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slides-bitcoin-bienne.tex (19021B)


      1 \documentclass[aspectratio=169,t]{beamer}
      2 
      3 \input texinputs/taler-macros
      4 
      5 \usepackage{tikz}
      6 \usepackage{ragged2e}
      7 \usepackage{graphicx}
      8 \usetikzlibrary{positioning,fit,patterns}
      9 
     10 %
     11 %  Presentation at "P15 Biel/Bienne le 30 avril 2026"
     12 %   Copyright (C) 2026 Emmanuel Benoist,
     13 
     14 %    This program is free software: you can redistribute it and/or modify
     15 %    it under the terms of the GNU General Public License as published by
     16 %    the Free Software Foundation, either version 3 of the License, or
     17 %    (at your option) any later version.
     18 %
     19 %    This program is distributed in the hope that it will be useful,
     20 %    but WITHOUT ANY WARRANTY; without even the implied warranty of
     21 %    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     22 %    GNU General Public License for more details.
     23 %
     24 %    You should have received a copy of the GNU General Public License
     25 %    along with this program.  If not, see <http://www.gnu.org/licenses/>.
     26 %
     27 
     28 % *Especially* edit these...
     29 % \setbeameroption{show notes on second screen=right} % Both
     30 
     31 \newcommand{\SPEAKER}{Emmanuel Benoist}
     32 \newcommand{\DATE}{} {}
     33 
     34 \newcommand{\TITLE}{Presentation of GNU Taler}
     35 \newcommand{\SUB}{30.04.26, Bitcoin @ P15 , Biel/Bienne}
     36 \newcommand{\AUTHOR}{Emmanuel Benoist}
     37 \newcommand{\INST}{https://www.taler.net}
     38 
     39 % Do not edit this part
     40 \title{\TITLE}
     41 \subtitle{\SUB}
     42 \date{\DATE}
     43 \author[\SPEAKER]{\AUTHOR}
     44 \institute{\INST}
     45 
     46 \usepackage{amsmath}
     47 \usepackage{multimedia}
     48 \usepackage[percent]{overpic}
     49 \usepackage{url}
     50 \usepackage{pifont}
     51 \usepackage[absolute,overlay]{textpos}
     52 \usepackage{listings}
     53 
     54 \usepackage{tikz, xcolor}
     55 \usetikzlibrary{shapes,arrows,positioning} 
     56 \tikzset{
     57     %Define standard arrow tip
     58     >=stealth',
     59     %Define style for boxes
     60     punkt/.style={
     61            rectangle,
     62            rounded corners,
     63            draw=black, very thick,
     64            minimum width=3.5em,
     65            minimum height=2em,
     66            text centered},
     67     % Define arrow style
     68     pull/.style={
     69            <->,
     70            thick,draw=red,
     71            shorten <=2pt,
     72            shorten >=2pt,},
     73     % Define arrow style
     74     pil/.style={
     75            ->,
     76            thick,
     77            shorten <=2pt,
     78            shorten >=2pt,}
     79 }
     80 
     81 
     82 %\usepackage{tikz, xcolor}
     83 %\usetikzlibrary{shapes,arrows}
     84 
     85 
     86 \tikzstyle{decision} = [diamond, draw, text width=4.5em, 
     87                         text badly centered, node distance=2cm, 
     88                         inner sep=0pt]
     89 \tikzstyle{block} = [rectangle, draw, text width=5em, 
     90                      text centered, rounded corners, 
     91                      minimum height=4em, node distance=3cm]
     92 \tikzstyle{line} = [draw, -latex']
     93 \tikzstyle{lineeee} = [draw]
     94 \tikzstyle{cloud} = [draw, ellipse, node distance=2.5cm, minimum height=2em]
     95 \tikzstyle{walet} = [draw, rectangle, node distance=0.2cm, minimum height=2em]
     96 \tikzstyle{reseau} = [node distance=0.2cm, minimum height=2em]
     97 \tikzstyle{blank} = [node distance=1cm]
     98 
     99 \usetikzlibrary{shapes,arrows}
    100 \usetikzlibrary{positioning}
    101 \usetikzlibrary{calc}
    102 
    103 
    104 
    105 
    106 
    107 \begin{document}
    108 
    109 \begin{frame}{GNU Taler}
    110   \vfill
    111   \begin{center}
