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+% This is a demonstration file distributed with the
+% Lecturer package (see lecturer-doc.pdf).
+%
+% You can recompile the file with a basic TeX implementation,
+% using pdfTeX or LuaTeX with the plain format.
+%
+% The reusable part ends somewhere around line 300.
+%
+% Author: Paul Isambert.
+% Date: July 2010.
+
+\input lecturer
+
+\font\maintitlefont = cmdunh10 at 23pt
+\font\slidetitlefont = cmss12 at 20pt
+\font\subtitlefont = cmss10
+\font\titlefont = cmssi10
+
+\newcolor{darkred}{rgb}{.6 0 0}
+\newcolor{lightgrey}{grey}{.85}
+\newcolor{darkgrey}{grey}{.7}
+
+\setparameter job:
+ mode = presentation % The handout is ready, just turn it on.
+ author = "Pete Agoras"
+ title = "The square root of 2 ain't rational"
+ date = "Some centuries B.C."
+ fullscreen = true
+ autofullscreen = true
+ font = \tenrm % Plain TeX's default, but must be specified
+ % to set it back after a \step with another font.
+
+\setparameter slide:
+ everyslide = \everyslide
+ hsize = ".6\pdfpagewidth"
+ top = 76pt
+ bottom = 42pt
+ areas* = "title author date"
+ bookmarkstyle = italic
+ baselineskip = 12pt
+ topskip = \baselineskip
+
+\def\everyslide{%
+ \position{topleft}\Title
+ \position{topright}\sectiontitle
+ \position{titlebar}\slidetitle
+ \position{bottomleft}\Author
+ \position{bottommiddle}{%
+ \noindent
+ \dobutton\firstslide\FirstPage
+ \dobutton\prevslide\PrevPage
+ \dobutton\prevstep\PrevStep\kern.3em
+ \dobutton\showbookmarks\Bookmarks\kern.3em
+ \dobutton\nextstep\NextStep
+ \dobutton\nextslide\NextPage
+ \dobutton\lastslide\LastPage\unskip}
+ \position{bottomright}\Date
+ \presentationonly{
+ \position{math}{%
+ ${a\over b}=\sqrt2$\par
+ $({a\over b})^2=2$\par
+ ${a^2\over b^2}=2$\par
+ $a^2=2b^2$\par
+ $(2k)^2=2b^2$\par
+ $4k^2=2b^2$\par
+ $2k^2=b^2$\par
+ ${a\over b}\neq\sqrt2$}}
+ }
+\def\dobutton#1#2{%
+ #1[push]{\rlap#2\buttonborder}\hskip1em
+ }
+
+%
+% Top and bottom bars.
+%
+
+\setarea{topleft topright bottomleft bottommiddle bottomright}
+ height = 18pt
+
+\setarea{topleft bottomleft}
+ background = darkred
+ foreground = white
+
+\setarea{topright bottomright}
+ background = darkgrey
+ foreground = darkred
+
+\setarea{topright bottomleft bottomright}
+ font = \subtitlefont
+
+\setarea{topleft topright}
+ width = ".5\pdfpagewidth"
+ right left = 1em
+
+\setarea{bottomleft bottommiddle bottomright}
+ vshift* = 0pt
+ width = "\pdfpagewidth/3"
+ hpos = rr
+
+\setarea{topleft}
+ hpos = rf
+ font = \titlefont
+
+\setarea{topright}
+ hshift* = 0pt
+ hpos = fr
+
+\setarea{titlebar}
+ vshift = 18pt
+ left = 1em
+ height = 40pt
+ background = lightgrey
+ foreground = darkred
+ topskip = 30pt
+ hpos = fr
+ font = \slidetitlefont
+
+% bottomleft is already fully specified.
+
+\setarea{bottommiddle}
+ hshift = "\pdfpagewidth/3"
+ topskip = "\symbolheight\buttonborder+3pt"
+ background = lightgrey
+ foreground = white
+
+\setarea{bottomright}
+ hshift* = 0pt
+
+%
+% The maths on the right.
+%
+\setarea{math}
+ width = ".2\pdfpagewidth"
+ hshift* = 0pt
+ vshift = 58pt
+ vshift* = 18pt
+ foreground = "grey .75"
+ hpos = fr
+ vpos = center
+ baselineskip = 18pt
+
+
+%
+% The title slide.
