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Proofs Without Words II: More Exercises in Visual Thinking (Classroom Resource Materials) (v. 2) 1st Edition

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Roger B. Nelsen (Author)
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4 out of 5 stars 2 customer reviews
ISBN-13: 978-0883857212
ISBN-10: 0883857219
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Product Details

  • Series: Classroom Resource Materials
  • Paperback: 142 pages
  • Publisher: The Mathematical Association of America; 1st edition (February 15, 2001)
  • Language: English
  • ISBN-10: 0883857219
  • ISBN-13: 978-0883857212
  • Product Dimensions: 6 x 0.5 x 9 inches
  • Shipping Weight: 8 ounces (View shipping rates and policies)
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #883,240 in Books (See Top 100 in Books)

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18 of 21 people found the following review helpful
The Mystery of the Missing Words
By Mary P. Campbell on February 25, 2003
Format: Paperback
Most of the "proofs" in this book will be of more
use and interest to math teachers -- how many
people want to see 10 different diagrams showing
trigonometric identities? Still, much is of great
use to teachers; the standard textbooks are often
redundant in their figures and thus bore students
in their predictability. As well, students are in
need of stretching their mathematical intuitions
and understanding -- when all right triangles are
shown with the legs parallel to the pages' sides,
when all variables are either x or y, people think
that math is a matter of grinding through standard
procedures. PROOFS WITHOUT WORDS II links
subjects that are usually treated disparately:
geometry is connected to combinatorics (a fancy
name for counting), calculus, and linear algebra.
Many of the most technical figures are accompanied
by equations and words explaining the use. The
back cover blurb does admit that many of the
proofs aren't actually wordless, but I'm sure no
one will sue them for false advertising -- these
problems would be difficult to interpret
otherwise.
However, the math enthusiast will be most rewarded
by the figures with the least amount of words, for
they provide mini-mysteries to be solved. The
book starts with six different figures proving the
Pythagorean Theorem -- and only one has any kind
of "language" on it (a few variables and their
products). These examples' author range from a
10th century Arab mathematician, a 3rd century
Chinese mathematician, and Leonardo da Vinci to
current contributors to the journals from the
Mathematical Association of America.Read more ›
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1 of 1 people found the following review helpful
While these are not proofs in the formal sense, they are in the practical sense
By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on April 17, 2008
Format: Paperback
While the entries in this book are not proofs in the classical sense, they are so in the effective sense. The simple diagrams show the way to the solution and in most cases, all that is needed is to include the words that justify the inclusion of the various features of the diagram. Humans are visual creatures, there is no better way to teach and understand than by the presentation of an effective diagram.
Teaching mathematics is largely an exercise in giving the students an explanation as to why something is true, initially rigor is beyond them. In fact, maintaining formal mathematical rigor early in the introduction is generally counterproductive. The sensible and understandable diagram is the best approach and this book contains diagrams that will allow the student (and teacher) to make sense of many mathematical topics.
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