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sections/german/09/09.md
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<div class="layout-content-only">
<div class="layout-content">
<h1><span class="emoji">🧮</span><br/>Mathematische Formeln</h1>
<h1>Mathematische Formeln</h1>
</div>
</div>
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<div class="layout-content-and-preview">
<div class="layout-content">
<h2>Formel-Umgebungen</h2>
<h2>Formel-Umgebungen <span class="emoji">🧮</span></h2>
<pre class="lang-tex hljs"><code>$2 \sqrt{\frac{\pi^2}{3} \cdot c_2}$</code></pre>
<p>Die mathematische Umgebung wird durch zwei Dollarzeichen abgegrenzt. Außerdem gibt es eine Blockumgebung.</p>
<p>Mathematische Formeln können <strong>nur im sogenannten Mathmode</strong> gesetzt werden, der inline durch zwei Dollarzeichen aktiviert wird. Außerdem gibt es eine Blockumgebung:</p>
<pre class="lang-tex hljs"><code>\begin{equation}
2 \sqrt{\frac{\pi^2}{3} \cdot c_2}
\end{equation}</code></pre>
<p>Die Nummerierung kann durch durch einen »\*« in <code>\begin{equation\*}</code> und <code>\end{equation\*}</code> unterdrückt werden.</p>
<p>Pakete: <code>amsmath</code>, <code>amsthm</code>, <code>amssymb</code>, <code>mathtools</code></p>
</div>
<div class="layout-preview">
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<th>Ergebnis</th>
</tr>
<tr class="fragment">
<td>`$`<code>\sqrt{16}$</code></td>
<td><code>\sqrt{16}</code></td>
<td>$\sqrt{16}$</td>
</tr>
<tr class="fragment">
<td>`$`<code>\frac{3}{4}$</code></td>
<td><code>\frac{3}{4}</code></td>
<td>$\frac{3}{4}$</td>
</tr>
<tr class="fragment">
<td>`$`<code>e^{\pi}$</code></td>
<td><code>e^{\pi}</code></td>
<td>$e^{\pi}$</td>
</tr>
<tr class="fragment">
<td>`$`<code>\sum\_{i=1}^{n}x^2$</code></td>
<td><code>\sum\_{i=1}^{n}x^2</code></td>
<td>$\sum_{i=1}^{n} x^2$</td>
</tr>
<tr class="fragment">
<td>`$`<code>12 \leq 4 x^2 + 13$</code></td>
<td><code>12 \leq 4 x^2 + 13</code></td>
<td>$12 \leq 4 x^2 + 13$</td>
</tr>
</table>
<p class="fragment">Durch <code>$</code><code>^{…}$</code> und <code>$</code><code>&lowbar;{…}$</code> werden Inhalte hoch- oder tiefgestellt.</p>
<p class="fragment">Durch <code>^{…}</code> und <code>&lowbar;{…}</code> werden die Inhalte in den Klammern hoch- oder tiefgestellt.</p>
</div>
</div>
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<th>Ergebnis</th>
</tr>
<tr>
<td>`$`<code>(x), [x], \lbrace x\rbrace, \lvert x\rvert$</code></td>
<td><code>(x),&thinsp;[x],&thinsp;\lbrace x\rbrace,&thinsp;\lvert x\rvert</code></td>
<td>$(x), [x], \lbrace x\rbrace, \lvert x\rvert$</td>
</tr>
<tr>
<td>`$`<code>\exists,\forall,\in,\notin,\infty$</code></td>
<td><code>\exists,&thinsp;\forall,&thinsp;\in,&thinsp;\notin,&thinsp;\infty</code></td>
<td>$\exists,\forall,\in,\notin,\infty$</td>
</tr>
<tr>
<td>`$`<code>\alpha, \beta, \Gamma, \Delta, \varepsilon, \pi$</code></td>
<td><code>\alpha,&thinsp;\beta,&thinsp;\Gamma,&thinsp;\Delta,&thinsp;\varepsilon,&thinsp;\pi</code></td>
<td>$\alpha, \beta, \Gamma, \Delta, \varepsilon, \pi$</td>