+%
+\setslide{titleslide}
+ areas = "title author date topleft topright"
+ bookmark = false
+ hpos = rr
+ everyslide = {}
+
+\setarea{title}
+ hshift* = 1cm
+ vshift = 2.5cm
+ height = 45pt
+ topskip = 25pt
+ background = darkred
+ foreground = white
+ top = 1em
+ frame = "width=.2em, corner=round, color=darkgrey"
+ hpos = rr
+ font = \maintitlefont
+
+\setarea{author}
+ hshift* = 5cm
+ vshift = 6cm
+ height = 28pt
+ topskip = 20pt
+ background = lightgrey
+ foreground = white
+ frame = "width=.5em, corner=round"
+ hpos = rr
+ font = \slidetitlefont
+
+\setarea{date}
+ hshift* = 5.5cm
+ vshift = 9cm
+ height = 22pt
+ topskip = 10pt
+ background = white
+ foreground = black
+ top = 5pt
+ frame = "width=.5em, corner=bevel, color=lightgrey"
+ hpos = rr
+
+
+%
+% For the appendices.
+% We remove the math area instead
+% of redefining \everyslide.
+%
+\setslide{appslide}
+ areas* = "math title author date"
+
+%
+% Default step.
+%
+\setparameter step:
+ everyvstep = "\quitvmode\llap{\itemsymbol\kern.5em}"
+ vskip = 18pt
+
+%
+% Foreground math.
+%
+\setstep\emptystep
+ everyvstep everyhstep = {}
+ vskip hskip = 0pt
+
+\def\domath#1 #2 #3 {%
+ \emptystep[on=#2,off=#3]
+ \domathstep{#1}%
+ }
+\def\Domath#1 #2 {%
+ \emptystep[off=#2,visible=true]
+ \domathstep{#1}%
+ }
+\def\domathstep#1{%
+ \presentationorhandout{\position{math}[0pt,#1\dimexpr18pt\relax]}{\position{math}}
+ {\quitvmode\llap{\mathsym\kern.3em}\usecolor{black}{\typemath{#1}}}%
+ }
+
+\def\typemath#1{%
+ $\ifcase#1
+ {a\over b}=\sqrt2
+ \or ({a\over b})^2=2
+ \or {a^2\over b^2}=2
+ \or a^2=2b^2
+ \or (2k)^2=2b^2
+ \or 4k^2=2b^2
+ \or 2k^2=b^2
+ \or {a\over b}\neq\sqrt2
+ \fi$}
+%
+% Navigation symbols.
+%
+\newcolor{button}{grey}{.95}
+\newcolor{darkbutton}{grey}{.68}
+\newsymbol\buttonborder[.7pt]
+ {color button,
+ + 0 16, + 16 0, stroke,
+ color darkbutton,
+ move 0 0, + 16 0, + 0 16
+ }
+\newsymbol\NextStep[.7pt]
+ {move 3 3,
+ + 10 5,+ -10 5,
+ }
+\newsymbol\PrevStep[.7pt]
+ {move 3 3,
+ move + 10 0, + -10 5,+ 10 5,
+ }
+\newsymbol\NextPage[.7pt]
+ {move 3 3,
+ + 10 5,+ -10 5, close,
+ }
+\newsymbol\PrevPage[.7pt]
+ {move 3 3,
+ move + 10 0, + -10 5,+ 10 5, close,
+ }
+\newsymbol\LastPage[.7pt]
+ {move 3 3,
+ + 10 5,+ -10 5, close,
+ move 3 3,
+ move + 10 0, + 0 10,
+ }
+\newsymbol\FirstPage[.7pt]
+ {move 3 3,
+ move + 10 0, + -10 5, + 10 5, close,
+ move 3 3, + 0 10,
+ }
+\newsymbol\Bookmarks[.7pt]
+ {move 3 3,
+ move + 0 1, + 10 0,
+ move 3 3,
+ move + 0 5, + 10 0,
+ move 3 3,
+ move + 0 9, + 10 0,
+ }
+%
+% Item symbols.
+%
+\newsymbol\itemsymbol[.6em,padding=0pt]
+ {color darkred, + 1 0, + 0 1, + -1 0, fill,}
+\newsymbol\mathsym[.5em,padding=0pt]
+ {color darkred,
+ + 1 .5, + -1 .5, fill,}
+\newsymbol\backsym[.5em,padding=0pt]
+ {color darkred, move 1 0, + -1 .5, + 1 .5, fill,}
+%
+% Navigation to the appendices.
