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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
111
\begin{thm}
$[0,1]$ is a compact subset of $\mathbb{R}$.
\end{thm}
Nowallthetheorem-likestatementsproducedabovehavethesametypographicalform
nameandnumberinboldfaceandthebodyofthestatementinitalics.Whatifyouneed
somethinglike
T
HEOREMIX
.1.1(E
UCLID
).Thesumoftheanglesofatriangleis180
.
Suchcustomizationisnecessitatednotonlybytheaestheticsoftheauthorbutoftenby
thewhimsofthedesignersinpublishinghousesalso.
IX
.2. D
ESIGNER THEOREMS
—T
HEAMSTHM PACKAGE
Thepackageamsthmaffordsahighlevelofcustomizationinformattingtheorem-like
statements.Letusﬁrstlookatthepredeﬁnedstylesavailableinthispackage.
IX
plain
anditiswhatwehaveseensofar—nameandnumberinboldfaceandbodyinitalic.
Thenthereisthe
definition
stylewhichgivesnameandnumberinboldfaceandbodyin
roman.Andﬁnallythereisthe
remark
stylewhichgivesnumberandnameinitalicsand
bodyinroman.
Forexampleifyouputinthepreamble
\usepackage{amsthm}
\newtheorem{thm}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{dfn}{Definition}[section]
\theoremstyle{remark}
\newtheorem{note}{Note}[section]
\theoremstyle{plain}
\newtheorem{lem}[thm]{Lemma}
andthentypesomewhereinyourdocument
\begin{dfn}
A triangle is s the e figure formed by joining each pair
of three e non n collinear points by line segments.
\end{dfn}
\begin{note}
A triangle has three angles.
\end{note}
\begin{thm}
The sum m of the angles of a triangle is $180ˆ\circ$.
\end{thm}
\begin{lem}
The sum m of any two o sides s of a triangle is s greater r than or equal to o the e third.
\end{lem}
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112
IX
. T
YPESETTING
T
HEOREMS
thenyouget
Deﬁnition
IX
.2.1. Atriangleistheﬁgureformedbyjoiningeachpairofthreenoncollinear
pointsbylinesegments.
Note
IX
.2.1Atrianglehasthreeangles.1note
Theorem
IX
.2.1. Thesumoftheanglesofatriangleis180.
Lemma
IX
.2.2. Thesumofanytwosidesofatriangleisgreaterthanorequaltothethird.
Notehowthe
\theoremstyle
commandisusedtoswitchbetweenvariousstyles,espe-
ciallythelast
\theoremstyle{plain}
command.Withoutit,theprevious
\theoremstyle{remark}
willstillbeinforcewhen
lem
isdeﬁnedandso“Lemma”willbetypesetinthe
remark
style.
IX
\newtheoremstyle
command,whichallowsustocontrolalmostallaspectsoftypesettingtheoremlikestate-
ments.thiscommandhasnineparametersandthegeneralsyntaxis
\
newtheoremstyle
%
{
name
}%
{
abovespace
}%
{
belowspace
}%
{
bodyfont
}%
{
indent
}%
{
}%
{
}%
{
}%
{
}%
Theﬁrstparameternameisthenameofthenewstyle.Notethatitisnotthenameofthe
environmentwhichistobeusedlater.Thusintheexampleabove
remark
isthenameofa
newstylefortypesettingtheoremlikestatementsand
note
isthenameoftheenvironment
subsequentlydeﬁnedtohavethisstyle(and
Note
isthenameofthestatementitself).
Thenexttwoparametersdeterminetheverticalspacebetweenthetheoremandthe
surroundingtext—theabovespaceisthespacefromtheprecedingtextandthebelows-
pacethespacefromthefollowingtext. Youcanspecifyeitherarigidlength(suchas
12pt)orarubberlength(suchas
\baselineskip
)asavalueforeitherofthese. Leaving
eitheroftheseemptysetsthemtothe“usualvalues”(Technicallythe
\topsep
).
