Tikz – esempio 14

Benvenuti nel nostro esempio 14 di utilizzo del pacchetto Tikz, una risorsa utilissima del linguaggio per comporre immagini di altissima qualità. In questo articolo proponiamo un esempio di utilizzo. Segnaliamo anche il precedente Tikz – esempio 13 e il successivo Tikz – esempio 15 per ulteriore materiale.

Buona lettura!

 

Prima di ogni figura ricordare di mettere

\documentclass[usenames,dvipsnames]{article}
\usepackage{pgfplots}

Figura 1

codice prima figura

\begin{tikzpicture}
\begin{axis}[
axis x line=center,
axis y line=center,
xmin = -0.95,
xmax = 5.95,
ymin = -2.5,
ymax = 2.95,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.6cm}O$},
]

\addplot[very thick, domain=0:6, samples=100,MidnightBlue,name path=radice] {sqrt(x)};
\addplot[very thick, samples=10,MidnightBlue,name path=retta] {x-2};
\addplot[very thick, samples=10,name path=asse,domain=0:4] {0};
\addplot[Orchid!30] fill between [of=asse and radice, soft clip={domain=0:2}];
\addplot[Orchid!30] fill between [of=retta and radice, soft clip={domain=2:4}];
\addplot[Dandelion!30] fill between [of=asse and retta, soft clip={domain=2:4}];

\addplot[mark=*,draw=none] coordinates {(0,0) (4,0) (4,2)} node[above left] {$C$};
\addplot[mark=*,draw=none] coordinates {(2,0)} node[above left] {$A$};
\addplot[very thick,dashed,no marks] coordinates {(4,2) (4,0)} node[above right] {$B$};

\addplot[MidnightBlue] coordinates {(0.9,-1.15)} node[below,rotate=45] {$y=x-2$};
\addplot[MidnightBlue] coordinates {(2,1.5)} node[above,rotate=18] {$y=\sqrt{x}$};
\end{axis}
\end{tikzpicture}

seconda figura

codice seconda figura

\begin{tikzpicture}
\begin{axis}[
scale=1,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 3.95,
ymin = -3.5,
ymax = 3.95,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.5cm}O$},
cycle list name=color list,
xtick={-3,-2,-1,1,2,3},
ytick={-3,-2,-1,1,2,3},
xticklabel style = {xshift={0.5ex}, yshift={0.5ex}, font=\tiny},
yticklabel style = {xshift={0.5ex}, yshift={0.75ex}, font=\tiny}
]

\foreach \x in {-3,-2,...,3} {
\foreach \y in {-3,-2,...,3} {
\addplot+[mark=*] coordinates {(\x,\y)};
};};
\addplot[ultra thick, domain=-2:2, samples=100,MidnightBlue] {sqrt(4-x^2)};
\addplot[ultra thick, domain=-2:2, samples=100,MidnightBlue] {-sqrt(4-x^2)};
\addplot[ultra thick, domain=-sqrt(5):sqrt(5), samples=100,MidnightBlue,dashed] {sqrt(5-x^2)};
\addplot[ultra thick, domain=-sqrt(5):sqrt(5), samples=100,MidnightBlue,dashed] {-sqrt(5-x^2)};
\addplot[thick,black,dotted] coordinates {(0,2) (1,2) (1,0)};
\addplot[thick,black,dotted] coordinates {(0,0) (1,2)};
\end{axis}
\end{tikzpicture}

terza figura

codice terza figura

\begin{tikzpicture}
\begin{axis}[
axis on top,
width=\textwidth,
height=0.6\textwidth,
axis x line=center,
axis y line=center,
xmin = -4.9,
xmax = 4.9,
ymin = -2.9,
ymax = 2.9,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.6cm}O$},
]

\addplot[very thick,OrangeRed,samples=100] {x^2-2};
\addplot[very thick,Orange,samples=100] {x^2-1};
\addplot[very thick,YellowOrange,samples=100] {x^2};
\addplot[very thick,Dandelion,samples=100] {x^2+3/4^(4/3)};
\addplot[very thick,Goldenrod,samples=100] {x^2+1};
\addplot[very thick,yellow,samples=100] {x^2+2};
\addplot[very thick,domain=0:4,samples=200,NavyBlue] {sqrt(x)};
\addplot[very thick,domain=0:4,samples=200,NavyBlue] {-sqrt(x)};

\addplot[mark=diamond*,only marks,OrangeRed,mark size=2pt] coordinates {(1,-1) (1.831,1.353)};
\addplot[mark=diamond*,only marks,Orange,mark size=2pt] coordinates {(0.525,-0.724) (1.49,1.221)};
\addplot[mark=diamond*,only marks,YellowOrange,mark size=2pt] coordinates {(0,0) (1,1)};

\addplot[mark=*,Orchid,mark size=2pt] coordinates {(0.3968,0.6299)};
\addplot[NavyBlue,no marks] coordinates {(2,-1.4142)} node[rotate=-15,below] {$x^2=y$};
\addplot[OrangeRed,no marks] coordinates {(-2,1.5)} node[rotate=-68,below] {$y=x^2+c$};
\addplot[no marks] coordinates {(-1,-2)} node[left] {$\scriptsize c = {\color{OrangeRed}-2},\ {\color{Orange} -1},\ {\color{YellowOrange} 0},\ {\color{Dandelion} \dfrac{3}{4\sqrt[3\,]{4}}},\ {\color{Goldenrod} 1},\ \color{yellow} 2$};
\end{axis}
\end{tikzpicture}

quarta figura

codice quarta figura

\begin{tikzpicture}
\begin{axis}[
scale=0.8,
disabledatascaling,
axis equal image,
axis x line=none,
axis y line=none,
xmin = -1.2,
xmax = 1.2,
ymin = -1.2,
ymax = 1.2,
]

\draw[very thick,color=Blue] (axis cs:0,0) circle [radius=1];

\addplot[mark=*,very thick,BurntOrange] coordinates {(-0.707,0.707) (-0.5,-0.866) (1,0)};
\addplot[mark=*,very thick,Orchid] coordinates {(-0.707,0.707) (0,1) (1,0)};
\addplot[mark=*,very thick] coordinates {(-0.707,0.707) (1,0)};
\addplot[no marks,BurntOrange] coordinates {(-0.1,-0.1)} node {$T$};
\addplot[no marks,Orchid] coordinates {(0.05,0.65)} node {$S$};
\end{axis}
\end{tikzpicture}

 
 

Risorse didattiche aggiuntive per approfondire la matematica