Marvels of Math: Fascinating Reads and Awesome Activities

331 Pages·1998·0.99 MB·English

by  Kendall Haven

Marvels of Math : Fascinating Reads and
title:
Awesome Activities
author: Haven, Kendall F.
publisher: Libraries Unlimited
isbn10 | asin: 1563085852
print isbn13: 9781563085857
ebook isbn13: 9780585219011
language: English
Mathematics--History, Mathematics--
subject
Miscellanea.
publication date: 1998
lcc: QA21.H32 1998eb
ddc: 510
Mathematics--History, Mathematics--
subject:
Miscellanea.
Page iii
Marvels of Math
Fascinating Reads and Awesome Activities
Kendall Haven
1998
Teacher Ideas Press
A Division of Libraries Unlimited, Inc.
Englewood, Colorado
Page iv
To every person who has found joy and intrigue
in a math puzzle, and to every mind who ever
gazed with wonder and curiosity at our system of
numbers and math.
Copyright © 1998 Kendall Haven All Rights Reserved Printed in the
United States of America
No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise, without the prior
written permission of the publisher. An exception is made for individual
librarians and educators, who may make copies of portions of the book
(up to 15 pages) for use in a single school or library. Standard citation
information should appear on each page.
TEACHER IDEAS PRESS A Division of Libraries Unlimited, Inc. P.O.
Box 6633 Englewood, CO 80155-6633 1-800-237-6124 www.lu.com/tip
Production Editor: Kevin W. Perizzolo Copy Editor: Curtis D. Holmes
Proofreader: Susie Sigman Indexer: Lee Brower Typesetter: Kay Minnis
Library of Congress Cataloging-in-Publication Data
Haven, Kendall F.
Marvels of math: fascinating reads and awesome activities /
by Kendall Haven.
xii, 172 p. 17×25 cm.
Includes bibliographical references and index.
ISBN 1-56308-585-2 (pbk.)
1. MathematicsHistory. 2. MathematicsMiscellanea. I. Title.
QA21.H32 1998510dc21 98-34084
CIP
Page v
CONTENTS
Introduction ix
Stories About Numbers
Numbers in the Sand 3
The Invention of Irrational Numbers by the Pythagoreans
circa 520 BC
At a Glance 3
Terms to Know 3
Numbers in the Sand 5
Follow-on Questions and Activities to Explore 12
Something from Nothing 13
The Invention of Zero as a Number by al-Khwarizmi in AD
800
At a Glance 13
Terms to Know 14
Something from Nothing 15
Follow-on Questions and Activities to Explore 22
Imagine That 23
The Invention of Imaginary Numbers by Rafael Bombelli in
1545
At a Glance 23
Terms to Know 24
Imagine That 25
Follow-on Questions and Activities to Explore 30

Page vi
Infinity . . . and Beyond! 31
The Invention of "Surreal" Numbers by John Conway and
Martin Kruskal in 1992
At a Glance 31
Terms to Know 32
Infinity . . . and Beyond! 33
Follow-on Questions and Activities to Explore 39
Stories About Geometry
Elementary Elements 43
The Invention of Euclidean Geometry by Euclid in 295 BC
At a Glance 43
Terms to Know 44
Elementary Elements 45
Follow-on Questions and Activities to Explore 50
"Flying" High 51
The Invention of Cartesian Coordinates by Rend Descartes
in the 1620s
At a Glance 51
Terms to Know 51
"Flying" High 53
Follow-on Questions and Activities to Explore 59
Shadow Boxing 60
The Invention of Perspective Geometry by Girard Desargues
in 1635
At a Glance 60
Terms to Know 60
Shadow Boxing 62
Follow-on Questions and Activities to Explore 69
Stories About Mathematical Concepts
The Weighing Game 73
The Invention of Specific Gravity and Buoyancy by
Archimedes in 232 BC
At a Glance 73
Terms to Know 73
The Weighing Game 75
Follow-on Questions and Activities to Explore 81
Page vii
The Odds Are . . . 83
The Invention of Probability Theory by Pierre de Fermat in
1654
At a Glance 83
Terms to Know 83
The Odds Are 85
Follow-on Questions and Activities to Explore 92
Smaller Makes Bigger 93
The Invention of Calculus by Isaac Newton in 1666
At a Glance 93
Terms to Know 94
Smaller Makes Bigger 95
Follow-on Question and Activity to Explore 102
A Bridge to Math 104
The Invention of Topology by Leonhard Euler in 1736
At a Glance 104
Terms to Know 104
A Bridge to Math 106
Follow-on Questions and Activities to Explore 112
The Truth About "M. Le Blanc" 113
Sophie Germain's Start Toward Her Development of the
Theory of Elasticity in 1794
At a Glance 113
Terms to Know 113
The Truth About "M. Le Blanc" 114
Follow-on Questions and Activities to Explore 119
Out of Time 120
The Invention of Group Theory by Evarstie Galois in 1831
At a Glance 120
Terms to Know 120
Out of Time 122
Follow-on Questions and Activities to Explore 128
Page viii
One Step Forward, One Step Back 129
The Theory of Sequences and lmproved Algebraic
Solutions by Sonya Kovalevsky, in the 1870s
At a Glance 129
Terms to Know 129
One Step Forward, One Step Back 131
Follow-on Questions and Activities to Explore 138
Stories About Calculating Machines
No Bones About It! 141
The Invention of "Napier's Bones" by John Napier in 1605
At a Glance 141
Terms to Know 141
No Bones About It! 143
Follow-on Questions and Activities to Explore 150
Amazing Grace 152
The Invention of Computer Languages by Grace Hopper in
1944
At a Glance 152
Terms to Know 153
Amazing Grace 154
Follow-on Questions and Activities to Explore 159
References 161
Index 167
About the Author 172
Page ix
INTRODUCTION
We tend to view math as either an interesting game to play, or an endless
maze of rote memorization, unintelligible rules and theorems, and mind-
numbing equations stuffed with incomprehensible symbols.
I have heard middle school students groan, "Where'd this stuff come from?"
When I have asked where they thought it came from, the general answer is
that our current set of real and complex numbers and the full range of
arithmetic, algebra, geometry, trigonometry, and calculus have always been
here. It's as if the Big Bang created both expanding hydrogen and helium
particles and the numbers and math processes to describe and analyze them.
They feel that mathematics is a rigid, unfriendly system that has existed
inalterably throughout all time.
They couldn't be more mistaken. Mathematics has evolved to meet specific
human problem-solving needs. People created every bit of our number and
math systems. They invented it. They created the math that they needed to
solve everyday, practical problems, and to describe everyday, real-world
phenomenafrom the first invention of whole numbers to describe the
members of groups (the number of sheep in a pen, saber-tooth tigers on the
hunt, or mouths to feed at dinner) to the recent development of chaos theory
and surreal numbers.
All of math was not invented back in dim-dark ancient history. Roman
numerals do not have a zero, and neither did the Greek letter-based system for
representing numbers. Zero was first recognized as a number in 800.
AD
It wasn't until the thirteenth century that most of Europe accepted, and began
to use, the Arabic number system and zero. As late as the fourteenth century,
many cultures didn't acknowledge the existence of negative numbers,
claimingas did the mighty Greeksthat it was impossible to have less than
nothing. Complex numbers weren't created until the sixteenth century.
Even more exciting, new math concepts and approaches are still being
discovered and invented. For example, surreal numbers, a nifty way to count
beyond infinity, were invented in 1992. Much of the math learned over your