\contentsline {section}{\numberline {1}Geometria piana}{1}{section.1}
\contentsline {subsection}{\numberline {1.1}Segmento}{1}{subsection.1.1}
\contentsline {subsection}{\numberline {1.2}Retta}{1}{subsection.1.2}
\contentsline {subsubsection}{\numberline {1.2.1}Distanza punto-retta}{1}{subsubsection.1.2.1}
\contentsline {subsubsection}{\numberline {1.2.2}Distanza retta-retta}{1}{subsubsection.1.2.2}
\contentsline {subsubsection}{\numberline {1.2.3}Condizioni di parallelismo}{2}{subsubsection.1.2.3}
\contentsline {subsubsection}{\numberline {1.2.4}Condizioni di perpendicolarita'}{2}{subsubsection.1.2.4}
\contentsline {subsubsection}{\numberline {1.2.5}Equazioni parametriche}{3}{subsubsection.1.2.5}
\contentsline {subsection}{\numberline {1.3}Asse di un segmento}{4}{subsection.1.3}
\contentsline {subsection}{\numberline {1.4}Bisettrice}{4}{subsection.1.4}
\contentsline {subsection}{\numberline {1.5}Sistemi di riferimento}{5}{subsection.1.5}
\contentsline {subsubsection}{\numberline {1.5.1}Traslazione}{5}{subsubsection.1.5.1}
\contentsline {subsubsection}{\numberline {1.5.2}Rotazione}{5}{subsubsection.1.5.2}
\contentsline {subsubsection}{\numberline {1.5.3}Rototraslazione}{5}{subsubsection.1.5.3}
\contentsline {section}{\numberline {2}Geometria proiettiva}{5}{section.2}
\contentsline {subsection}{\numberline {2.1}Piano proiettivo}{6}{subsection.2.1}
\contentsline {subsection}{\numberline {2.2}Coordinate omogenee}{6}{subsection.2.2}
\contentsline {subsubsection}{\numberline {2.2.1}Conversione di coordinate}{7}{subsubsection.2.2.1}
\contentsline {subsubsection}{\numberline {2.2.2}Punto improprio di una retta}{8}{subsubsection.2.2.2}
\contentsline {subsection}{\numberline {2.3}Equazione di una retta dati due punti}{9}{subsection.2.3}
\contentsline {section}{\numberline {3}Coniche}{10}{section.3}
\contentsline {subsubsection}{\numberline {3.0.1}Tipi di coniche}{10}{subsubsection.3.0.1}
\contentsline {subsubsection}{\numberline {3.0.2}Retta-Conica}{11}{subsubsection.3.0.2}
\contentsline {subsubsection}{\numberline {3.0.3}Classi di coniche}{12}{subsubsection.3.0.3}
\contentsline {subsection}{\numberline {3.1}Equazioni ridotte e invarianti}{12}{subsection.3.1}
\contentsline {subsection}{\numberline {3.2}Equazione retta tangente}{17}{subsection.3.2}
\contentsline {subsection}{\numberline {3.3}Equazioni canoniche}{19}{subsection.3.3}
\contentsline {subsubsection}{\numberline {3.3.1}Parabola}{19}{subsubsection.3.3.1}
\contentsline {subsubsection}{\numberline {3.3.2}Iperbole e ellisse}{20}{subsubsection.3.3.2}
\contentsline {subsection}{\numberline {3.4}Polarita'}{21}{subsection.3.4}
\contentsline {subsubsection}{\numberline {3.4.1}Costruzione della retta polare}{22}{subsubsection.3.4.1}
\contentsline {subsubsection}{\numberline {3.4.2}Diametri e centri}{24}{subsubsection.3.4.2}
\contentsline {subsection}{\numberline {3.5}Ellisse o iperbole}{24}{subsection.3.5}
\contentsline {subsection}{\numberline {3.6}Parabola}{28}{subsection.3.6}
\contentsline {subsection}{\numberline {3.7}Circonferenza}{31}{subsection.3.7}
\contentsline {section}{\numberline {4}Fascio di coniche}{33}{section.4}
\contentsline {subsection}{\numberline {4.1}Proprieta' del fascio}{35}{subsection.4.1}
\contentsline {subsection}{\numberline {4.2}Calcolare l'equazione del fascio}{36}{subsection.4.2}
\contentsline {subsubsection}{\numberline {4.2.1}Dati 4 punti}{36}{subsubsection.4.2.1}
\contentsline {subsubsection}{\numberline {4.2.2}Dato un fuoco e direttrice}{37}{subsubsection.4.2.2}
\contentsline {subsection}{\numberline {4.3}Studio del fascio}{38}{subsection.4.3}
\contentsline {section}{\numberline {5}Spazio a tre dimensioni}{38}{section.5}
\contentsline {subsection}{\numberline {5.1}Vettore geometrico}{39}{subsection.5.1}
\contentsline {subsection}{\numberline {5.2}Condizioni di perp e parall}{40}{subsection.5.2}
