Mathematical Fallacies and Paradoxes [Paperback]

Bryan Bunch (Author)

Book Description

Publication Date: July 1, 1997

Stimulating, thought-provoking analysis of a number of the most interesting intellectual inconsistencies in mathematics, physics, and language. Delightful elucidations of methods for misunderstanding the real world of experiment (Aristotle's Circle paradox), being led astray by algebra (De Morgan's paradox), and other mind-benders. 1982 edition.

Product Details

• Paperback: 224 pages
• Publisher: Dover Publications (July 1, 1997)
• Language: English
• ISBN-10: 0486296644
• ISBN-13: 978-0486296647
• Product Dimensions: 8.5 x 5.4 x 0.5 inches
• Shipping Weight: 8.8 ounces (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #756,780 in Books (See Top 100 in Books)

More About the Author

BOOKS BY BRYAN BUNCH
201? Figures among the Stars (YA novel about adventures of young Archimedes and his friends)
2004 The History of Science and Technology, Houghton-Mifflin (with Alexander
Hellemans); also available in leather-bound Easton Press edition.
2003 Discover Science Almanac, Hyperion (with Jenny Tesar)
2001 Blackbirch Encyclopedia of Science and Invention, Blackbirch Press (with Jenny Tesar).
2000 Penguin Desk Encyclopedia of Science and Mathematics, Penguin U.S.A. (with Jenny Tesar--named by AAAS Science Books as one of the three best science reference books of the year)
The Kingdom of Infinite Number: A Field Guide, W.H. Freeman (Natural Science Book Club selection; New York Public Library 2001 Books for Teen Age List)
1998 Satellites and Probes (with Clint Hachett; vol. 12 of Outer Space), Grolier. Highly recommended by Book Report November/December 1998.
Family Encyclopedia of Disease, W. H. Freeman (Editor).
1997 Mathematical Fallacies and Paradoxes, Dover Publications (paperbound)
1996 The Globe Junior High School Science Series, New Revised Edition, Globe Book Company (Senior Author).
Handbook of Current Science and Technology (Gale Research).
1994 Handbook of Current Health and Medicine (Gale Research).
1993 The Timetables of Technology (with Alexander Hellemans), Simon and Schuster; also available as a CD ROM in 1997.
1992 The Henry Holt Handbook of Current Science and Technology, Henry Holt and Company; listed by Library Journal as one of the best science books of 1992 and by the American Librarians Association among the best reference sources of 1992.
1991 The Timetables of Science, new, updated edition (with Alexander Hellemans), Touchstone Books (Library of Science Book Club, Quality Paperback Book Club)
1990 Excel in Graphing Level H (with Margaret Hill), Modern Curriculum Press.
1989 Reality's Mirror: Exploring the Mathematics of Symmetry, John Wiley; listed by Library Journal as one of the best science books of 1989; also published in Japan in Japanese.
1988 The Timetables of Science (with Alexander Hellemans), Simon and Schuster; also published in England, in Germany (in German), in Japan (in Japanese), and Romania (in Rumanian).
1986 The Globe Junior High School Science Series, Globe Book Company (Senior Author).
1985 Harper & Row Elementary Mathematics, Grades K 8, Macmillan McGraw (Co author).
1984 The Science Almanac, Doubleday
A Practical Herb Garden (with recipes), TAB Books.
1983 Algebra One, McDougal, Littell (Co author). Fun with Math, World Book Childcraft.
1982 Mathematical Fallacies and Paradoxes, Van Nostrand Reinhold Company (Library of Science Book Club); also published in Japan in Japanese.
Mathematics 7 and Mathematics 8, Harper & Row Publishers (Co author).
ARTICLES BY BRYAN H. BUNCH
2006 Additional articles in Diseases, 3rd Edition, Grolier/Scholastic
2001 Various articles in Diseases, 2nd Edition, Grolier
1998 16 biographies of scientists for Notable Twentieth-Century Scientists, Gale Research; 50 or more Science, Technology, and Science features for the McGraw-Hill Elementary Science 2000, McGraw-Hill. "Physical and Psychological Stress" and "The Cell" for Grolier Information Service. Fourth-grade physics units for Harcourt Elementary Science 2000 (Harcourt Brace).
1997 "Pythagoras of Samos" and "Huygens, Christiaan," The New Book of Knowledge, Grolier." Alzheimer's Disease," "Depressive Illness," "Hepatitis," and "Trigonometry" for Grolier Information Service.
1996 Various articles in Diseases, Grolier. "Gauss, Karl Friedrich," The New Book of Knowledge, Grolier.
1995 Revision of "Calculus," The Volume Library, Southwestern.
1993 "History of Mathematics" and "Number Names," The New Book of Knowledge, Grolier. Revision of The Mathematics Volume of The Volume Library, Southwestern.
1990 "Ice Ages," The New Book of Knowledge, Grolier.
1989 "The Electron Microscope," The New Book of Knowledge, Grolier.
1988 Revision of The Mathematics Volume of The Volume Library, Southwestern
1987 "Technology and Society" and "The Growth of the Factory" The New Book of Popular Science, Grolier "New Energy Technology" and "Timeline of Technology," The Volume Library, Southwestern. "Taking Major Tests," The Family Handbook, Southwestern.
1984 "Anthropology" and "Archaeology", The Volume Library, Southwestern.
1983 "Mathematics" (Volume 1 and volume 2) Student Handbook, Southwestern. The World Book of Math Power (coauthor), World Book Childcraft.
1982 "Religion," "Animal Behavior," "Astronautics," "Growing Plants," "New Concepts in Mathematics," and "Cosmology," The Volume Library, Southwestern.
1981 "Arithmetic," The Volume Library, Southwestern.
1979 Revision of "Mathematics," The New Book of Knowledge, Grolier.
1965 "Mathematics," "Number," "Numeral," and "Sets," The New Book of Knowledge,
Grolier.
1961 "Miniature Giants," Encyclopedia Yearbook, Grolier.
1959 64 Annual "The Year in Science," The Book of Knowledge Annual, Grolier.
1957 Poem "Excerpt from a Lecture," Riverside Poets 3, Twayne.



