Tikz – esempio 13

Benvenuti nel nostro esempio 13 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 12 e il successivo Tikz – esempio 14 per ulteriore materiale.

Buona lettura!

 

Prima di ogni figura ricordare di mettere

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

Prima figura

codice prima figura

\begin{tikzpicture}
\def\centerarc[#1](#2)(#3:#4:#5) % Syntax: [draw options] (center) (initial angle:final angle:radius)
{ \draw[#1] ($(#2)+({#5*cos(#3)},{#5*sin(#3)})$) arc (#3:#4:#5); }
% Macro \centerarc presa da https://tex.stackexchange.com/a/66220
% Richiede \usetikzlibrary{calc}
\begin{axis}[
disabledatascaling,
axis equal image,
scale=0.70,
axis x line=none,
axis y line=none,
xmin = -0.7,
xmax = 0.7,
ymin = -0.7,
ymax = 0.7,
]
\draw[ultra thick,color=CornflowerBlue] (axis cs:0,0) circle[radius=1/sqrt(3)];
\addplot[no marks,very thick,SeaGreen] coordinates {(-0.289,-0.167) (0.289,0.167)};
\addplot[no marks,very thick,samples=10] coordinates {(-1/sqrt(3),0) (1/2/sqrt(3),-1/2) (1/2/sqrt(3),1/2) (-1/sqrt(3),0)} \closedcycle;
\addplot[no marks,very thick,samples=10,RubineRed] coordinates {(-0.408,-0.408) (0.408,0.408)};
\addplot[no marks,thick,samples=10,dashed,RubineRed] coordinates {(-1,-1) (1,1)};
% \addplot[mark=*,samples=10,mark size=1.5pt] coordinates {(-0.408,-0.408) (0.408,0.408)};
\addplot[no marks,very thick,samples=10,mark size=1.5pt] coordinates {(0,0) (1/2/sqrt(3),-1/2)};
\addplot[no marks,thick,dotted] coordinates {(0,0) (1/sqrt(3),0)};
\addplot[mark=*,mark size=1.5pt] coordinates {(0,0)} node[above left] {$O$};
\addplot[mark=*,mark size=1.5pt] coordinates {(-1/sqrt(3),0)} node[left] {$A$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),-1/2)} node[below right] {$B$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),1/2)} node[above right] {$C$};
\addplot[mark=*,mark size=1.5pt] coordinates {(1/2/sqrt(3),0)} node[below right] {$D$};
\addplot[mark=*,mark size=1.5pt,RubineRed] coordinates {(0.289,0.289)} node[right] {$P\rule{0pt}{10pt}$};
\addplot[mark=*,mark size=1.5pt,RubineRed] coordinates {(-0.211,-0.211)} node[below] {$Q\rule{0pt}{10pt}$};
\addplot[no marks] coordinates {(0.20,0.145)} node[below] {$\vartheta$};
\addplot[no marks] coordinates {(-0.144,0.25)} node[above left] {1};
\centerarc[thick](0,0)(0:45:0.11);
\centerarc[thick](0,0)(0:45:0.13);
\centerarc[thick]({1/2/sqrt(3)},-1/2)(90:120:0.13);
\centerarc[thick]({1/2/sqrt(3)},-1/2)(120:150:0.11);
\end{axis}
\end{tikzpicture}

seconda figura

codice seconda figura

\begin{tikzpicture}
\begin{axis}[
axis equal image,
disabledatascaling,
width=0.75\textwidth,
axis x line=none,
axis y line=none,
axis on top,
xmin = -0.5,
xmax = 3.5,
ymin = -0.3,
ymax = 1.5
]
\addplot[very thick,samples=10,no marks,fill=Apricot!30] coordinates {(0,0) (1,0) (0,1.272) (0,0)} \closedcycle;
\addplot[very thick,samples=10,no marks,fill=Magenta!30] coordinates {(2,0) (3,0) (2,0.786) (2,0)} \closedcycle;
\addplot[no marks,thick] coordinates {(0,0.1) (0.1,0.1) (0.1,0)};
\addplot[no marks,thick] coordinates {(2,0.1) (2.1,0.1) (2.1,0)};
\centerarc[thick](0,1.272)(-90:-52:0.2);
\centerarc[thick](2,0.786)(-90:-35:0.15);
\addplot[no marks] coordinates {(0,1.272)} node[above left] {$A$};
\addplot[no marks] coordinates {(0,0)} node[below left] {$B$};
\addplot[no marks] coordinates {(1,0)} node[below right] {$C$};
\addplot[no marks] coordinates {(2,0.786)} node[above left] {$A$};
\addplot[no marks] coordinates {(2,0)} node[below left] {$B$};
\addplot[no marks] coordinates {(3,0)} node[below right] {$C$};
\end{axis}
\end{tikzpicture}

