From 071fc0a9d9941bfdcddbb564d60b248378cbb45f Mon Sep 17 00:00:00 2001
From: 06295db534a9872198b1363b8b12f920
 <06295db534a9872198b1363b8b12f920@app-learninglab.inria.fr>
Date: Thu, 6 Mar 2025 14:44:25 +0000
Subject: [PATCH] test

---
 module2/exo1/toy_notebook_en.ipynb | 32 +++++++++++-------------------
 1 file changed, 12 insertions(+), 20 deletions(-)

diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb
index c027cbf..7580ee9 100644
--- a/module2/exo1/toy_notebook_en.ipynb
+++ b/module2/exo1/toy_notebook_en.ipynb
@@ -70,7 +70,7 @@
     "## 1.3 Using a surface fraction argument\n",
     "\n",
     "A method that is easier to understand and does not make use of the sin function is based on the\n",
-    "fact that if *X ∼ U(0, 1)* and *Y ∼ U(0, 1)* then P[X^2 + Y^2 ≤ 1] = &#960;/4 (see [\"Monte Carlo method\"\n",
+    "fact that if *X ∼ U(0, 1)* and *Y ∼ U(0, 1)* then P[X<sup>2</sup> + Y<sup>2</sup> ≤ 1] = &#960;/4 (see [\"Monte Carlo method\"\n",
     "on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
    ]
   },
@@ -108,6 +108,16 @@
     "ax.set_aspect('equal')\n"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "It is then straightforward to obtain a (not really good) approximation to π by counting how\n",
+    "many times, on average, X<sup>2</sup> + Y<sup>2</sup> is smaller than 1:"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": 4,
@@ -125,25 +135,7 @@
     }
    ],
    "source": [
-    "4*np.mean(accept)\n"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-6-2b522dbd7382>, line 1)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  File \u001b[0;32m\"<ipython-input-6-2b522dbd7382>\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m    4*np.mean(accept.5f)\u001b[0m\n\u001b[0m                     ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
-   "source": [
-    "\n"
+    "4*np.mean(accept)"
    ]
   },
   {
-- 
2.18.1