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<section>
<h1>Das Koch Fraktal</h1>
<small>Von Marvin Borner, TGI 12.1</small>
</section>
<section>
<h3>Gliederung</h3>
<ol>
<li>Fraktale</li>
<li>Koch Fraktal</li>
<li>Varianten des Koch Fraktals</li>
<!-- engl. Wikipedia -->
<li>Umfang des Koch Fraktals</li>
<li>Fläche des Koch Fraktals</li>
</ol>
</section>
<section>
<h3>Fraktale</h3>
</section>
<section>
<!-- Vorstellung -->
<section>
<h3>Regeln</h3>
<ol>
<li>Mit einer geraden Linie starten</li>
<li>Linie in drei Teile aufteilen</li>
<li>Den mittleren Teil der Linie "radieren"</li>
<li>Den mittleren Teil zu einem gleichseitigen Dreieck verbinden</li>
</ol>
</section>
<section>
<div id="iterationCtr"></div>
<div class="flexContainer">
<canvas id="koch"></canvas>
</div>
</section>
</section>
<section>
<!-- Mit zwei browsern visualisieren (tiling!) -->
<section>
<h3>Umfang des Koch Fraktals</h3>
<div class="fragment fade-right" style="float: left;">
<p>Anzahl der Linien:</p>
<p>\[ N_n = N_{n-1} \cdot 4 = 4^n \]</p>
</div>
<div class="fragment fade-left" style="float: right;">
<p>Länge der Linien:</p>
<p>\[ S_n = \frac{S_{n-1}}{3} = \frac{s}{3^n} \]</p>
</div>
<div data-action="nebenrechnung" class="fragment fade-up" style="float: left;">
<p>Umfang:</p>
<p>\[ P_n = N_n\cdot S_n = s\cdot\left(\frac{4}{3}\right)^n \]</p>
</div>
<div class="fragment fade-up" style="float: right;">
<p>Grenzwert:</p>
<p>\[ \lim_{n\to\infty}P_n = \infty \]</p>
</div>
<span data-action="gooo" class="fragment" style="display: none !important;"></span>
</section>
<section>
<h3>Nebenrechnung</h3>
<p class="fragment fade-up">\[ N_n = N_{n-1} \cdot 4 = 4^n \]</p>
<p class="fragment fade-up">\[ S_n = \frac{S_{n-1}}{3} = \frac{s}{3^n} \]</p>
<p class="fragment fade-up">
\[ P_n = N_n\cdot S_n = 4^n \cdot \frac{s}{3^n} = \frac{s \cdot 4^n}{3^n} = s \cdot
\frac{4^n}{3^n} \]
</p>
<span data-action="umfang-back" class="fragment" style="display: none !important;"></span>
</section>
</section>
<section>
<h3>Summenzeichen</h3>
<p>\[ \sum_{x=1}^{5} x^2 \]</p>
<p class="fragment fade-up">\[ = 1^2 + 2^2 + 3^2 + 4^2 + 5^2 = 55 \]</p>
</section>
<section>
<h3>Fläche des Koch Fraktals</h3>
</section>
<section>
<h3>Varianten des Koch Fraktals</h3>
<img
class="plain"
style="background: none;"
src="imgs/KochFlake.svg"
alt="Hier könnte ihre Werbung stehen!"
/>
</section>
<section>
<h3>Fläche des Koch Fraktals</h3>
</section>
<section>
<h3>Quellen</h3>
<p>Bilder</p>
<a href="https://en.wikipedia.org/wiki/Koch_snowflake#/media/File:KochFlake.svg" target="_blank">
https://en.wikipedia.org/wiki/Koch_snowflake#/media/File:KochFlake.svg
</a>
<p>Wissen</p>
<a href="https://en.wikipedia.org/wiki/Koch_snowflake" target="_blank">
https://en.wikipedia.org/wiki/Koch_snowflake
</a>
<a
href="http://www.mathematik.uni-ulm.de/stochastik/lehre/ws06_07/seminar_fraktale/daikeler.pdf"
target="_blank"
>
http://www.mathematik.uni-ulm.de/stochastik/lehre/ws06_07/seminar_fraktale/daikeler.pdf
</a>
</section>
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