The A to Z of Mathematics: A Basic Guide

483 Pages·2002·1.41 MB·English

by  Thomas H. Sidebotham

The A to Z of Mathematics
The A to Z of Mathematics
A Basic Guide
Thomas H. Sidebotham
St.Bede’sCollege
Christchurch,NewZealand
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TheAtoZofMathematics:ABasicGuide—ThomasH.Sidebotham
ISBN0-471-15045-2
PrintedintheUnitedStatesofAmerica.
10 9 8 7 6 5 4 3 2 1
Tomywife,Patricia
Whopersuadedmetogetstartedand
supportedmeuntilitwasfinished
Contents
Preface...................................................................ix
Acknowledgments........................................................xi
A.........................................................................1
B........................................................................48
C........................................................................63
D.......................................................................145
E.......................................................................167
F.......................................................................197
G.......................................................................214
H.......................................................................234
I........................................................................245
K.......................................................................269
L.......................................................................272
M......................................................................281
N.......................................................................296
O.......................................................................306
P.......................................................................314
vii
viii CONTENTS
Q.......................................................................358
R.......................................................................371
S.......................................................................399
T.......................................................................433
U.......................................................................463
V.......................................................................464
W......................................................................471
X.......................................................................472
Y.......................................................................473
Z.......................................................................474
Preface
Throughouttheworldmanypeoplesufferfromthesameproblem:mathanxiety.No
other area of skill seems to polarize people so readily into two contrasting groups,
thosewhocandomathandthosewhocannot.Ofthetwogroups,thesecondoneis
byfarthelarger.Tosucceedinmathematicsyouneedtounderstandthebasics,and
onlythencanyoulearnwithconfidence.Manypeoplefallatthisfirsthurdleandthen
strugglelater.Myaiminwritingthisbookistoguideyouthroughthebasicssothat
youcandevelopanunderstandingofmathematicalprocesses.Asyoustudythisbook
you will become aware of how mathematics relates to everyday life and situations
withwhichyouarefamiliar.Studythisbookindepth,simplybrowse,orsearchfor
themeaningofaword,andlearnyourmathagain.Whyshouldyougotothistrouble?
Whateveryourage,mathematicsisoneofthebasicrequirementsoflife.Thisstudy
ofmathematicswillmakeadifference.
Thisbookiswritteninanappropriatelanguageforexplainingbasicmathematics
tothegeneralreader,andusesexamplesdrawnfromeverydaylife.Therearemany
workedexampleswithdetailedstepsofworking.Eachstepofworkingisaccompa-
niedbyanexplanation.ItisthisprocessofshowingHOWandexplainingWHYthat
givesthisbookitsuniquestyle.Thosemathematicalabbreviationsthatoftenfrustrate
readersarewritteninfullandthetextis“user-friendly.”Forquickreferencethefor-
matofthebookisalphabetical,anditcoverstopicsinbasicmathematics.Theyare
linkedtogetherwithcross-referencessothatathemecanbefollowedthrough.This
bookisagreatdealmorethanadictionary.Undereachentrythereisastraightfor-
wardexplanationoftheterm,followedinmanycasesbycarefullyworkedexamples,
showing the relevance of mathematics in the world around us. At the end of some
entriesthereaderisdirectedtootherreferencesinthebookifsomepriorknowledge
isneeded.Themathematicsisreliableanduptodate,andencompassesawiderange
oftopicssothateveryonewillfindsomethingofinterest.
ix
x PREFACE
Thematerialinthebookfallsintothreecategories.
1. Thereareprocessesthatexplainspecificskills;atypicalexampleistheentry
Algebra.
2. There are straightforward definitions of words with applications in the world
aroundus,asintheentryProportion.
3. There is a variety of enrichment material that has good entertainment value,
likeHexomino.
I believe there is something of interest for everyone. If you are curious about
mathematics and it intrigues you, now may be the time to take the initiative and
discover that you indeed have skills in this area of knowledge. Some people need
the maturity of a few more years before they achieve success. If you are making a
career change and need to revise your mathematical knowledge, then this book is
foryou.Thebookwillappealtoeveryone,evenstudents,whomaybeinterestedin,
or need to catch up on, basic mathematics. If you are a parent who desires to help
yoursonordaughterandlacktheexpertise,thenthisbookisforyoualso.Thestyle
and presentation of the book are chosen specifically to suit the lay reader. It is a
usefulresourceforhomeschoolingsituations.Ihopeitisarichsourceofideasfor
mathematicsteachersandalsothosewhoareinteachertraining,whateversubjectin
whichtheyarespecializing.
You will need a scientific calculator to follow through the steps of working in
some of the examples. In statistical topics the reader is referred to the calculator
handbook for its use, because brands of calculators can vary so much. The whole
bookiscross-referenced.Ifreadersarenotfamiliarwiththeexplanationsgivenina
specificentry,theyareadvisedtofirstreadthereferencesattheendoftheentryto
prepare the groundwork. This book contains an abundance of diagrams, equations,
tables,graphs,andworkedexamples.AnemphasisisplacedonSIunitsthroughout.
Ifyouarekeentoacquirethebasicskillsofmathematicsinthisbook,Iofferthe
followingadvice.Donotreaditlikeyoumayreadanovelinwhichyoucanskimand
stillenjoythebookandhaveagoodgraspofthestoryandplot.Tograspmathematics
youmustexaminethedetailofeverywordandsymbol.Haveapen,acalculator,and
paperathandtotryouttheprocessesandverifythemforyourself.
It is my hope that this book will be on a bookshelf in every home, and will be
usedbyfamilymembersasareferenceandguide.Iamsureyouwillfindituseful,
interesting,andentertaining.
TomSidebotham
Acknowledgments
I take this opportunity to thank the following persons, without whose help and
guidance this book would not have been possible: Steve Quigley, for encouraging,
enthusing,andredirectingme,andforsharingthevision;HeatherHaselkorn,forall
her efforts on my behalf to keep the project afloat and for maintaining the lines of
communication;DavidByatt,forscrutinizingthetextandofferingjudiciousalterna-
tives(theaccuracyisentirelytheresponsibilityoftheauthor);Dr.DavidSidebotham,
forhiscomputerskillsinenablingmetotransplantthebookinNewYork;Stephanie
Lentz and her team at TechBooks for transforming my manuscript so wonderfully
well;andlastly,theAngelatmyelbowthroughoutthewriting.
xi
TheAtoZofMathematics:ABasicGuide.
ThomasH.Sidebotham
Copyright(cid:182)2002JohnWiley&Sons,Inc.
ISBN:0-471-15045-2
A
ABSOLUTEVALUE
The absolute value of a number is the distance of the number from the origin 0,
measuredalongthenumberline.Intheaccompanyingfiguretheabsolutevalueof3
atpoint B isthedistanceofpoint B from0,whichis3.Theabsolutevalueof−2at
point Aisthedistanceofpoint Afrom0,whichis2.
A B
−3 −2 −1 0 1 2 3 4
The symbol for the absolute value of a number is two vertical parallel lines placed
aroundthenumber.AtthepointB,theabsolutevalueof3iswrittenas
|pointB−point0|=|3−0|
=|3|
=3
If the subtraction had taken place in the opposite way, the answer would still be 3,
buttheworkingwouldbe
Absolutevalueof3=|point0−pointB|
=|0−3|
=|−3|
=3 asbefore
SimilarlyforthepointA:
Absolutevalueof−2=|pointA−point0|
=|−2−0|
=|−2|
=2
1