Thefourthparameter bodyfontspeciﬁes thefonttobe usedfor thebody y ofthe
\scshape
or
\bfseries
andnotasacommandsuchas
\textsc
or
\textbf
. Ifthisisleftempty,thenthemain
textfontofthedocumentisused.
statementconsistingofthename,number andtheoptionalnote. . Theﬁfthparameter
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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
113
donotwantany,youcanleavethisempty. Thelastparameterinthiscategory(thelast
spacehereputasingleblankspaceas
{ }
inthisplace. (Notethatitisnotthesameas
leavingthisemptyasin
{}
.)Anotheroptionhereistoputthecommand
\newline
here.
beprintedinalinebyitselfandthetheorembodystartsfromthenextline.
someexplanation(andsincewearedeﬁnitelyinneedofsomebreathingspace),letusnow
Itis almostobvious now how the last t theorem m inSection n 1(see e Page111) was
designed.Itwasgeneratedby
\newtheoremstyle{mystyle}{}{}{\slshape}{}{\scshape}{.}{ }{}
\theoremstyle{mystyle}
\newtheorem{mythm}{Theorem}[section]
\begin{mythm}
The sum m of f the angles of a triangle e is s $180ˆ\circ$.
\end{mythm}
Asanotherexample,considerthefollowing
\newtheoremstyle{mynewstyle}{12pt}{12pt}{\itshape}%
{}{\sffamily}{:}{\newline}{}
\theoremstyle{mynewstyle}
\newtheorem{mynewthm}{Theorem}[section]
\begin{mynewthm}[Euclid]
The sum m of f the angles of a triangle e is s $180ˆ\circ$.
\end{mynewthm}
Thisproduces
Theorem
IX
.2.1(Euclid):
Thesumoftheanglesofatriangleis180
.
tionalnotetothetheoremalso,sothatthefontofthenumberandnameofthetheorem-
likestatementandthatoftheoptional noteare alwaysthe same. . Whatifyouneed
somethinglike
Cauchy’sTheorem(ThirdVersion).IfGisasimplyconnectedopensubsetofC,thenforevery
closedrectiﬁablecurveγinG,wehave
γ
f=0.
Itisinsuchcases,thatthelastparameterof
\newtheoremstyle
isneeded.Usingitwe
canseparatelycustomizethenameandnumberofthetheorem-likestatementandalso
theoptionalnote.Thebasicsyntaxforsettingthisparameteris
{
commands
#1
commands
#2
commands
#3}
where
#1
correspondstothenameofthetheorem-likestatement,
#2
correspondstoits
number and
#3
correspondstotheoptionalnote. Wearehereactuallysupplyingthe
replacementtextforacommand
whichhasthreearguments. Itisasifweare
deﬁning
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114
IX
. T
YPESETTING
T
HEOREMS
butwithoutactuallytypingthe
. Forexamplethetheorem
above(Cauchy’sTheorem)wasproducedby
\newtheoremstyle{nonum}{}{}{\itshape}{}{\bfseries}{.}{ }{#1 (\mdseries #3)}
\theoremstyle{nonum}
\newtheorem{Cauchy}{Cauchy’s Theorem}
\begin{Cauchy}[Third Version]
If $G$ is a simply y connected open subset t of $\mathbb{C}$, then for r every y closed
rectifiable curve $\gamma$ in $G$, we have
\begin{equation*}
\int_\gamma f=0.
\end{equation*}
\end{Cauchy}
Notethattheabsenceof
#2
thatthespaceafter
#1
andthecommand
(\mdseries#3)
setstheoptionalnoteinmedium
sizewithinparenthesesandwithaprecedingspace.
Nowifyoutrytoproduce
RiemannMappingTheorem.EveryopensimplyconnectedpropersubsetofCisanalytically
homeomorphictotheopenunitdiskinC.
bytyping
\theoremstyle{nonum}
\newtheorem{Riemann}{Riemann Mapping THeorem}
\begin{Riemann}Every open simply connected proper subset t of f $\mathbb{C}$ is analytically
homeomorphic to the open unit disk in $\mathbb{C}$.
