LaTeX-examples/documents/math-minimal-distance-to-cubic-function/math-minimal-distance-to-cubic-function.tex

\documentclass[a4paper,oneside,DIV15,BCOR12mm]{scrbook}
\usepackage{amssymb, amsmath} % needed for math
\usepackage{mathtools}      % \xRightarrow
\usepackage[utf8]{inputenc} % this is needed for umlauts
\usepackage[english]{babel} % this is needed for umlauts
\usepackage[T1]{fontenc}    % this is needed for correct output of umlauts in pdf
\usepackage[margin=2.5cm]{geometry} %layout
\usepackage{hyperref}   % links im text
\usepackage{braket}         % needed for \Set
\usepackage{parskip}
\usepackage[colorinlistoftodos]{todonotes}
\usepackage{pgfplots}
\pgfplotsset{compat=1.7,compat/path replacement=1.5.1}
\usepackage{tikz}
\usepackage[framed,amsmath,thmmarks,hyperref]{ntheorem}
\usepackage{framed}
\usepackage{nicefrac}
\usepackage{siunitx}
\usepackage{csquotes}   % enquote
\usepackage{microtype}  % better document formatting

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% Define theorems                                                   %
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\theoremstyle{break}
\setlength\theoremindent{0.7cm}
\theoremheaderfont{\kern-0.7cm\normalfont\bfseries} 
\theorembodyfont{\normalfont} % nicht mehr kursiv

\def\mdr{\ensuremath{\mathbb{R}}}
\newcommand{\sgn}{\text{sgn}}
\renewcommand{\qed}{\hfill\blacksquare}

\newframedtheorem{theorem}{Theorem}
\newframedtheorem{lemma}[theorem]{Lemma}
\newtheorem{plaindefinition}{Definition}
\newenvironment{definition}{\begin{plaindefinition}}{\end{plaindefinition}}
\newenvironment{definition*}{\begin{plaindefinition*}}{\end{plaindefinition*}}
\newtheorem{example}{Example}
\theoremstyle{nonumberplain}
\newtheorem{proof}{Proof:}
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\title{Minimal distance from a point to polynomial functions of degree 3 or less}
\author{Martin Thoma}

\hypersetup{ 
  pdfauthor   = {Martin Thoma}, 
  pdfkeywords = {minimal distance, polynomial, function, degree 3, cubic, spline}, 
  pdftitle    = {Minimal distance from a point to polynomial functions of degree 3 or less} 
}

\def\mdr{\ensuremath{\mathbb{R}}}

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% Begin document                                                    %
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\begin{document}
\pagenumbering{roman}
\setcounter{page}{1}
\maketitle
\input{introduction}
\tableofcontents

\pagenumbering{arabic}
\setcounter{page}{1}
\input{problem-description.tex}
\input{constant-functions.tex}
\input{linear-functions.tex}
\input{quadratic-functions.tex}
\input{cubic-functions.tex}

\end{document}