    112     {\huge {L'argent \textbf{numérique} et \textbf{socialement responsable}.}}
    113   \end{center}
    114   \vfill
    115   \begin{center}
    116   \includegraphics[width=0.5\textwidth]{images/taler-logo-2021-inkscape.pdf}
    117   \end{center}
    118   \vfill
    119   \begin{center}
    120     Privacy preserving, useful, taxable, Free/Libre Software, Efficient
    121   \end{center}
    122  \vfill
    123  \vfill
    124 \ %
    125 \end{frame}
    126 
    127 
    128 \frame{\maketitle 
    129 }
    130 
    131 
    132 \begin{frame}
    133 \frametitle{GNU - Taler}
    134 \tableofcontents
    135 
    136 \end{frame}
    137 
    138 \section{GNU Taler principles}
    139 
    140 
    141 \begin{frame}
    142 \frametitle{Taler Overview}
    143 \begin{center}
    144 \begin{tikzpicture}
    145  \tikzstyle{def} = [node distance= 4.5em and 5.5em, inner sep=0.8em, outer sep=.3em];
    146  \node (origin) at (0,0) {};
    147  \node (exchange) [def,above=of origin,draw]{Exchange};
    148  \node (customer) [def, draw, below left=of origin] {Customer};
    149  \node (merchant) [def, draw, below right=of origin] {Merchant};
    150  \node (auditor) [def, draw, above right=of origin]{Auditor};
    151 % \node (regulator) [def, draw, above=of auditor]{CSSF};
    152 
    153  \tikzstyle{C} = [color=black, line width=1pt]
    154 
    155  \draw [<-, C] (customer) -- (exchange) node [midway, above, sloped] (TextNode) {withdraw coins};
    156  \draw [<-, C] (exchange) -- (merchant) node [midway, above, sloped] (TextNode) {deposit coins};
    157  \draw [<-, C] (merchant) -- (customer) node [midway, above, sloped] (TextNode) {spend coins};
    158  \draw [<-, C] (exchange) -- (auditor) node [midway, above, sloped] (TextNode) {verify};
    159 % \draw [<-, C] (regulator) -- (auditor) node [midway, above, sloped] (TextNode) {report};
    160 
    161 \end{tikzpicture}
    162 \end{center}
    163 \end{frame}
    164 
    165 
    166 \begin{frame}
    167   \frametitle{Principle : Planchet generation}
    168   \begin{columns}[t]
    169     \begin{column}{0.4\textwidth}
    170   \begin{block}{Alice withdraws e-cash to her wallet}
    171     \begin{itemize}
    172     \item The wallet generates a planchet (private / public key pair)
    173     \item Planchet is blinded (using a random number)
    174     \end{itemize}
    175   \end{block}
    176   \end{column}
    177     \begin{column}{0.4\textwidth}
    178       \begin{tikzpicture}
    179         [baseline=(b.base)]
    180    \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    181     \node (origin) at (0,0) {\includegraphics[width=0.2\textwidth]{images/dice.pdf}};
    182     \node (b) [def, draw=none, below = of origin] at (0,-0.2) {$b$};
    183     \node (blinded) [def, draw=none, below right=of b]{\includegraphics[width=0.2\textwidth]{images/blinded.pdf}};
    184     \node (planchet) [def, draw=none, above right=of blinded]{\includegraphics[width=0.15\textwidth]{images/planchet.pdf}};
    185     \node (exchange) [node distance=4em and 0.5em, draw, below =of blinded]{Exchange};
    186     \tikzstyle{C} = [color=black, line width=1pt]
    187 
    188     \draw [<-, C] (b) -- (origin) node [midway, above, sloped] (TextNode) {};
    189     \draw [<-, C] (blinded) -- (planchet) node [midway, above, sloped] (TextNode) {};
    190     \draw [<-, C] (blinded) -- (b) node [midway, above, sloped] (TextNode) {};
    191     \draw [<-, C] (exchange) -- (blinded) node [midway, above, sloped] (TextNode) {{\small transmit}};
    192   \end{tikzpicture}
    193 
    194     \end{column}
    195   \end{columns}
    196 \end{frame}
    197 
    198 \begin{frame}
    199   \frametitle{Principle : Signature of the coin}
    200  \begin{columns}[t]
    201     \begin{column}{0.4\textwidth}
    202   \begin{block}{Exchange signs the anonymized planchet}
    203     \begin{itemize}
    204     \item It generates a valid coin
    205     \item But the exchange can not see the real coin.