FREE LANCE WORK (BRYAN H. BUNCH)
2000 Writer/Editor: panoramas for Grolier Multi-Media Encyclopedia; Grolier. Consultant for
In the Jungle, Reader's Digest Children's Books.
1999 Writer/Editor: Earth Sciences for School (Macmillan); Consultant: Reader's Digest Children's Guide to the Universe (Reader's Digest); script for Gene Analysis (video, BFA Educational Media, with Alan McCormick)
1998 Consultant: Outer Space, Michael Friedman for Grolier ("Highly Recommended" by Book Report November/December 1998). Our Solar System, Looking into Space, The Human Body, The Solar System and The Human Body Zippers, Readers Digest.
1997 Consultant: CD ROM of The Timetables of Technology (Simon & Schuster Interactive/Byron Preiss).
1996 Consultant: The New York Public Library American History Desk Reference, Macmillan.
1995 Consultant: Member of Board of Advisors (for Mathematics) to The Gale Encyclopedia of Science (Gale Research). Mathematics consultant to The New Book of Knowledge (Grolier).
1994 Writer: Science test items for the states of Connecticut and Delaware. Consultant: New York Public Science Library Desk Reference (Prentice Hall).
1992 Writer: Science test items for the states of Kentucky and Connecticut. Sample Insight Card on Dialysis Machines (Mega Books). Consultant on Air and Space Adventure Cards (Grolier, Inc.).
1990 Writer: Criterion referenced tests for Scott Foresman mathematics program, Grade 7. Thematic tests in mathematics for Arizona. Editor: pre calculus mathematics for Houghton Mifflin.
1989 Writer: Problem solving worksheets, Grades 7 and 8, Macmillan elementary mathematics program. Tests for Grades 3 and 7, Scott Foresman mathematics program.
1987 Editor: "Hepatitis," "Plagues and History," and "Lung Cancer," Health and Medical Horizons 1988, Macmillan.
1986 Editor and Writer: Technology Volume in The Volume Library, Southwestern.
1984 Writer: Mathematics sections in Levels D F of Be a Better Reader, Prentice Hall. Environment and disease units for high school health textbook, Harcourt Brace Jovanovich.
1982 Writer: Mathematics history sections and features for Geometry, McDougal, Littell. Editor: "Health and Safety," "Life Science," "Physical Science," "Earth Science," "Space Science," "New Technology," "Biology," "Chemistry," and "Physics," Student Handbook, Southwestern.
1982 Writer: 12 chapters of elementary health for McDougal, Littell. 9 chapters of Jr. high health for Laidlaw Bros. Item Writer for science section of Survey of Basic Skills, Science Research Associates.
1980 Writer: Duplicating Masters for Grades 7 and 8 of Basic Reading Skills 7 & 8, Readers Digest.
1964 Editor: Mathematical Foundations for Social Analysis and Elements of Formal Logic, Bobbs Merrill.

