home important concepts. Beyond that, it will have a limited readership.--Harold D. Shane, Mathematics, Emeritus, Baruch Coll., CUNY

      Copyright 2013 Library Journal, LLC Used with permission.

Formats

  • Kindle Book
  • OverDrive Read
  • EPUB ebook

subjects

Languages

  • English

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