    206     \end{itemize}
    207   \end{block}
    208     \end{column}
    209     \begin{column}{0.4\textwidth}
    210       \begin{tikzpicture}
    211          [baseline=(b.base)]
    212    \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    213     \node (hammer) [def, draw=none] at (0,0) {\includegraphics[width=0.15\textwidth]{images/hammer.pdf}};
    214     \node (signed) [def, draw=none, below left=of hammer]{\includegraphics[width=0.2\textwidth]{images/sign.pdf}};
    215     \node (blinded) [def, draw=none, above left=of signed]{\includegraphics[width=0.15\textwidth]{images/blinded.pdf}};
    216     \node (customer) [node distance=4em and 0.5em, draw, below =of signed]{Customer};
    217     \tikzstyle{C} = [color=black, line width=1pt]
    218 
    219     \draw [<-, C] (signed) -- (hammer) node [midway, above, sloped] (TextNode) {};
    220     \draw [<-, C] (signed) -- (blinded) node [midway, above, sloped] (TextNode) {};
    221     \draw [<-, C] (customer) -- (signed) node [midway, above, sloped] (TextNode) {{\small transmit}};
    222   \end{tikzpicture}
    223     \end{column}
    224  \end{columns}
    225   
    226 \end{frame}
    227 
    228 \begin{frame}
    229   \frametitle{Principle : Unblind the coin}
    230  \begin{columns}[t]
    231     \begin{column}{0.4\textwidth}
    232   \begin{block}{Alice unblinds the coin}
    233     \begin{itemize}
    234     \item She becomes a valid coin that is untraceable.
    235     \item The coin is signed by the exchange, but the exchange does not know which coin it is.
    236     \end{itemize}
    237   \end{block}
    238     \end{column}
    239     \begin{column}{0.4\textwidth}
    240       \begin{tikzpicture}
    241          [baseline=(b.base)]
    242    \tikzstyle{def} = [node distance= 2em and 0.5em, inner sep=0em, outer sep=.3em];
    243     \node (b) [def, draw=none] at (0,0) {$b$};
    244     \node (coin) [def, draw=none, below left=of b]{\includegraphics[width=0.2\textwidth]{images/coin.pdf}};
    245     \node (signed) [def, draw=none, above left=of coin]{\includegraphics[width=0.15\textwidth]{images/sign.pdf}};
    246     \tikzstyle{C} = [color=black, line width=1pt]
    247 
    248     \draw [<-, C] (coin) -- (b) node [midway, above, sloped] (TextNode) {};
    249     \draw [<-, C] (coin) -- (signed) node [midway, above, sloped] (TextNode) {};
    250   \end{tikzpicture}
    251     \end{column}
    252  \end{columns}
    253 \end{frame}
    254 
    255 
    256 \begin{frame}
    257   \frametitle{Blind Signature implementations}
    258   \begin{block}{RSA}
    259     \begin{itemize}
    260     \item Chaum e-cash
    261     \end{itemize}
    262   \end{block}
    263   \begin{block}{Eliptic curves}
    264     \begin{itemize}
    265     \item Clause Schnorr
    266     \item Shorter
    267     \end{itemize}
    268   \end{block}
    269     \begin{block}{Post quantic cryptography}
    270     \begin{itemize}
    271     \item New protocol designed in NGI-Taler
    272     \item Implementation : work in progress 
    273     \end{itemize}
    274   \end{block}
    275 
    276 \end{frame}
    277 
    278 \section{Taler in Switzerland}
    279 \begin{frame}
    280   \frametitle{Use Taler in Switzerland}
    281   \begin{block}{Exchange = Taler Operations SA}
    282     \begin{itemize}
    283     \item {Operates since 2025 in Switzerland}
    284     \item Any person with a Swiss phone number and bank account can have a wallet.