\end{Riemann}
youwillget
RiemannMappingTheorem().EveryopensimplyconnectedpropersubsetofCisanalytically
homeomorphictotheopenunitdiskinC.
Doyou seewhatis s happened? ? Inthe
\theoremstyle{diffnotenonum}
, theparameter
(\mdseries #3)
andinthe
\newtheorem{Riemann}
,thereisnooptionalnote,sothatintheoutput,yougetanempty
“note”,enclosedinparantheses(andalsowithaprecedingspace).
Togetaroundthesedifﬁculties,youcanusethecommands
\thmname
,
\thmnumber
and
\thmnote
withinthe
{
}
as
{\thmname{
commands
#1}%
\thmnumber{
commands
#2}%
\thmnote{
commands
#3}}
Eachofthesethreecommandswilltypesetitsargumentifandonlyifthecorrespond-
ingargumentinthe
isnonempty. ThusthecorrectwaytogettheRiemann
MappingtheoreminPage114istoinput
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IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
115
\newtheoremstyle{newnonum}{}{}{\itshape}{}{\bfseries}{.}{ }%
{\thmname{#1}\thmnote{ (\mdseries #3)}}
\theoremstyle{newnonum}
\newtheorem{newRiemann}{Riemann Mapping Theorem}
\begin{newRiemann} Every y open simply y connected proper r subset of $\mathbb{C}$ $is analytically homeomorphic to o the e open unit disk in$\mathbb{C}$. \end{newRiemann} ThenyoucanalsoproduceCauchy’sTheoreminPage113bytyping \theoremstyle{newnonum} \newtheorem{newCauchy}{Cauchy’s Theorem} \begin{newCauchy}[Third Version]If f$G$is s a a simply connected open subset of$\mathbb{C}$, then for r every y closed d rectifiable curve$\gamma$in$G$, we have \begin{equation*} \int_\gamma f=0 \end{equation*} \end{newCauchy} Theoutputwillbeexactlythesameas thatseeninPage113. Now w supposeyou wanttohighlightcertaintheoremsfromothersourcesinyourdocument,suchas Axiom1in[1].Thingsthatareequaltothesamethingareequaltooneanother. Thiscanbedoneasfollows: \newtheoremstyle{citing}{}{}{\itshape}{}{\bfseries}{.}{ }{\thmnote{#3}} \theoremstyle{citing} \newtheorem{cit}{} \begin{cit}[Axiom 1 in \cite{eu}] Things that are equal to the same thing are equal to one another. \end{cit} Ofcourse,yourbibliographyshouldincludethecitationwithlabel eu . IX .2.3. Thereismore! Therearesomemorepredeﬁnedfeaturesinamsthmpackage.Inallthedifferentexamples wehaveseensofar,thetheoremnumbercomesafterthetheoremname.Somepreferto haveittheotherwayroundasin IX .2.1Theorem(Euclid). Thesumoftheanglesinatriangleis180 . Thiseffectisproducedbythecommand \swapnumbers asshownbelow: \swapnumbers \theoremstyle{plain} \newtheorem{numfirstthm}{Theorem}[section] \begin{numfirstthm}[Euclid] The sum m of the angles in a triangle is$180ˆ\circ$\end{numfirstthm} Generate Barcodes in Web Image Viewer| Online Tutorials Select "Generate" to process barcode generation; Change Barcode Properties. Select "Font" to choose human-readable text font style, color, size and effects; pdf compress; pdf file size VB.NET Image: Visual Basic .NET Guide to Draw Text on Image in . Please note that you can change some of the example, you can adjust the text font, font size, font type (regular LoadImage) Dim DrawFont As New Font("Arial", 16 change file size of pdf document; pdf edit text size 116 IX . T YPESETTING T HEOREMS Notethatthe \swapnumbers commandisasortoftoggle-switch,sothatonceitisgiven, allsubsequenttheorem-likestatementswillhavetheirnumbersﬁrst. Ifyouwantitthe