\relax 
\@writefile{toc}{\contentsline {chapter}{\numberline {9}Concluding remarks}{203}}
\@writefile{lof}{\addvspace {10\p@ }}
\@writefile{lot}{\addvspace {10\p@ }}
\@writefile{toc}{\contentsline {section}{\numberline {9.1}On the history of geometry}{203}}
\newlabel{sec!history}{{9.1}{203}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.1}Greek geometry and rigour}{203}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.2}The parallel postulate}{204}}
\newlabel{sec!parallels}{{9.1.2}{204}}
\citation{Gg}
\@writefile{lof}{\contentsline {figure}{\numberline {9.1a}{\ignorespaces The parallel postulate. To meet or not to meet?, that is the question.}}{205}}
\newlabel{tomeet}{{9.1a}{205}}
\@writefile{lof}{\contentsline {figure}{\numberline {9.1b}{\ignorespaces The parallel postulate in the Euclidean plane}}{206}}
\newlabel{parallel_axiom}{{9.1b}{206}}
\citation{Hil}
\@writefile{lof}{\contentsline {figure}{\numberline {9.1c}{\ignorespaces The ``parallel postulate'' in spherical geometry}}{207}}
\newlabel{sph_parallel_axiom}{{9.1c}{207}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.1.3}Coordinates versus axioms}{207}}
\@writefile{toc}{\contentsline {section}{\numberline {9.2}Group theory}{208}}
\newlabel{sec!gp_thy}{{9.2}{208}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.1}Abstract groups versus transformation groups}{208}}
\newlabel{ssec!gp_acts}{{9.2.1}{208}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.2}Homogeneous and principal homogeneous spaces}{209}}
\newlabel{ssec!torsor}{{9.2.2}{209}}
\@writefile{toc}{\contentsline {paragraph}{Definition}{209}}
\@writefile{toc}{\contentsline {paragraph}{Definition}{210}}
\@writefile{toc}{\contentsline {paragraph}{Example}{210}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.3}The Erlangen program revisited}{210}}
\newlabel{subsec!Erlangen_re}{{9.2.3}{210}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.2.4}Affine space as a torsor}{211}}
\newlabel{subsec!affdef}{{9.2.4}{211}}
\@writefile{toc}{\contentsline {section}{\numberline {9.3}The famous trichotomy}{212}}
\newlabel{sec!trichotomy}{{9.3}{212}}
\newlabel{fig!3tomy}{{9.3}{212}}
\@writefile{lof}{\contentsline {figure}{\numberline {9.3}{\ignorespaces The cap, flat plane and Pringle's chip }}{212}}
\@writefile{lof}{\contentsline {figure}{\numberline {9.3}{\ignorespaces The famous trichotomy}}{213}}
\newlabel{fig!surf}{{9.3}{213}}
\@writefile{toc}{\contentsline {section}{\numberline {9.4}Geometry in physics}{214}}
\newlabel{sec!geom&phys}{{9.4}{214}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.1}The Galilean group and Newtonian dynamics}{215}}
\newlabel{sec!galilei}{{9.4.1}{215}}
\newlabel{tab!conserve}{{9.4.1}{216}}
\@writefile{lot}{\contentsline {table}{\numberline {9.4}{\ignorespaces Symmetries and conservation laws}}{216}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.2}The Poincar\'e group and special relativity}{216}}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.3}Wigner's classification: elementary particles}{218}}
\newlabel{sec!wigner}{{9.4.3}{218}}
\citation{St}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.4}The Standard Model and beyond}{219}}
\newlabel{sec!stdmodel}{{9.4.4}{219}}
\citation{NSh}
\@writefile{toc}{\contentsline {subsection}{\numberline {9.4.5}Other connections}{220}}
\@writefile{toc}{\contentsline {section}{\numberline {9.5}Further directions}{220}}
\newlabel{sec!titles}{{9.5}{220}}
\newlabel{entry!maps}{{3}{220}}
\citation{Cx}
\citation{NSh}
\@setckpt{final}{
\setcounter{page}{222}
\setcounter{equation}{0}
\setcounter{enumi}{9}
\setcounter{enumii}{2}
\setcounter{enumiii}{0}
\setcounter{enumiv}{0}
\setcounter{footnote}{1}
\setcounter{mpfootnote}{0}
\setcounter{part}{0}
\setcounter{chapter}{9}
\setcounter{section}{5}
\setcounter{subsection}{0}
\setcounter{subsubsection}{0}
\setcounter{paragraph}{0}
\setcounter{subparagraph}{0}
\setcounter{figure}{4}
\setcounter{table}{1}
\setcounter{parentequation}{0}
\setcounter{cor}{9}
\setcounter{corn}{2}
\setcounter{constr}{1}
\setcounter{principle}{2}
\setcounter{prop}{34}
\setcounter{lem}{4}
\setcounter{lemn}{4}
\setcounter{cla}{2}
\setcounter{thm}{24}
}