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The most ubiquitous, and perhaps the most intriguing, number
pattern in mathematics is the Fibonacci sequence. In this simple
pattern beginning with two ones, each succeeding number is the sum
of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13,
21, ad infinitum). Far from being just a curiosity, this sequence
recurs in structures found throughout nature - from the arrangement
of whorls on a pinecone to the branches of certain plant stems. All
of which is astounding evidence for the deep mathematical basis of
the natural world. With admirable clarity, two veteran math
educators take us on a fascinating tour of the many ramifications
of the Fibonacci numbers. They begin with a brief history of a
distinguished Italian discoverer, who, among other accomplishments,
was responsible for popularizing the use of Arabic numerals in the
West. Turning to botany, the authors demonstrate, through
illustrative diagrams, the unbelievable connections between
Fibonacci numbers and natural forms (pineapples, sunflowers, and
daisies are just a few examples). In art, architecture, the stock
market, and other areas of society and culture, they point out
numerous examples of the Fibonacci sequence as well as its
derivative, the "golden ratio." And of course in mathematics, as
the authors amply demonstrate, there are almost boundless
applications in probability, number theory, geometry, algebra, and
Pascal's triangle, to name a few.Accessible and appealing to even
the most math-phobic individual, this fun and enlightening book
allows the reader to appreciate the elegance of mathematics and its
amazing applications in both natural and cultural settings.
We all learned that the ratio of the circumference of a circle to
its diameter is called pi and that the value of this algebraic
symbol is roughly 3.14. What we weren't told, though, is that
behind this seemingly mundane fact is a world of mystery, which has
fascinated mathematicians from ancient times to the present. Simply
put, pi is weird. Mathematicians call it a transcendental number
because its value cannot be calculated by any combination of
addition, subtraction, multiplication, division, and square root
extraction. In this delightful layperson's introduction to one of
math's most interesting phenomena, Drs. Posamentier and Lehmann
review pi's history from prebiblical times to the 21st century, the
many amusing and mind-boggling ways of estimating pi over the
centuries, quirky examples of obsessing about pi (including an
attempt to legislate its exact value), and useful applications of
pi in everyday life, including statistics. This enlightening and
stimulating approach to mathematics will entertain lay readers
while improving their mathematical literacy.
Dieses Lehrbuch ist eine leicht verstandliche Einfuhrung in
wichtige Grundbegriffe der Mathematik und es wendet sich sowohl an
kunftige als auch an bereits unterrichtende Mathematiklehrer. Die
zentralen Begriffe Menge, Relation und Funktion sind feste
Bestandteile des Mathematikunterrichts in allen Schulformen. Viele
mathematische Zusammenhange lassen sich mit Hilfe des
Mengenbegriffs anschaulich und einfach darstellen. Die wichtigsten
hierfur erforderlichen Grundlagen werden im Kapitel "Mengen"
bereitgestellt. Den Schwerpunkt im Kapitel "Relationen" bilden die
AEquivalenzrelationen und die Ordnungsrelationen, mit denen sich
die Mengen strukturieren lassen. Im Kapitel "Funktionen" werden
vorzugsweise solche grundlegenden Begriffe behandelt, die
einerseits im Mathematikunterricht bereits im Vorfeld der Analysis
eine Rolle spielen, andererseits der Vorbereitung auf die
Differential- und Integralrechnung dienen.
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.
If you've been waiting for a book that will evoke the delight and
intrigue that mathematics has to offer, this is the book for you.
What are the odds of finding two people who share the same birth
date in a room of thirty-five? Most people would guess they're
pretty low. In actuality, the probability is better than 80
percent. This is just one of many entertaining examples of
mathematical curiosities presented. Two veteran math educators have
created the perfect introduction to the wonders of mathematics for
the general reader, requiring only a high school background in the
subject.
Among the entertaining and useful tricks they teach are shortcuts
in arithmetic, such as ways to determine at a glance the exact
divisors of any given number. They also demonstrate how the
properties of certain numbers can lead to infinite loops. What is
particularly exciting is how many correct answers turn out to be
counterintuitive. Exploring all these features will instill
insights into the nature of numbers, improve your ability to
manipulate them, and give you an appreciation for the inherent
elegance of mathematics.
As you marvel at the many unusual relationships and novelties
revealed in this ingenious and delightful presentation, you'll be
learning more math than you ever thought possible - and will be
relishing every moment of it
An innovative and appealing way for the layperson to develop math
skills--while actually enjoying it
Most people agree that math is important, but few would say it's
fun. This book will show you that the subject you learned to hate
in high school can be as entertaining as a witty remark, as
engrossing as the mystery novel you can't put down--in short, fun
As veteran math educators Posamentier and Lehmann demonstrate, when
you realize that doing math can be enjoyable, you open a door into
a world of unexpected insights while learning an important skill.
The authors illustrate the point with many easily understandable
examples. One of these is what mathematicians call the "Ruth-Aaron
pair" (714 and 715), named after the respective career home runs of
Babe Ruth and Hank Aaron. These two consecutive integers contain a
host of interesting features, one of which is that their prime
factors when added together have the same sum.
The authors also explore the unusual aspects of such numbers as 11
and 18, which have intriguing properties usually overlooked by
standard math curriculums. And to make you a better all-around
problem solver, a variety of problems is presented that appear
simple but have surprisingly clever solutions.
If math has frustrated you over the years, this delightful approach
will teach you many things you thought were beyond your reach,
while conveying the key message that math can and should be
anything but boring.
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