new try

module2/exo1/toy_notebook_fr.ipynb

@@ -17,8 +17,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {},
+   "execution_count": 14,
+   "metadata": {
+    "scrolled": true
+   },
    "outputs": [
     {
      "name": "stdout",
@@ -43,7 +45,40 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3.128911138923655"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "np.random.seed(seed=42)\n",
+    "N = 10000\n",
+    "x = np.random.uniform(size=N, low=0, high=1)\n",
+    "theta = np.random.uniform(size=N, low=0, high=pi/2)\n",
+    "2/(sum((x+np.sin(theta))>1)/N)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Avec un argument \"frésuentiel\" de surface\n",
+    "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 $X \\sim \\mathcal{U}(0,1)$ et $Y \\sim \\mathcal{U}(0,1)$ alors $P\\left[X^2 + Y^2 \\leq 1\\right] = \\pi/4$\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -68,13 +103,14 @@
     "N=1000\n",
     "x = np.random.uniform(size=N, low=0, high=1)\n",
     "y = np.random.uniform(size=N, low=0, high=1)\n",
+    "\n",
     "accept = (x*x+y*y) <= 1\n",
     "reject = np.logical_not(accept)\n",
     "\n",
     "fig, ax = plt.subplots(1)\n",
     "ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n",
     "ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n",
-    "ax.set_aspect('equal')\n"
+    "ax.set_aspect('equal')"
    ]
   },
   {
@@ -86,7 +122,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
@@ -95,7 +131,7 @@
        "3.112"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -103,13 +139,6 @@
    "source": [
     "4*np.mean(accept)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {