From c9a985e3c856c46728d4bdbd0b777996131669d8 Mon Sep 17 00:00:00 2001 From: Hearot Date: Fri, 4 Aug 2023 11:56:43 +0200 Subject: [PATCH] feat(geometria/scheda): aggiunge nomi delle coniche --- .../Geometria 1/Scheda riassuntiva/main.pdf | 1070 ++++++++--------- .../Geometria 1/Scheda riassuntiva/main.tex | 19 +- 2 files changed, 550 insertions(+), 539 deletions(-) diff --git a/Primo anno/Geometria 1/Scheda riassuntiva/main.pdf b/Primo anno/Geometria 1/Scheda riassuntiva/main.pdf index a1e255d..fd07390 100644 --- a/Primo anno/Geometria 1/Scheda riassuntiva/main.pdf +++ b/Primo anno/Geometria 1/Scheda riassuntiva/main.pdf @@ -245,7 +245,7 @@ endobj endobj 164 0 obj << -/Length 9355 +/Length 9358 /Filter /FlateDecode >> stream @@ -263,31 +263,30 @@ n LSc<<UP֙&%h2`@_~d]Xʈy͡y{c&`zvSlp*h DH*@yi#MW&oqa !rK@+&<(cP` uu<֙?x㹩B'T8H~ۥ$xbاu#.p!ȥ1'TwDB8kJσ;"cCCskhMƊ1€ʦ+Gg2[; k-hTQJSH PQMf&k -q<RHIy6ƂIiNc4 LvI|^Dkf1q0@夔vanqg {yq\3oOVSnmu1e]k_v״3|hU+0+yB4λ3ā 53;L@%?{>TYTm@yEE0[MXzgBOmlnb|>4*7ԘA^tD9Xl-`vK@ &ɢNb$*̄h\奔2)ɩv)E~ƻBS~h6t8±ƭ={oǛror -T:6h]&fQ%=,(LXp/JrQŶ%s5vXl]Yq҉\憕CЉ:т0U//CF:*Nu} :33k9HD}9?(A& -,YC˘!ܲazIx&]L{8q ,]<yM== -e'_azH7rwtu ? 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[<93F0D33A2AAAC1BCA3CB0D4DC3129949> <93F0D33A2AAAC1BCA3CB0D4DC3129949>] >> +/ID [<6EA3B25F91DF9846EA90A42DA92EE5EC> <6EA3B25F91DF9846EA90A42DA92EE5EC>] >> startxref -471725 +473264 %%EOF diff --git a/Primo anno/Geometria 1/Scheda riassuntiva/main.tex b/Primo anno/Geometria 1/Scheda riassuntiva/main.tex index 76a0e6d..cb9c5b2 100644 --- a/Primo anno/Geometria 1/Scheda riassuntiva/main.tex +++ b/Primo anno/Geometria 1/Scheda riassuntiva/main.tex @@ -83,8 +83,8 @@ Due vettori $\vec{a}$, $\vec{b}$ si dicono paralleli se $\exists k \mid \vec{a} = k \vec{b}$, o equivalentemente se $\vec{a} \times \vec{b} = \vec{0}$. Altrettanto si può dire - se $\innprod{\vec{a}, \vec{b}} = \card{\vec{a}} \card{\vec{b}}$ (i.e. - $\cos(\theta) = 1 \implies \theta = 0$). + se $\innprod{\vec{a}, \vec{b}} = \card{\vec{a}} \card{\vec{b}}$ + (i.e.~$\cos(\theta) = 1 \implies \theta = 0$). Una retta in $\RR^3$ è un sottospazio affine della forma $\vec{v} + \Span(\vec{r})$. Analogamente @@ -2593,6 +2593,12 @@ \end{tabular} \end{center} + Tra le uniche coniche non degeneri di $\CC$, + $\mathcal{C}_1$ prende il nome di \textit{ellisse} e $\mathcal{C}_2$ + di \textit{parabola}. $\mathcal{C}_3$ rappresenta invece una + \textit{coppia di rette incidenti}, $\mathcal{C}_4$ una \textit{coppia di rette + parallele} e $\mathcal{C}_5$ un singolo \textit{punto}. + Sia $\KK=\RR$. Allora ogni conica è affinemente equivalente ad un'equazione canonica della seguente tabella, unicamente determinata dagli invarianti $\rg(\MM(p))$, $\rg(\AA(p))$, @@ -2616,6 +2622,15 @@ \end{tabular} \end{center} + Per $\KK=\RR$, $\mathcal{C}_1$ prende il nome di \textit{ellisse reale}, $\mathcal{C}_2$ + di \textit{iperbole} e $\mathcal{C}_3$ di \textit{parabola}. $\mathcal{C}_4$ rappresenta invece una + \textit{coppia di rette reali incidenti}, $\mathcal{C}_5$ una \textit{coppia di rette + reali parallele} e $\mathcal{C}_6$ un singolo \textit{punto}. $\mathcal{C}_7$ è + una \textit{ellisse immaginaria}, $\mathcal{C}_8$ una \textit{coppia di rette + immaginarie incidenti} e $\mathcal{C}_9$ una \textit{coppia di rette immaginarie + parallele}. Tutte queste coniche sono a centro eccetto per la parabola + ($\mathcal{C}_3$). + \vfill \hrule ~\\