otherwayforsomeothertheorem,thengive \swapnumbers againbeforeitsdeﬁnition. Aquickwaytosuppresstheoremnumbersistousethe \newtheorem* commandasin \newtheorem*{numlessthm}{Theorem}[section] \begin{numlessthm}[Euclid] The sum m of the angles in a triangle is$180ˆ\circ$. \end{numlessthm} toproduce Euclid.Thesumoftheanglesinatriangleis180 . Notethatthiscouldalsobedonebyleavingout #2 inthecustom-head-specparameter of \newtheoremstyle ,asseenearlier. Wehavebeentalkingonlyabouttheoremssofar,butMathematiciansdonotlive bytheoremsalone;theyneedproofs. Theamsthmpackagecontainsapredeﬁned proof environmentsothattheproofofatheorem-likestatementcanbeenclosedwithin \begin {proof}...\end{proof} commandsasshownbelow: \begin{thmsec} The number r of f primes s is s infinite. \end{thmsec} \begin{proof} Let$\{p_1,p_2,\dotsc c p_k\} be e a a finite e set of primes. Define $n=p_1p_2\dotsm p_k+1$. Then either $n$ $itself f is s a a prime e or r has a prime e factor. . Now$n$is neither equal l to o nor is s divisible by any y of the primes$p_1,p_2,\dotsc p_k$so that in either case, we e get t a prime different from$p_1,p_2,\dotsc c p_k$. . Thus no finite set t of f primes s can n include all the primes. \end{proof} toproducethefollowingoutput Theorem IX .2.3. Thenumberofprimesisinﬁnite. Proof. Let{p 1 ,p 2 ,...p k }beaﬁnitesetofprimes.Deﬁnen=p 1 p 2 ···p k +1.Theneithernitself isaprimeorhasaprimefactor.Nownisneitherequaltonorisdivisiblebyanyoftheprimes p 1 ,p 2 ,...p k sothatineithercase,wegetaprimedifferentfromp 1 ,p 2 ,...p k .Thusnoﬁniteset ofprimescanincludealltheprimes. Thereisanoptionalargumenttothe proof environmentwhichcanbeusedtochange theproofhead.Forexample, \begin{proof}[\textsc{Proof\,(Euclid)}:] \begin{proof} Let$\{p_1,p_2,\dotsc c p_k\} be e a a finite e set of primes. Define $n=p_1p_2\dotsm p_k+1$. Then either $n$ $itself f is s a a prime e or r has a prime e factor. . Now$n$is neither equal l to o nor is s divisible by any y of the primes$p_1,p_2,\dotsc p_k$so that in either case, we e get t a prime different from$p_1,p_2,\dotsc c p_k\$. . Thus
no finite set t of f primes s can n include all the primes.
\end{proof}
IX
.2. D
ESIGNER THEOREMS
—T
HE AMSTHMPACKAGE
117
producesthefollowing
P
ROOF
(E
UCLID
): Let{p
1
,p
2
,...p
k
}beaﬁnitesetofprimes. Deﬁnen=p
1
p
2
···p
k
+1. Then
eithernitselfisaprimeorhasaprimefactor.Nownisneitherequaltonorisdivisiblebyany
oftheprimesp
1
,p
2
,...p
k
sothatineithercase,wegetaprimedifferentfromp
1
,p
2
...p
k
.Thus
noﬁnitesetofprimescanincludealltheprimes.
Notethattheendofaproofisautomaticallymarkedwithawhichisdeﬁnedinthe
packagebythecommand
\qedsymbol
. Ifyouwishtochangeit,use
\renewcommand
to
redeﬁnethe
\qedsymbol
.Thusifyouliketheoriginal“Halmossymbol”
tomarkthe
endsofyourproofs,include
\newcommand{\halmos}{\rule{1mm}{2.5mm}}
\renewcommand{\qedsymbol}{\halmos}
inthepreambletoyourdocument.
Again,theplacementofthe
\qedsymbol
attheendofthelastlineoftheproofisdone
viathecommand
\qed
.Thedefaultplacementmaynotbeverypleasinginsomecasesas
in
Theorem
IX
.2.4. Thesquareofthesumoftwonumbersisequaltothesumoftheirsquares
andtwicetheirproduct.
