Commit 8d50ce20 authored by Manuela's avatar Manuela

nouvelle version

parent 85645a26
......@@ -360,14 +360,14 @@ display: none;
<h1>En demandant à la lib maths</h1>
<p>Mon ordinateur m’indique que <span class="math inline">\(\pi\)</span>
vaut approximativement</p>
<pre><code>pi</code></pre>
<pre><code>##[1] 3.141595</code></pre>
<pre class="r"><code>pi</code></pre>
<pre><code>## [1] 3.141593</code></pre>
</div>
<div id="en-utilisant-la-méthode-des-aiguilles-de-buffon" class="section level1">
<h1>En utilisant la méthode des aiguilles de Buffon</h1>
<p>Mais calculé avec la <strong>méthode</strong> des <a href="https://fr.wikipedia.org/wiki/Aiguille_de_Buffon">aiguilles de
Buffon</a>, on obtiendrait comme <strong>approximation</strong> :</p>
<pre><code>set.seed(42)
<pre class="r"><code>set.seed(42)
N = 100000
x = runif(N)
theta = pi/2*runif(N)
......@@ -375,10 +375,8 @@ theta = pi/2*runif(N)
<pre><code>## [1] 3.14327</code></pre>
<p>#Avec un argument “fréquentiel” de surface</p>
<p>Sinon, une méthode plus simple à comprendre et ne faisant pas
intervenir d’appel à la fonction sinus se base sur le fait que si
<em>X∼U(0,1)</em> et <span class="math inline">\(Y∼U(0,1)\)</span> alors
<span class="math inline">\(P[X^2+Y^2 ≤1]= \pi/4\)</span> voir [méthode
de Monte Carlo sur Wikipedia ] (<a href="https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80" class="uri">https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80</a>).
intervenir d’appel à la fonction sinus se base sur le fait que si <span class="math inline">\(X\sim U(0,1)\)</span> et <span class="math inline">\(Y\sim U(0,1)\)</span> alors <span class="math inline">\(P[X^2+Y^2 \leq1]= \pi/4\)</span> voir [méthode de
Monte Carlo sur Wikipedia] (<a href="https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80" class="uri">https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80</a>)).
Le code suivant illustre ce fait:</p>
<pre class="r"><code>set.seed(42)
N = 1000
......@@ -389,11 +387,12 @@ library(ggplot2)</code></pre>
<pre class="r"><code>ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() +
theme_bw()</code></pre>
<p><img role="img" src="data:image/png;base64,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" width="672" /></p>
<p>Il est alors aisé d’obtenir une approximation (pas terrible) de π en
comptant combien de fois, en moyenne, <span class="math inline">\(X^2 +
Y^2\)</span> est inférieur à 1:</p>
<pre><code>4*mean(df$Accept)</code></pre>
<p>Il est alors aisé d’obtenir une approximation (pas terrible) de <span class="math inline">\(\pi\)</span> en comptant combien de fois, en
moyenne, <span class="math inline">\(X^2 + Y^2\)</span> est inférieur à
1:</p>
<pre class="r"><code>4*mean(df$Accept)</code></pre>
<pre><code>## [1] 3.156</code></pre>
<pre class="r"><code>## [1] 3.156</code></pre>
</div>
......
Markdown is supported
0% or
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment