Tikz – esempio 26

Benvenuti nel nostro esempio 26 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 25 e il successivo Tikz – esempio 27 per ulteriore materiale.

Buona lettura!

 

Prima figura

 

 

Codice prima figura

 

\begin{tikzpicture}
\begin{axis}[
axis equal image,
scale=1.65,
axis x line=center,
axis y line=center,
xmin = -11*pi/4-1,
xmax = 11*pi/4+1,
ymin = -11*pi/4-1,
ymax = 11*pi/4+1,
xlabel = {$x$},
ylabel = {$y$},
xtick = {-2*pi,-pi,pi,2*pi},
xticklabels = {$-2\pi$, $\phantom{2}-\pi\phantom{2}$, $\phantom{2}\pi\phantom{2}$, $2\pi$},
ytick = {-2*pi,-pi,pi,2*pi},
yticklabels = {$-2\pi$, $\phantom{2}-\pi\phantom{2}$, $\phantom{2}\pi\phantom{2}$, $2\pi$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.6cm}O$},
tick label style={font=\scriptsize},
domain=-9*pi/4:9*pi/4,
% restrict y to domain=-7.854:7.854
]

\foreach \r in {2,3,...,8} {
\addplot[thick,color=red,samples=100,domain=-\r:\r] {sqrt(\r*\r-x^2)};
\addplot[thick,color=red,samples=100,domain=-\r:\r] {-sqrt(\r*\r-x^2)};
};
\foreach \r in {2,3,...,8} {
\addplot[thick,color=red,samples=100,domain=-10:-\r] {sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=-10:-\r] {-sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=\r:10] {sqrt(x^2-\r*\r)};
\addplot[thick,color=red,samples=100,domain=\r:10] {-sqrt(x^2-\r*\r)};

\addplot[thick,color=red,samples=100,domain=-10:10] {sqrt(\r*\r+x^2)};
\addplot[thick,color=red,samples=100,domain=-10:10] {-sqrt(\r*\r+x^2)};
};

\addplot[thick,color=red,samples=20,domain=-10:10] {x};
\addplot[thick,color=red,samples=20,domain=-10:10] {-x};
\end{axis}
\end{tikzpicture}

 

Seconda figura

 

 

Terza figura

 

 

Codice terza figura

 

\begin{tikzpicture}
\begin{axis}[
scale=2.5,
axis equal image,
axis x line=center,
axis y line=center,
xmin = -8.5,
xmax = 8.5,
ymin = -8.5,
ymax = 8.5,
xlabel = {$x$},
ylabel = {$y$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.9cm}0$},
y label style={anchor=north east}
]

\addplot[thin, samples=10,name path=asse,domain=-8.5:8.5] {0};
\addplot[white, thin, samples=10,name path=assedown,domain=-8.5:8.5] {-8};
\addplot[white, thin, samples=10,name path=asseup,domain=-8.5:8.5] {8};
\addplot[black, very thick, dashed, domain=(-2*sqrt(2):2*sqrt(2)),samples=400,name path=radiceup] {sqrt(-x^2+8)};
\addplot[black, very thick, dashed, domain=(-2*sqrt(2):2*sqrt(2)),samples=400,name path=radicedown] {-sqrt(-x^2+8)};
\addplot[black, very thick, dashed, domain=(-8:-3),samples=400,name path=iperbole-1] {-pi/x};
\addplot[black, very thick, dashed, domain=(-1.2:-0.3),samples=400,name path=iperbole-1a] {-pi/x};
\addplot[black, very thick, dashed, domain=(3:8),samples=400,name path=iperbole-1b] {-pi/x};
\addplot[black, very thick, dashed, domain=(0.3:1.2),samples=400,name path=iperbole-1c] {-pi/x};
\addplot[black, very thick, dashed, domain=(-8:-3),samples=400,name path=iperbole1] {pi/x};
\addplot[black, very thick, dashed, domain=(-1.2:-0.3),samples=400,name path=iperbole1a] {pi/x};
\addplot[black, very thick, dashed, domain=(3:8),samples=400,name path=iperbole1b] {pi/x};
\addplot[black, very thick, dashed, domain=(0.3:1.2),samples=200,name path=iperbole1c] {pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole2] {2*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole-2] {-2*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole-3] {-3*pi/x};
\addplot[black, very thick, dashed, domain=(-8:-0.1),samples=200,name path=iperbole3] {3*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole2] {2*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole-2] {-2*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole-3] {-3*pi/x};
\addplot[black, very thick, dashed, domain=(0.1:8),samples=200,name path=iperbole3] {3*pi/x};

\addplot[pink] fill between [of=asse and assedown, soft clip={domain=-8.5:-2.828}];
\addplot[pink] fill between [of=asse and asseup, soft clip={domain=-8.5:-2.828}];
\addplot[pink] fill between [of=asse and assedown, soft clip={domain=2.828:8}];
\addplot[pink] fill between [of=asse and asseup, soft clip={domain=2.828:8}];
\addplot[pink] fill between [of=radicedown and assedown, soft clip={domain=-2.828:2.828}];
\addplot[pink] fill between [of=asseup and radiceup, soft clip={domain=-2.828:2.828}];

\end{axis}
\end{tikzpicture}

 
 

Risorse didattiche aggiuntive per approfondire la matematica