    285     \item Any swiss account owner can be a merchant
    286     \end{itemize}
    287   \end{block}
    288   \begin{block}{Limitations}
    289     \begin{itemize}
    290     \item Withdraw limited to CHF 2'500 /  month or 15'000 / year for normal users (KYC necessary above a limit)
    291     \item Payments to merchants unlimited (KYB necessary above a limit)
    292     \end{itemize}
    293   \end{block}
    294 \end{frame}
    295 
    296 \subsection{Install Taler Wallet}
    297 \begin{frame}
    298   \frametitle{Install the Wallet}
    299   \begin{columns}
    300     \begin{column}{0.35\textwidth}
    301       \begin{block}{Google Play Store}
    302       \end{block}
    303       \begin{center}
    304 \includegraphics[width=0.5\textwidth]{./images/google_play_GNU_Taler.jpg}
    305 \end{center}
    306 \end{column}
    307 \begin{column}{0.35\textwidth}
    308   \begin{block}{Apple Store}    
    309   \end{block}
    310       \begin{center}
    311         \includegraphics[width=0.5\textwidth]{./images/Apple-Store-taler-app.png}
    312       \end{center}
    313     \end{column}
    314 \begin{column}{0.35\textwidth}
    315   \begin{block}{F-Droid}    
    316   \end{block}
    317       \begin{center}
    318         \includegraphics[width=0.5\textwidth]{./images/QR-Code-f-droid.png}
    319       \end{center}
    320 
    321 \end{column}
    322 
    323   \end{columns}
    324 \end{frame}
    325 
    326 
    327 
    328 \subsection{Pay with Taler}
    329 \begin{frame}
    330   \frametitle{Pay with Taler I}
    331   \begin{columns}
    332     \begin{column}{0.4\textwidth}
    333  \begin{block}{Withdraw e-cash}
    334     \begin{itemize}
    335     \item Withdraw in the app
    336     \item Transfer money to the Exchange
    337     \item Wait until the transfer is finalized
    338     \end{itemize}
    339   \end{block}
    340 
    341     \end{column}
    342     \begin{column}{0.5\textwidth}
    343 \begin{center}
    344   \includegraphics[width=0.4\textwidth]{./images/screenShot-withdraw.jpeg}
    345 \end{center}
    346 \end{column}
    347 
    348   \end{columns}
    349 
    350 \end{frame}
    351 
    352 \begin{frame}
    353   \frametitle{Pay with Taler II}
    354   \begin{columns}
    355     \begin{column}{0.4\textwidth}
    356   \begin{block}{Scan the QR code presented by the merchand}
    357     \begin{itemize}
    358     \item Validate the payment in the app
    359     \item DONE
    360     \end{itemize}
    361   \end{block}
    362 
    363     \end{column}
    364     \begin{column}{0.5\textwidth}
    365 \begin{center}
    366   \includegraphics[width=0.4\textwidth]{./images/taler-snack-automat.jpg}
    367 \end{center}
    368     \end{column}
    369 
    370   \end{columns}
    371 
    372 \end{frame}
    373 
    374 
    375 \begin{frame}
    376   \frametitle{Where can you pay?}
    377   \begin{columns}
    378     \begin{column}{0.4\textwidth}
    379   \begin{block}{Map of the merchants accepting Taler}
    380     \begin{itemize}
    381     \item \url{https://taler-ops.ch/en/map.html}
    382     \end{itemize}
    383   \end{block}
    384     \end{column}
    385     \begin{column}{0.5\textwidth}
    386 
    387   \includegraphics[width=1.1\textwidth]{./images/screenshot-map-taler-ops-ch.png}
    388     \end{column}
    389 
    390   \end{columns}
    391 
    392 \end{frame}
    393 
    394 
    395 \subsection{Merchant Backend}
    396 \begin{frame}
    397   \frametitle{Merchant Backend}
    398 
    399   \begin{block}{Directly installed on-site by interested merchants}
    400     \begin{itemize}
    401     \item Control 100\% of everything
    402     \item available as source
    403     \item available as binary for Linux, Windows and OSX.
    404     \end{itemize}
    405   \end{block}
    406 
    407   \begin{block}{For small merchants}
    408   \begin{itemize}
    409   \item One central server
    410   \item Each user has an account
    411   \item Can see all the transactions
    412   \end{itemize}
    413   \end{block}
    414   
    415 \end{frame}
    416 
    417 \section{Demo}
    418 
    419 \begin{frame}{Demonstration: Merchant Backend}
    420 
    421   \begin{block}{Merchant creates an account}
    422   \begin{itemize}
    423   \item \url{https://my.taler-ops.ch}
    424   \item Must accept terms of service.
    425   \item Must generate a mini transaction from a CH account (for KYC procedure).
