File:Tree structure of mathematical first-order terms.pdf
Summary
| Description |
English: Tree structure of the mathematical first-order terms (n*(n+1))/2 and n*((n+1)/2), depicted left and right, with red and blue background, respectively. Both trees are syntactically unequal, but evaluate to the same value provided (a*b)/c=a*(b/c) holds. |
| Date | |
| Source | Own work |
| Author | Jochen Burghardt |
| Other versions | File:Tree structure of mathematical first-order terms svg.svg |
LaTeX source code |
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\documentclass[12pt]{article}
\usepackage[pdftex]{color}
\usepackage[paperwidth=175mm,paperheight=75mm]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{170mm}
\setlength{\textheight}{70mm}
\setlength{\evensidemargin}{0cm}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\setlength{\parskip}{1ex}
\setlength{\unitlength}{1mm}
\sloppy
\begin{document}
% foreground
\definecolor{fB} {rgb}{0.00,0.00,0.20} % branch
\definecolor{fN} {rgb}{0.00,0.20,0.00} % node
% background
\definecolor{bTL} {rgb}{0.99,0.90,0.90} % left tree
\definecolor{bTR} {rgb}{0.90,0.90,0.99} % right tree
\definecolor{bN} {rgb}{0.99,0.99,0.99} % node
\LARGE
\begin{picture}(170,70)(-5,-5)
\thicklines
% left
\textcolor{bTL}{\put(-5,65){\makebox(0,0)[tl]{\rule{70mm}{70mm}}}}%
\textcolor{bN}{\put(20,00){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(20,00){\makebox(0,0){$n$}}}%
\textcolor{bN}{\put(60,00){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(60,00){\makebox(0,0){$1$}}}%
\textcolor{fB}{\put(37,17){\vector(-1,-1){14}}}%
\textcolor{fB}{\put(43,17){\vector(+1,-1){14}}}%
\textcolor{bN}{\put(00,20){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(00,20){\makebox(0,0){$n$}}}%
\textcolor{bN}{\put(40,20){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(40,20){\makebox(0,0){$+$}}}%
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\textcolor{bN}{\put(20,40){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(20,40){\makebox(0,0){$*$}}}%
\textcolor{bN}{\put(60,40){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(60,40){\makebox(0,0){$2$}}}%
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\textcolor{fB}{\put(43,57){\vector(+1,-1){14}}}%
\textcolor{bN}{\put(40,60){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(40,60){\makebox(0,0){$/$}}}%
% right
\textcolor{bTR}{\put(095,65){\makebox(0,0)[tl]{\rule{70mm}{70mm}}}}%
\textcolor{bN}{\put(100,00){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(100,00){\makebox(0,0){$n$}}}%
\textcolor{bN}{\put(140,00){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(140,00){\makebox(0,0){$1$}}}%
\textcolor{fB}{\put(117,17){\vector(-1,-1){14}}}%
\textcolor{fB}{\put(123,17){\vector(+1,-1){14}}}%
\textcolor{bN}{\put(120,20){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(120,20){\makebox(0,0){$+$}}}%
\textcolor{bN}{\put(160,20){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(160,20){\makebox(0,0){$2$}}}%
\textcolor{fB}{\put(137,37){\vector(-1,-1){14}}}%
\textcolor{fB}{\put(143,37){\vector(+1,-1){14}}}%
\textcolor{bN}{\put(100,40){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(100,40){\makebox(0,0){$n$}}}%
\textcolor{bN}{\put(140,40){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(140,40){\makebox(0,0){$/$}}}%
\textcolor{fB}{\put(117,57){\vector(-1,-1){14}}}%
\textcolor{fB}{\put(123,57){\vector(+1,-1){14}}}%
\textcolor{bN}{\put(120,60){\makebox(0,0){\rule{1em}{3ex}}}}%
\textcolor{fN}{\put(120,60){\makebox(0,0){$*$}}}%
\end{picture}
\end{document}
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Original upload log
The original description page was here. All following user names refer to en.wikipedia.
- 20:51, June 12, 2013 Jochen Burghardt (390 bytes) (+390) . . (Uploading a self-made file using File Upload Wizard)
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