Solution 4

module2/exo1/toy_notebook_en.ipynb

@@ -12,7 +12,7 @@
    "metadata": {},
    "source": [
     "## Asking the maths library\n",
-    "My computer tells me that $\\pi$ is approximatively"
+    "My computer tells me that $\\pi$ is *approximatively*"
    ]
   },
   {
@@ -37,13 +37,13 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Buffalo's needle\n",
+    "## Buffon's needle\n",
     "Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -52,7 +52,7 @@
        "3.128911138923655"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 10,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -63,21 +63,21 @@
     "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)\n"
+    "2/(sum((x+np.sin(theta))>1)/N)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1.3 Using a surface fraction argument"
+    "## Using a surface fraction argument"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\\sim U(0, 1)$ and $Y\\sim U(0, 1)$, then $P[X^2+Y^2\\leq 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
+    "A method that is easier to understand and does not make use of the sin function is based on the fact that if $X\\sim U(0,1)$ and $Y\\sim U(0,1)$, then $P[X^2+Y^2\\leq 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
    ]
   },
   {
@@ -99,7 +99,7 @@
     }
    ],
    "source": [
-    "%matplotlib inline\n",
+    "%matplotlib inline \n",
     "import matplotlib.pyplot as plt\n",
     "\n",
     "np.random.seed(seed=42)\n",