    426   \end{itemize}
    427   \end{block}
    428   \begin{block}{Merchants can manage their inventar}
    429     \begin{itemize}
    430     \item Create items in the inventory
    431     \item Create orders selling items
    432     \item Create templates (to sell without dealing with inventory)
    433     \end{itemize}
    434   \end{block}
    435 \end{frame}
    436 
    437 \begin{frame}{Demonstration: Test Playground}
    438   \begin{block}{Play with demo money}
    439     \begin{itemize}
    440     \item In the wallet, you can get ``demo money'' (KUDOS)
    441     \item Get and send money (peer to peer) to your neighbour(s).
    442     \item Create a merchant account on \url{https://my.demo.taler.net}
    443     \item Buy / Sell / Transfer money as you want
    444     \item To get your money back to a bank, generate a bank account at: \url{https://bank.demo.taler.net}
    445     \end{itemize}
    446   \end{block}
    447 \end{frame}
    448 
    449 
    450 \section{Deploymerizer}
    451 
    452 \begin{frame}{Depolymerizer}{Taler for paying in BTC or ETH}
    453     % \begin{tikzpicture}[remember picture,overlay]
    454     %     \node (N1)[above right=22mm and 56mm of current page.center]    {\includegraphics[width=18mm]{./images/google_play_GNU_Taler.jpg}};
    455     %     \node [below=-2mm of N1]{wallet.taler.net};
    456     % \end{tikzpicture}
    457     \begin{center}
    458         \begin{tikzpicture}[
    459             rect/.style={rectangle, draw=black, minimum width=30mm},
    460             sym/.style={stealth-stealth, shorten >= 2pt, shorten <= 2pt},
    461             block/.style={rectangle,draw=black,fill=black!10,minimum size=7mm},
    462         ]
    463     
    464         %% Architecture
    465         \node(Tt){Taler};
    466         \node[rect,below=0cm of Tt](Tc){Exchange};
    467         \node[rect,fit={(Tt) (Tc)}](T){};
    468     
    469         \node[rect,below=7mm of Tc](D) {\textbf{Depolymerizer}};
    470     
    471         \node[rect,below=7mm of D](Bc){Node};
    472         \node[below=0cm of Bc](Bt){Blockchain};
    473         \node[rect,fit={(Bt) (Bc)}](B){};
    474     
    475         \draw[sym] (T) -- (D);
    476         \draw[sym] (D) -- (B);
    477     
    478         %% Blockchain
    479         \node[block,right=8mm of B] (1){};
    480         \node[block,right=4mm of 1] (2){};
    481         \node[block,right=4mm of 2] (3){};
    482         \node[block,right=4mm of 3] (4){};
    483         \node[block,right=4mm of 4] (5){};
    484         \node[block,right=4mm of 5] (6){};
    485         \draw[-stealth] (1) -- (2);
    486         \draw[-stealth] (2) -- (3);
    487         \draw[-stealth] (3) -- (4);
    488         \draw[-stealth] (4) -- (5);
    489         \draw[-stealth] (5) -- (6);
    490     
    491         \node[left=4mm of 1] (S){};
    492         \node[right=4mm of 6] (E){};
    493         \draw[-stealth] (S) -- (1);
    494         \draw[-stealth] (6) -- (E);
    495     
    496         %% Taler
    497         \node[block, below right=-7.5mm and 20.5mm of T] (off){Off-chain transactions};
    498         \node[above=-0.5mm of off] {\includegraphics[height=7mm]{./images/taler.png}};
    499     
    500         %% Depolymerization
    501         \node[right=12mm of D] {\small{Credit}};
    502         \node[right=55mm of D] {\small{Debit}};
    503         \draw[dashed,-stealth] (1.north) |- (off.west);
    504         \draw[dashed,-stealth] (off.east) -| (6.north);
    505     
    506         %% Separation
    507         \draw[dotted] (-2.1,-1.3) -- (9,-1.3);
    508         \draw[dotted] (-2.1,-2.5) -- (9,-2.5);
    509     \end{tikzpicture}
    510     \end{center}
    511 \end{frame}
    512 
    513 \begin{frame}
    514 \frametitle{Overview of the Depolymerizer}
    515 \begin{center}
    516   \includegraphics[width=8.5cm]{images/triangle-taler-en.pdf}
    517 %   \begin{tikzpicture}
