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A colleague asked me to help produce drawings with TikZ to include them in a LaTeX document. Not being a specialist of TikZ, I was not able to help and I do not know if GeoGebra can reproduce these drawings. Any hints on how to solve this problem?

enter image description here

enter image description here

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2  
Questions about how to draw specific graphics that just post an image of the desired result are really not reasonable questions to ask on the site. Please post a minimal compilable document showing that you've tried to produce the image and then people will be happy to help you with any specific problems you may have. See minimal working example (MWE) for what needs to go into such a document. –  Henri Menke Jan 26 at 19:35
4  
Sorry, I was not aware of these rules. I will try to post what I tried. –  amine Jan 26 at 19:37

2 Answers 2

This is my attempt on the Tikz draw, leaving the math typsetting for you. Since I don't read your handwriting clearly, some label texts may need corrections.

Here, two styles myarrow for arrow head decoration and dot for solid circle are defined.

enter image description here

Code

\documentclass[]{article}
\usepackage[margin=1cm]{geometry}
\usepackage{tikz}
\begin{document}

\usetikzlibrary{decorations.markings,arrows}

\tikzset{myarrow/.style={decoration={markings,
mark=at position 0.3 with {\arrow{stealth'}},
mark=at position 0.7 with {\arrow{stealth'}}
},postaction={decorate}
}}  

\tikzset{dot/.style = {
        draw,  fill,
        circle,
        inner sep=0pt,
        outer sep=0pt,
        minimum size=2pt
    }}
\begin{tikzpicture}]
\node[dot,label={right:$z_0$}]    at (0,0) (z0){};
\node[dot,label={above:$0$}]      at (-3,-3) (0){}; 
\node[dot,label={above:$1$}]      at (0,-3) (1){};
\node[dot,label={above:$\infty$}] at (4,-3) (inf){};
\draw[myarrow] (0,0) .. controls (-8,-5) and (-3,-5) .. (0,0);
\draw[myarrow] (0,0) .. controls (-2,-5) and (2,-5)  .. (0,0);
\draw[myarrow] (0,0) .. controls (4,-5)  and (10,-5) .. (0,0);
\end{tikzpicture}

\begin{tikzpicture}[scale=1, z={(.707,.3)}]
\draw (-10,0) -- (-3,0);
\draw[->] (-3,1)node[left]{$\mathcal H$} to[out=90,in=180]node[midway,above]{$\sigma=\frac{v_1}{v_2}$} (2,3);
\draw[very thick](-9,0)--(-6,0);
\draw (-9,2pt ) -- (-9,-2pt) node[above]{$0$};
\draw (-6,2pt ) -- (-6,-2pt) node[above]{$1$};
\draw (-3,2pt ) -- (-3,-2pt) node[above]{$\infty$};
% -- Pyramid
\draw (2,3,2)node[above](A){A} -- (0,0,0) node[left](B){B} -- (4,0,0) node[right](C){C} -- (4,0,4) -- (2,3,2) -- (4,0,0);
\draw[dashed] (2,3,2) -- (0,0,4)  -- (0,0,0);
\draw[dashed] (0,0,4) -- (4,0,4);
\draw (2,3,2) node[midway,shift={(3,2.5)}]{$c\pi$} -- (2,2,2.2)  arc (-90:-120:1.5);
\draw (0,0,0) node[midway,shift={(1.3,0.5)}]{$b\pi$} -- (1,0,0) arc (0:45:1);
\draw (3,0,0) node[midway,shift={(2.5,0.5)}]{$a\pi$} arc (180:98:1);
\fill[gray,opacity=0.3] (0,0,0)--(4,0,0)--(2,3,2)--cycle;
\end{tikzpicture}
\end{document}
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Many thanks, Jesse, I will compare it with my own solution! –  amine Jan 27 at 6:48
    
@amine Nay, happy I can help out. –  Jesse Jan 27 at 6:57
up vote 3 down vote accepted

With a help of a colleague, I managed to solve the problem:

enter image description here

\begin{tikzpicture}
\begin{scope}
\draw [->,>=stealth] (-1,0)--(3,0) node[below]{$\infty$};
\draw [very thick] (0,0) node[below]{$0$} -- (1,0) node[below]{$1$};
\node at (0.5,1)[scale=2] {$\mathcal H$};
\end{scope}


\begin{scope} [xshift=9cm]
% La face grisée
\draw [fill=gray!20](0,0) node[below]{$\lambda\pi$} 
.. controls ++(-0.25,0.25) and ++(0.5,0) ..
(-1.5,0.5) node[left]{$\nu\pi$} -- (0,2) node[above]{$\mu\pi$} -- cycle;
% l'autre face visible
\draw (0,0) .. controls ++(0.25,0.25) and ++(-0.5,0) .. (1.5,0.5)--(0,2);
\end{scope}


\begin{scope} [xshift=5cm,yshift=1cm]
\draw [->,>=stealth] (-2,0) .. controls ++(1,0.7) and ++(-1,0.25) .. (2,0.5)
node[midway,above] {$\sigma=\frac{\nu_1}{\nu_2}$}; 
\end{scope}
\end{tikzpicture}

\vspace{3cm}

\begin{tikzpicture}
\begin{scope}
\draw (0,0) node{$\bullet$} node[above] {$0$};
\draw (2,0) node{$\bullet$} node[above] {$1$};
\draw (5,0) node{$\bullet$} node[above] {$\infty$};
% La boucle autour de 0
\draw (2,2) node{$\bullet$} node [above]{$z_0$}
.. controls ++(-1,-0.8) and ++(-0.9,0.9) .. (-0.5,-0.5) node[near start,sloped]{$<$}
.. controls ++(0.7,-0.7) and ++(-0.8,-1) .. (2,2);
% La boucle autour de 1
\draw (2,2) 
.. controls ++(-0.3,-1) and ++(-0.9,0) .. (2,-0.7) node[near start,sloped]{$<$}
.. controls ++(0.7,0) and ++(0.3,-1) .. (2,2);
% La boucle autour de OO
\draw (2,2) 
.. controls ++(1,-1) and ++(-0.5,-0.5) .. (5.5,-0.5) node[near start,sloped]{$>$}
.. controls ++(0.9,0.9) and ++(1,-0.5) .. (2,2);
\end{scope}
\end{tikzpicture}
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