OCCUPATIONS (BRYAN H. BUNCH)
1983 President, Scientific Publishing, Inc.
1983-1998 Adjunct Instructor in mathematics at Pace University, Pleasantville, New York
1981 Member of Board of Directors, Midstate College (Peoria, Illinois) accredited by the North Central Association of Colleges and Schools--since 1987, Secretary of the Board; from 1987 to 2001 Vice-President of the College
1981 Member of The Hudson Group, an organization of people who write books for a living; President 1984 1986, 1989, 1996
1980 Author and consultant.
1975 79 Senior Vice President and Editor in Chief, American Book Company, a company engaged solely in publishing elementary and secondary school textbooks; in charge of editorial and art departments and, for a time, the production department..
1960 75 Mathematics and Science Editor (1960 70) and head both departments; Associate Director of the School Department (1971 75), Harcourt Brace Jovanovich, supervising editorial development of elementary and secondary school textbooks.
1958 60 Assistant Editor of the Encyclopedia Yearbook, Grolier, Inc.
1957 58 English Teacher and Librarian, Tonica High School, Tonica, Illinois.

EDUCATION
1988 Audited History of Mathematics, Pace University
1959 65 Graduate studies in mathematics, New York University.
1957 58 Teaching Remedial Reading, Bradley University, Poetry Workshop,New School for Social Research
1954 57 BA in English, Trinity College, Hartford

ORGANIZATIONS AND HONORS
Who's Who in American Education: 1992 1993, Marquis Who's Who
Who's Who in Media and Communications: 1998 1999, Marquis Who's Who
Dictionary of International Biography, 28th Edition, International Biographical Centre
Outstanding People of the 20th Century, 1999, International Biographical Centre
Board of Directors, Pleasant Valley Library 1996-2010
Rotary 2004, President Rotary Club of Millbrook 2008-09
Board of Directors, Mid-Hudson Addiction Recovery Centers, Inc. 2003-
Board of Directors, MARC Foundation, Inc. 2002- President, 2004-

PERSONAL
Married, 3 children, 6 grandchildren


SCIENTIFIC PUBLISHING, INC. PROJECTS


Scientific Publishing is a corporate extension used primarily for development and production of books or other materials edited by or written by Bryan Bunch. It often produces finished pages--as files on disk today--for use in making film and plates, but can deliver manuscript instead of pages as needed by the publisher.

2006 Diseases , 3rd ed. (Grolier/Scholastic). Jenny Tesar, co-editor
2004 The History of Science and Technology, Houghton-Mifflin (with Alexander
Hellemans)
2001 Diseases, 2nd ed. (Grolier)
2000 The Penguin Desk Encyclopedia of Science and Mathematics, Penguin USA. The New York Times Almanac 2001 (science section), Penguin USA.
1999 The New York Times Almanac 2000 (science section), Penguin USA.
1998 Family Encyclopedia of Disease (W.H. Freeman). The New York Times Almanac 1999 (science section), Penguin USA. Updates of 31 articles for Grolier Information Service.
1997 Diseases (Grolier)--"highly recommended" by Booklist and The Book Report. The New York Times Almanac 1998 (science section), Penguin USA.
1996 Handbook of Current Science and Technology (Gale Research). The Universal Almanac, 1997 (Science section), Andrews and McNeel.
1995 The Universal Almanac, 1996 (Science section), Andrews and McNeel. Production of Globe Science Series (Globe Fearon).
1994 Handbook of Current Health and Medicine (Gale Research). The Universal Almanac, 1995 (Science section), Andrews and McNeel.
1993 The Timetables of Technology, Simon and Schuster. The Universal Almanac, 1994 (Science section), Andrews and McNeel.
1992 The Henry Holt Handbook of Current Science and Technology, Henry Holt and Company. The Universal Almanac, 1993 (Science section), Andrews and McNeel.
1991 The Timetables of Science, new updated edition, Touchstone Books. Wildlife Adventure Cards (initial set and teacher's material), Grolier. "Taking Major Tests," Volume Library, Southwestern. Data analysis of Encyclopedia Americana, Grolier. The Universal Almanac, 1992 (Science section), Andrews and McNeel.
1990 The Universal Almanac, 1991 (Science section), Andrews and McNeel.
1989 The Universal Almanac, 1990 (Science section), Andrews and McNeel. 10 new monthly issues of the Teacher's Guide to Partners in English, Reader's Digest.
1988 The Timetables of Science, Simon and Schuster. The New Golden Encyclopedia (Science and Technology articles), Western. Teacher's Guide to Partners in English (10 monthly issues), Reader's Digest.
1987 Technology Volume of The New Book of Popular Science, Grolier. Math Skillbuilder 5 (Golden Step Ahead Plus program), Western.
1986 Scientific Yearbook 1986, Facts on File. Math Skillbuilders 3 and Multiplication & Division (both Grades 3 and 4, Golden Step Ahead Plus series), Western.
1985 Medical Update 1986, World Book. Scientific Yearbook 1985, Facts on File.
1984 The Science Almanac, 1985 86, Doubleday. Medical Update 1985, World Book. Six books in the Golden Step Ahead series, Western.

