Commit 4a342017 authored by Lucile Sainmont's avatar Lucile Sainmont

rendu

parent 39651d18
......@@ -30,4 +30,23 @@ theta = pi/2*runif(N)
2/(mean(x+sin(theta)>1))
```
## Avec un argument “fréquentiel” de surface
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 $X∼U(0,1)$ et $Y∼U(0,1)$ alors $P[X^2+Y^2≤1]=π/4$ ([voir méthode de Monte Carlo sur Wikipedia](https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80)). Le code suivant illustre ce fait:
```{r message=FALSE}
set.seed(42)
N = 1000
df = data.frame(X = runif(N), Y = runif(N))
df$Accept = (df$X**2 + df$Y**2 <=1)
library(ggplot2)
ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()
```
Il est alors aisé d’obtenir une approximation (pas terrible) de π en comptant combien de fois, en moyenne, $X^2+Y^2$
est inférieur à 1:
```{r}
4*mean(df$Accept)
```
\ No newline at end of file
......@@ -213,6 +213,21 @@ theta = pi/2*runif(N)
2/(mean(x+sin(theta)&gt;1))</code></pre>
<pre><code>## [1] 3.14327</code></pre>
</div>
<div id="avec-un-argument-frequentiel-de-surface" class="section level2">
<h2>Avec un argument “fréquentiel” de surface</h2>
<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 <span class="math inline">\(X∼U(0,1)\)</span> et <span class="math inline">\(Y∼U(0,1)\)</span> alors <span class="math inline">\(P[X^2+Y^2≤1]=π/4\)</span> (<a href="https://fr.wikipedia.org/wiki/M%C3%A9thode_de_Monte-Carlo#D%C3%A9termination_de_la_valeur_de_%CF%80">voir méthode de Monte Carlo sur Wikipedia</a>). Le code suivant illustre ce fait:</p>
<pre class="r"><code>set.seed(42)
N = 1000
df = data.frame(X = runif(N), Y = runif(N))
df$Accept = (df$X**2 + df$Y**2 &lt;=1)
library(ggplot2)
ggplot(df, aes(x=X,y=Y,color=Accept)) + geom_point(alpha=.2) + coord_fixed() + theme_bw()</code></pre>
<p><img 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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></p>
<p>est inférieur à 1:</p>
<pre class="r"><code>4*mean(df$Accept)</code></pre>
<pre><code>## [1] 3.156</code></pre>
</div>
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