+%
+\def\Back#1{%
+ \presentationonly{\usecolor{darkred}{\gotoB{#1}{\subtitlefont\backsym\kern.3em Back}}}%
+ }
+\def\To#1{%
+ \presentationorhandout{\usecolor{darkred}{\gotoA{#1}{\subtitlefont\mathsym\kern.3em See why}}}
+ {{\usecolor{darkred}{\subtitlefont\mathsym\kern.3em(See Appendices)}}}%
+ }
+%
+% And some structure.
+%
+\def\section#1{%
+ \def\sectiontitle{#1}%
+ \createbookmark[nosubmenutext,open]{.5}{#1}%
+ }
+
+
+% \endinput
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% %
+% UNCOMMENT THE PREVIOUS LINE TO USE THIS FILE AS A TEMPLATE, %
+% OR REMOVE EVERYTHING BELOW. %
+% %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+\titleslide
+
+\position{title}\Title
+\position{author}[0cm,-1.7cm]{\it\usecolor{black}{A Casual Talk By}}
+\position{author}\Author
+\position{date}\Date
+
+\endtitleslide
+
+
+
+
+
+\section{Demonstration}
+
+\slide[A simple assumption]
+
+\domath0 A B
+\domath1 B C
+\domath2 C D
+\domath3 D {}
+
+\step Some say the square root of 2 isn't rational.
+\step Suppose it were.
+
+\step[A] Then we could write it as this, where $a$ and $b$ are
+integers without a common factor.
+\To{app1}
+
+\step[B] But then we can also write this.
+\step[C] And this.
+\step[D] And finally this.
+\step Which means that $a^2$ is even.
+
+\endslide
+
+
+
+\slide[Its consequences]
+
+\Domath3 A
+\domath4 A B
+\domath5 B C
+\domath6 C D
+
+\step[visible="true"] So what?
+\step So $a$ is even. Because only even numbers produce even squares.
+\To{app2}
+
+\step[A] Being even means being expressible in the form $2k$, where $k$ is
+any integer.
+\step[B] And $(2k)^2$ square gives $4k^2$.
+
+\step[C] Let's simplify.
+\step Thus $b^2$ is even.
+\step And $b$ is too.
+
+\endslide
+
+
+
+\slide[The problem]
+
+\domath7 A {}
+
+\step[visible=true] And but so we said $a$ and $b$ have no common factor.
+
+\step If both are even they do have a common factor: 2.
+\step Which is absurd.
+
+\step Thus, our basic assumption is false.
+\step[A] There are no such $a$ and $b$.
+
+\step The square root of 2 is irrational.
+\step Too bad.
+
+\endslide
+
+
+
+
+
+\section{Appendices}
+
+
+
+\appslide[All fractions are reducible]
+
+
+\step[visible=true]
+Suppose $c\over d$ is a rational number. If c and d have no common
+factor, then $a=b$ and $b=d$. If they have a common factor,
+divide both by their greatest common divisor. The result
+is $a\over b$, with no common factor.
+
+\vskip\baselineskip
+\Back{app1}
+
+\endappslide
+
+
+
+\appslide[An even square has an even root,scale=true]
+
+\step[visible=true]
+An even number, by definition, is expressible
+in the form $2k$, where $k$ is any integer.
+On the other hand, an odd number is expressible
+by $$2k+1$$
+Thus the square of an odd number is
+$$(2k+1)^2$$
+i.e. $$4k^2+4k+1$$
+i.e. $$2\times2(k^2+k)+1$$
+which is of the form $2k+1$
+with $2(k^2+k)$ as $k$.
+Hence, an odd number produces an odd square,
+and thus if a square is even its root is even too.
+
+\vskip\baselineskip
+\Back{app2}
+
+\step[visible=true,font=\it] You might have noticed
+that this page is slightly scaled to accommodate
+its content to the slide's declared {\tt\usecolor{darkred}{vsize}}
+parameter. Actually, it is scaled because I stretch this
+paragraph so as to have too much content. Which is kind
+of paradoxical. Or just opportunistic.
+
+\endappslide
+
+\bye
+
+
+