Customer Reviews

Most Helpful Customer Reviews

34 of 35 people found the following review helpful:

5.0 out of 5 stars Intriguing, March 28, 2000

By 

mcgalaxy - See all my reviews

This review is from: Mathematical Fallacies and Paradoxes (Paperback)

Being a physicist who has always had an interest in math, I've found this book a good way to learn about aspects of mathematics usually saved for metamathematical philosophy courses. The book is not a textbook but it has enough depth for you to understand why paradoxes like Godel's, Grelling's and Russell arise and what their implications are. Each chapter gets more interesting and more complicated than the previous. Even though the book does not have a completely polished feel, I recommend it to any recreational mathematician.

18 of 18 people found the following review helpful:

5.0 out of 5 stars This is a Great Book for Math Fans, December 11, 2001

By A Customer

This review is from: Mathematical Fallacies and Paradoxes (Paperback)

This is a great book for people who love mathematics, including: recreational math enthusiasts, math teachers, professors and other university level math instructors, curious and self-motivated students, etc. This book provides numerous examples of how seemingly logical steps can lead to mathematically fallacious results. The level of math ranges from advanced high school to college level math, but the level is not really important ... what is important is the insights one can get from looking at common mathematical mistakes.

This book may also be of interest to neuroscientists, cognitive scientists, and psychologists who are interested in how human beings learn and apply mathematics. On a somewhat related note, I have noticed that (for some strange reason) this book has attracted a set of rather bizarre reviewers (see below). Please ignore them and buy this inexpensive and insightful book on math.

9 of 10 people found the following review helpful:

5.0 out of 5 stars Informal and engaging, August 21, 2005

By 

Skymariner (Canberra, Australia) - See all my reviews

This review is from: Mathematical Fallacies and Paradoxes (Paperback)

This is a great informal treatment of some of the more notable paradoxes and fallacies of mathematics and mathematical reasoning, old and new. Bunch's prose style is clear and unencumbered and his presentation of each topic - from his easily resolved fallacies and paradoxes of basic algebra and geometry to the deeper and unresolved paradoxes of logic and analysis - is always clean, well-illustrated and engaging.

At a glance, he treats:

The Liar paradox and Godel's Incompleteness theorems

Zeno's and the Sorites paradoxes and the conceptual difficulties associated with the continuum

The existence of irrational magnitudes and some basic philosophical issues associated with existence proofs

The Petersburg paradox

The paradoxes of Infinity and the Formalist and Intuitionist responses to them

The set theoretic paradoxes of Cantor, Russell, and Burali-Forti

The paradoxes of the axiom of choice including the Cantor diagonilisation, Skolem, Hausdorff and Tarski-Banach parodoxes

and a range of thought experiments which highlight the difficulties that may be asociated with applying abstract reasoning to the real world - notably those of the Thompson lamp experiment and Tarski-Banach golden sphere manufacturing plant.

If you want a good popular treatment of the subject matter with a detailed and informal emphasis on the key themes mathematical logic, then this is the book for you. The informal description Godel's first Incompleteness theorem is excellent, as is the discussion of the paradoxes of self reference as they appear in set theory and logic. As such, I would recommend it as excellent recreational reading for anyone with a budding interest in mathematical logic, whether they be math graduates or high-school students.