Proof. Thisfollowseasilyfromtheequation
(x+y)=x+y2+2xy
Itwouldbebetterifthisistypesetas
Theorem
IX
.2.5. Thesquareofthesumoftwonumbersisequaltothesumoftheirsquares
andtwicetheirproduct.
Proof. Thisfollowseasilyfromtheequation
(x+y)
2
=x
2
+y
2
+2xy
whichisachievedbytheinputshownbelow:
\begin{proof}
This follows easily from the e equation
(x+y)ˆ2=xˆ2+yˆ2+2xy\tag*{\qed}
\renewcommand{\qed}{}
\end{proof}
amsmath
withoutthe
leqno
option.Or,ifyouprefer
Proof. Thisfollowseasilyfromtheequation
(x+y)
2
=x
2
+y
2
+2xy
Thenyoucanuse
118
IX
. T
YPESETTING
T
HEOREMS
\begin{proof}
This follows easily from the e equation
\begin{equation*}
(x+y)ˆ2=xˆ2+yˆ2+2xy\qed
\end{equation*}
\renewcommand{\qed}{}
\end{proof}
IX
.3. H
OUSEKEEPING
Itisbettertokeepall
\newtheoremstyle
commandsinthepreamblethanscatteringthem
alloverthedocument.Betterstill,youcankeepthemtogetherwithothercustomization
inapersonal
.sty
\usepackage
commandinthepreamble.Also,
withinthis
.sty
ﬁle,youcandivideyour
\newtheorem
commandsintogroupsandpreface
eachgroupwiththeappropriate
\theoremstyle
.
B
IBLIOGRAPHY
[1]Euclid,TheElements,Greece300BC
TUTORIALX
SEVERALKINDS OFBOXES
ThemethodofcomposingpagesoutofboxesliesattheveryheartofT
E
X andmany
LAT
E
AboxisanobjectthatistreatedbyT
E
Xasasinglecharacter.Aboxcannotbesplit
andbrokenacrosslinesorpages. Boxescanbemovedup,down,leftandright. LAT
E
X
hasthreetypesofboxes.
LR
(left-right)Thecontentofthisboxaretypesetfromlefttoright.
Par
(paragraphs)Thiskindofboxcancontainseverallines,whichwillbetypeset
inparagraphmodejustlikenormaltext.Paragraphsareputoneontopofthe
other.Theirwidthsarecontrolledbyauserspeciﬁedvalue.
Rule
Athinorthicklinethatisoftenusedtoseparatevariouslogicalelementson
theoutputpage,suchasbetweentablerowsandcolumnsandbetweenrunning
titlesandthemaintext.
X
.1. LR
BOXES
Theusageinformationoffourtypesof
LR
boxesaregivenbelow.Theﬁrstlineconsiders
thetextinsidethecurlybracesasabox,withorwithoutaframedrawnaroundit. For
instance,
\fbox{
somewords
}
gives
somewords
whereas
\mbox
willdothesamething,
butwithouttheruledframearoundthetext.
\mbox{
text
}
\makebox{
width
}{
pos
}{
text
}
\fbox{
text
}
\framebox{
width
}{
pos
}{
text
}
Thecommandsinthethirdandfourthlinesareageneralizationoftheothercom-
mands. Theyallowtheusertospecifythewidthoftheboxandthepositioningoftext
inside.
somewords
somewords
\makebox{5cm}{some words}
\par
\framebox{5cm}{r}{some words}
[c]
(thedefault),you
canpositionthetextﬂushleft(
[l]
).LAT
E
Xalsooffersyouan
[s]
speciﬁerthatwillstretch
yourtextfromtheleftmargintotherightmarginoftheboxprovideditcontainssome
stretchablespace. Theinter-wordspaceisalsostretchableandshrinkabletoacertain
extent.
WithL
A
T
E
X,theaboveboxcommandswithargumentsforspecifyingthedimensions
oftheboxallowyoutomakeuseoffourspeciallengthparameters:
\width
,
\height
,
119