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diff --git a/Master/texmf-dist/doc/generic/lecturer/LecturerDemo-Mondrian.tex b/Master/texmf-dist/doc/generic/lecturer/LecturerDemo-Mondrian.tex new file mode 100644 index 00000000000..41df071e8ae --- /dev/null +++ b/Master/texmf-dist/doc/generic/lecturer/LecturerDemo-Mondrian.tex @@ -0,0 +1,236 @@ +% 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 150. +% +% Author: Paul Isambert. +% Date: July 2010. + +\input lecturer + +%\showgrid{1cm} + +\setparameter job: + fullscreen = true + font = \mainfont + +\setparameter slide: + width height = 12cm + top = 0cm + bottom = 3cm + left = 5cm + right = 1.6cm + topskip = 0pt + background = black % For the lines between squares. + foreground = white + vpos = center + hpos = ff + +\setarea{area1 area2 matharea} + width = 3cm + +\setarea{area1 area2} + height = 4.3cm + background = white + +\setarea{area2} + vshift = 4.7cm + +\setarea{matharea footnotearea} + height = 2.6cm + vshift* = 0pt + topskip = .1cm + baselineskip = .333cm + vpos = center + +\setarea{matharea} + background = blue + foreground = white + hpos = rr + +% Below the slide's text. +\setarea{mainarea} + hshift = 3.4cm + hshift* = 0pt + height = 9cm + background = red + +\setarea{footnotearea} + hshift = 3.4cm + hshift* = 1.8cm + left right = .3cm + background = white + font = \footnotefont + hpos = ff + +\setarea{area6 area7} + width = 1.4cm + hshift* = 0pt + height = 1.1cm + +\setarea{area6} + vshift = 9.4cm + background = white + +\setarea{area7} + vshift* = 0pt + background = yellow + + + +\setparameter step: + vskip = \baselineskip + +\setstep\emptystep + vskip = 0pt + +% Used for the maths. +\def\mathstep#1 #2 #3{\emptystep[on=#1,off=#2]\position{matharea}[0pt,0pt]{$#3$}\ignorespaces} +\def\Mathstep#1 #2{\emptystep[off=#1,visible=true]\position{matharea}[0pt,0pt]{$#2$}\ignorespaces} + +% The footnote. Since the same name is given +% to each footnote step, there must be at most +% one per slide. Otherwise, a name should be given +% manually (or automatically with a number in the name, +% and a counter to increment it on every footnote call). +\def\footnote#1{% + \showorhide{toggle=footnote}{\super{\usecolor{blue}{*}}} + \emptystep[footnote,on=] + \position{footnotearea}{\quitvmode\llap{* }#1}% + } + +% On the last equation. +\newsymbol\cross[1.7em]{% + pen 0.1, + move 0 -.5, .5 .9, stroke, + move 0 .9, .5 -.5, stroke, + } +% Font for text. +\font\mainfont=cmss10 +\font\supmainfont=cmss10 at 7.5pt +% Simple superscript (I'm not very good with +% math font family... I'm no mathematician after all). +\def\super#1{\raise.3em\hbox{\supmainfont#1}} +\font\footnotefont=cmss8 at 7pt +\mainfont +\frenchspacing + +% Font for maths. +\font\mathfont=cmss12 at 16pt +\font\scriptmathfont=cmss12 at 10pt +\font\scriptscriptmathfont=cmss12 at 8pt +\textfont0=\mathfont +\scriptfont0=\scriptmathfont +\scriptscriptfont0=\scriptscriptmathfont +\font\mathfont=cmss12 at 16pt +\font\scriptmathfont=cmss12 at 12pt +\font\scriptscriptmathfont=cmss12 at 8pt +\textfont1=\mathfont +\scriptfont1=\scriptmathfont +\scriptscriptfont1=\scriptscriptmathfont +\font\Tensy=cmsy10 at 18pt +\font\scriptTensy=cmsy10 at 10pt +\font\scriptscriptTensy=cmsy10 at 8pt +\textfont2=\Tensy +\scriptfont2=\scriptTensy +\scriptscriptfont2=\scriptscriptTensy +\font\Tenex=cmex10 at 18pt +\font\scriptTenex=cmex10 at 12pt +\font\scriptscriptTenex=cmex10 at 8pt +\textfont3=\Tenex +\scriptfont3=\scriptTenex +\scriptscriptfont3=\scriptscriptTenex + + + +% \endinput +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% % +% UNCOMMENT THE PREVIOUS LINE TO USE THIS FILE AS A TEMPLATE, % +% OR REMOVE EVERYTHING BELOW. % +% % +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + +\slide[A simple assumption] + +\mathstep A B {{a\over b}=\sqrt2} +\mathstep B C {({a\over b})^2=2} +\mathstep C D {{a^2\over b^2}=2} +\mathstep D {} {a^2=2b^2} + +\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.% +\footnote{% + Suppose c/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/b, with no common factor.} + +\step[B] But then we can also write this. +\step[C] And this. +\step[D] And finally this. +\step Which means that a\super2 is even. + +\endslide + + + +\slide[Its consequences] + +\Mathstep A {a^2=2b^2} +\mathstep A B {(2k)^2=2b^2} +\mathstep B C {4k^2=2b^2} +\mathstep C D {2k^2=b^2} + +\step[visible=true] So what? +\step So a is even. Because only even numbers produce even squares.% +\footnote{% + 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)\super2, i.e. 4k\super2+4k+1, i.e. + 2x2(k\super2+k)+1, which is of the form 2k+1, + with 2(k\super2+k) as k. + Hence, an odd number produces an odd square, + and thus if a square is even its root is even too.} + +\step[A] Being even means being expressible in the form 2k, where k is +any integer. +\step[B] And (2k)\super2 square gives 4k\super2. + +\step[C] Let's simplify. +\step Thus b\super2 is even. +\step And b is too. + +\endslide + + + +\slide[The problem] + +\Mathstep A {{a\over b}=\sqrt2} +\mathstep A {} {\rlap\cross{a\over b}=\sqrt2} + +\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. + +\endslide + +\bye
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