\contentsline {subsection}{\numberline {5.3}Piano}{40}{subsection.5.3}
\contentsline {subsubsection}{\numberline {5.3.1}Parallelismo e perpendicolarita'}{41}{subsubsection.5.3.1}
\contentsline {subsubsection}{\numberline {5.3.2}Passante per tre punti}{41}{subsubsection.5.3.2}
\contentsline {subsubsection}{\numberline {5.3.3}Casi vari}{42}{subsubsection.5.3.3}
\contentsline {subsection}{\numberline {5.4}Retta}{42}{subsection.5.4}
\contentsline {subsubsection}{\numberline {5.4.1}Retta in forma parametrica}{43}{subsubsection.5.4.1}
\contentsline {subsubsection}{\numberline {5.4.2}Parallelismo e perpendicolarita'}{43}{subsubsection.5.4.2}
\contentsline {subsubsection}{\numberline {5.4.3}Piano - Retta}{43}{subsubsection.5.4.3}
\contentsline {subsubsection}{\numberline {5.4.4}Passante per due punti}{44}{subsubsection.5.4.4}
\contentsline {subsection}{\numberline {5.5}Piano improprio}{45}{subsection.5.5}
\contentsline {subsection}{\numberline {5.6}Rette sghembe}{46}{subsection.5.6}
\contentsline {subsection}{\numberline {5.7}Distanze nello spazio}{47}{subsection.5.7}
\contentsline {subsection}{\numberline {5.8}Quadriche}{48}{subsection.5.8}
\contentsline {subsection}{\numberline {5.9}Vertice}{48}{subsection.5.9}
\contentsline {subsubsection}{\numberline {5.9.1}Classificazione delle quadriche}{51}{subsubsection.5.9.1}
\contentsline {subsection}{\numberline {5.10}Quadrica-retta}{52}{subsection.5.10}
\contentsline {subsubsection}{\numberline {5.10.1}Quadrica-piano}{52}{subsubsection.5.10.1}
\contentsline {subsection}{\numberline {5.11}Sfera}{52}{subsection.5.11}
\contentsline {subsubsection}{\numberline {5.11.1}Cerchio assoluto}{53}{subsubsection.5.11.1}
\contentsline {subsection}{\numberline {5.12}Cono}{53}{subsection.5.12}
\contentsline {subsubsection}{\numberline {5.12.1}Cilindro}{55}{subsubsection.5.12.1}
\contentsline {subsubsection}{\numberline {5.12.2}Proprieta'}{55}{subsubsection.5.12.2}
\contentsline {subsubsection}{\numberline {5.12.3}Proprieta' analitiche}{56}{subsubsection.5.12.3}
\contentsline {subsection}{\numberline {5.13}Tangente}{58}{subsection.5.13}
\contentsline {subsection}{\numberline {5.14}Punti iperbolici, ellittici, parabolici}{61}{subsection.5.14}
\contentsline {subsubsection}{\numberline {5.14.1}Tabella riassuntiva}{63}{subsubsection.5.14.1}
\contentsline {subsection}{\numberline {5.15}Sezioni piane - Cono-Cilindro}{63}{subsection.5.15}
\contentsline {subsubsection}{\numberline {5.15.1}Classificazione}{63}{subsubsection.5.15.1}
\contentsline {subsubsection}{\numberline {5.15.2}Tipi di coniche}{64}{subsubsection.5.15.2}
\contentsline {subsection}{\numberline {5.16}Sezioni piane - Quadriche non degeneri}{65}{subsection.5.16}
\contentsline {subsubsection}{\numberline {5.16.1}Ellissoide}{65}{subsubsection.5.16.1}
\contentsline {subsubsection}{\numberline {5.16.2}Iperboloide}{65}{subsubsection.5.16.2}
\contentsline {subsubsection}{\numberline {5.16.3}Paraboloide}{65}{subsubsection.5.16.3}
\contentsline {subsection}{\numberline {5.17}Equazioni ridotte e invarianti}{65}{subsection.5.17}
\contentsline {subsubsection}{\numberline {5.17.1}Equ. ridotte}{66}{subsubsection.5.17.1}
\contentsline {subsubsection}{\numberline {5.17.2}Equazioni canoniche}{66}{subsubsection.5.17.2}
\contentsline {subsubsection}{\numberline {5.17.3}Invarianti}{69}{subsubsection.5.17.3}
\contentsline {subsection}{\numberline {5.18}Polare}{71}{subsection.5.18}
\contentsline {subsubsection}{\numberline {5.18.1}Cono-Cilindro circoscritto a $Q$}{73}{subsubsection.5.18.1}
\contentsline {subsection}{\numberline {5.19}Quadriche di rotazione}{73}{subsection.5.19}
\contentsline {subsection}{\numberline {5.20}Esercizi vari}{76}{subsection.5.20}
\contentsline {subsection}{\numberline {5.21}Figure di quadriche}{78}{subsection.5.21}