</tr>
<tr>
<td>`$`<code>\rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \Leftrightarrow$</code></td>
<td><code>\rightarrow,&thinsp;\leftarrow,&thinsp;\Rightarrow,&thinsp;\Leftarrow,&thinsp;\Leftrightarrow</code></td>
<td>$\rightarrow, \leftarrow, \Rightarrow, \Leftarrow, \Leftrightarrow$</td>
</tr>
<tr>
<td>`$`<code>(A \cup B) \cap C$</code></td>
<td><code>(A&thinsp;\cup&thinsp;B)&thinsp;\cap&thinsp;C</code></td>
<td>$(A \cup B) \cap C$</td>
</tr>
<tr>
<td>`$`<code>(A \lor B) \land C$</code></td>
<td><code>(A&thinsp;\lor&thinsp;B)&thinsp;\land&thinsp;C</code></td>
<td>$(A \lor B) \land C$</td>
</tr>
<tr>
<td>`$`<code>(A \cdot B) \times C$</code></td>
<td><code>(A&thinsp;\cdot&thinsp;B)&thinsp;\times&thinsp;C</code></td>
<td>$(A \cdot B) \times C$</td>
</tr>
</table>
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<th>Ergebnis</th>
</tr>
<tr class="fragment">
<td>`$`<code>\left( \frac{1}{2} \right)$</code></td>
<td><code>\left( \frac{1}{2} \right)</code></td>
<td>$\left(\frac{1}{2} \right)$</td>
</tr>
<tr class="fragment">
<td>`$`<code>\left\lbrace \frac{1}{2} \right\rbrace$</code></td>
<td><code>\left\lbrace \frac{1}{2} \right\rbrace</code></td>
<td>$\left\lbrace\frac{1}{2} \right\rbrace$</td>
</tr>
<tr class="fragment">
<td>`$`<code>\left[ \frac{1}{2} \right]$</code></td>
<td><code>\left[ \frac{1}{2} \right]</code></td>
<td>$\left[\frac{1}{2} \right]$</td>
</tr>
</table>
<pre class="fragment hljs lang-tex"><code>$4 \cdot \left(\frac{1}{2} + \frac{3}{12 \cdot \left(\ 2 + frac{1}{26 \cdot \left(\frac{1}{2} \+ 24 right)} \right) }\right)$</code></pre>
<pre class="fragment hljs lang-tex"><code>$4 \cdot \left( \frac{1}{2} % …</code></pre>
<p class="fragment" style="text-align: center;">$4 \cdot \left(\frac{1}{2} +\frac{3}{ 12 \cdot \left( 2 + \frac{1}{86 \cdot \left(\frac{1}{2} + 24 \right)} \right)} \right)$</p>
</div>
</div>
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<h2>Ausrichtung von mehreren Gleichungen</h2>
<p>Die Umgebung <code>align</code> erlaubt es, Gleichungen zum Beispiel am »=« auszurichten.</p>
<pre class="hljs lang-tex"><code>\begin{align}
13 \cdot (4a - 3)^2 &= 13 \cdot (16a^2 - 24a + 9) \\\\
13 \cdot (4a - 3)^2 &= 13 … \\\\
&= 208a^2 - 312a + 117
\end{align}</code></pre>
<ul>
<li class="fragment">Ausgerichtet wird am »&«-Zeichen.</li>
<li class="fragment">Zeilenumbrüche werden mit »\\\\« eingefügt.</li>
<li class="fragment">Die Nummerierung kann auch hier durch durch einen »\*« in <code>\begin{align\*}</code> und <code>\end{align\*}</code> unterdrückt werden.</li>
<li class="fragment">Die Nummerierung kann bei `align` und `equation` durch durch ein Sternchen nach dem Umgebungsnamen (z.&thinsp;B. <code>\begin{align\*}</code> und <code>\end{align\*}</code>) unterdrückt werden.</li>
</ul>
</div>
<div class="layout-preview">

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4
sections/german/09/simple-maths.tex
View File

@ -7,6 +7,8 @@
\begin{document}
\thispagestyle{empty}
$2 \sqrt{\frac{\pi^2}{3} \cdot c_2}$
$$
2 \sqrt{\frac{\pi^2}{3} \cdot c_2}
$$
\end{document}