terza figura

codice terza figura

\begin{tikzpicture}
\begin{axis}[
width=0.66\textwidth,
height=0.4\textwidth,
axis x line=center,
axis y line=center,
axis on top,
xmin = -0.25,
xmax = 2.9,
ymin = -0.5,
ymax = 2.9,
xlabel = {$b$},
ylabel = {$a$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}\phantom{/}O\phantom{/}$},
]
\addplot[very thick,samples=100,DarkOrchid,domain=0:2.5] {x^2};
\addplot[very thick,samples=100,SeaGreen,domain=0:2.5] {2^(-x)};
\addplot[mark=*,thick,mark options={fill=BurntOrange},mark size=3pt,draw=none] coordinates {(0.767,0.588)};
\addplot[no marks] coordinates {(1,2)} node[right] {$\color{DarkOrchid} b^2$};
\addplot[no marks] coordinates {(2,0.6)} node[right] {$\color{SeaGreen} 2^{-b}$};
\end{axis}
\end{tikzpicture}

quarta figura

codice quarta figura

\begin{tikzpicture}
\begin{axis}[
axis equal image,
scale=0.65,
axis x line=center,
axis y line=center,
xmin = -3.5,
xmax = 3.5,
ymin = -3.9,
ymax = 3.9,
xlabel = {$x$},
ylabel = {$y$},
xtick = {-pi,-pi/2,pi/2,pi},
xticklabels = {$\phantom{/}-$$\pi\phantom{/}$, $-$$\pi/2$,$\pi/2$, $\phantom{/}\pi\phantom{/}$},
extra x ticks = {0},
extra x tick label = {$\hspace{0.45cm}O$},
colormap={yellowpurple}{rgb255(0cm)=(240, 225, 48); rgb255(1cm)=(204, 204, 255)}
]
\addplot[very thick,samples=100,mesh,point meta=x,domain=-3.5:-1.6] {1/cos(deg(x))-1};
\addplot[very thick,samples=100,mesh,point meta=x,domain=-1.53:1.53] {1/cos(deg(x))-1};
\addplot[very thick,samples=100,mesh,point meta=x,domain=1.6:3.5] {1/cos(deg(x))-1};
\addplot[no marks] coordinates {(pi/3,-3)} node {\fbox{e}};
\end{axis}
\end{tikzpicture}

quinta figura

codice quinta figura

\begin{tikzpicture}
\begin{axis}[
width=0.75\textwidth,
height=0.5\textwidth,
axis x line=center,
axis y line=center,
axis on top,
xmin = -pi/6,
xmax = 7.5,
ymin = -1.4,
ymax = 1.4,
xlabel = {$x$},
ylabel = {$y$},
xtick = {pi/2,pi,3*pi/2,2*pi},
xticklabels = {$\pi/2$, $\phantom{/}\pi\phantom{/}$, $3\pi/2$, $\phantom{/}2\pi\phantom{/}$},
extra x ticks = {0},
extra x tick label = {$\hspace{-0.45cm}\phantom{/}O\phantom{/}$},
x tick label style={above},
domain=-pi:2.5*pi
]

\path[name path=below] (axis cs:0,-2) -- (axis cs:2*pi,-2);
\path[name path=above] (axis cs:0,+2) -- (axis cs:2*pi,2);
\addplot[Gray!10] fill between[of = below and above, soft clip={domain=0:2*pi}];
\addplot[very thick,samples=100,Emerald] {sin(deg(x))^3};
\addplot[very thick,samples=100,BurntOrange] {-cos(deg(x))^2};
\addplot[no marks,dashed] coordinates {(2*pi,-5) (2*pi,5)};
\addplot[mark=*,Purple,mark size=3pt,draw=none] coordinates {(3.997,-0.43) (5.428,-0.43)};
\addplot[no marks] coordinates {(2.1,1)} node[right] {$\color{Emerald} \sin^3(x)$};
\addplot[no marks] coordinates {(0.3,-1)} node[right] {$\color{BurntOrange} -\cos^2(x)$};
\end{axis}
\end{tikzpicture}

 
 

Risorse didattiche aggiuntive per approfondire la matematica