    518 %  \tikzstyle{def} = [node distance= 4.5em and 6em, inner sep=1em, outer sep=.3em];
    519 %  \node (origin) at (0,0) {};
    520 %  \node (exchange) [def,above=of origin,draw]{Service d'échange};
    521 %  \node (customer) [def, draw, below left=of origin] {Portefeuille};
    522 %  \node (merchant) [def, draw, below right=of origin] {Backend commerçant};
    523 % % \node (auditor) [def, draw, above right=of origin]{Auditor};
    524 %  \tikzstyle{C} = [color=black, line width=1pt]
    525 %  \draw [<-, C] (customer) -- (exchange) node [midway, above, sloped]
    526 %  (TextNode) {retire des jetons};
    527 %  \draw [<-, C] (exchange) -- (merchant) node [midway, above, sloped]
    528 %  (TextNode) {dépose les jetons};
    529 %  \draw [<-, C] (merchant) -- (customer) node [midway, above, sloped]
    530 %  (TextNode) {dépense les jetons};
    531 % % \draw [<-, C] (exchange) -- (auditor) node [midway, above, sloped] (TextNode) {verify};
    532 % \end{tikzpicture}
    533 \end{center}
    534 \end{frame}
    535 
    536 \begin{frame}{Difference Depolymerizer / Lightening}
    537 
    538   \begin{block}{Main difference: Centralized / Decentralized}
    539     \begin{itemize}
    540     \item One deploymerizer
    541     \item Many lightening networks
    542     \end{itemize}
    543   \end{block}
    544   \begin{block}{Anonymity}
    545     \begin{itemize}
    546     \item Full anonymity of the payer,
    547     \item no anonymity of the payee.
    548     \item Goal : no money laundering, no crime financing, no tax evasion.
    549     \end{itemize}
    550   \end{block}
    551 \end{frame}
    552   
    553 \section{Q \& A}
    554 
    555 \begin{frame}
    556   \frametitle{Questions ?}
    557       \begin{columns}
    558       \begin{column}{0.3\textwidth}
    559         \begin{center}
    560           \includegraphics[width=0.9\textwidth]{./images/3d-question-mark}
    561         \end{center}
    562       \end{column}
    563       \begin{column}{0.65\textwidth}
    564 
    565 
    566         \begin{block}{Contacts}
    567           \begin{itemize}
    568           \item \url{https://www.taler.net}
    569           \item emmanuel.benoist@bfh.ch
    570           \item christian.grothoff@bfh.ch 
    571           \end{itemize}
    572         \end{block}
    573   \end{column}
    574 \end{columns}
    575 \end{frame}
    576 
    577 
    578 \begin{frame}{Acknowledgements}
    579 
    580   \begin{minipage}{0.45\textwidth} \ \\
    581     {\tiny Funded by the European Union (Project 101135475).}
    582 
    583     \begin{center}
    584       \includegraphics[width=0.5\textwidth]{./images/bandera.jpg}
    585     \end{center}
    586   \end{minipage}
    587   \hfill
    588   \begin{minipage}{0.45\textwidth}
    589     {\tiny Funded by SERI (HEU-Projekt 101135475-TALER).}
    590 
    591     \begin{center}
    592       \includegraphics[width=0.65\textwidth]{./images/sbfi.jpg}
    593     \end{center}
    594   \end{minipage}
    595 
    596   \vfill
    597 
    598   {\tiny Views and opinions expressed are however those of the author(s) only
    599     and do not necessarily reflect those of the European Union. Neither the
    600     European Union nor the granting authority can be held responsible for
    601     them.}
    602 \end{frame}
    603 
    604 
    605 
    606 
    607 \end{document}
    608 \begin{frame}
    609   \frametitle{Example}
    610       \begin{columns}
    611       \begin{column}{0.47\textwidth}
    612 \begin{center}
    613       \includegraphics[width=0.8\textwidth]{./images/3d-question-mark.jpg}
    614 
    615 \end{center}
    616 \end{column}
    617       \begin{column}{0.47\textwidth}
    618 
    619         \begin{block}{Title for block}
    620           \begin{itemize}
    621           \item Item number 1
    622           \end{itemize}
    623         \end{block}
    624   \end{column}
    625 \end{columns}
    626 \end{frame}
    627 
    628 
    629