second commit

module2/exo1/toy_notebook_en.ipynb

@@ -4,18 +4,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# <center>toy_notebook_en</center>\n",
-    "\n",
-    "<center>March 28, 2019</center>"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "# 1 On the computation of $π$\n",
-    "## 1.1 Asking the maths library\n",
-    "My computer tells me that $π$ is *approximatively*"
+    "# On the computation of $π$\n",
+    "## Asking the maths library\n",
+    "My computer tells me that $\\pi$ is *approximatively*"
    ]
   },
   {
@@ -40,7 +31,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1.2 Buffon’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**"
    ]
   },
@@ -73,9 +64,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1.3 Using a surface fraction argument\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 $P[X^2 + Y^2 ≤ 1] = π/4$ (see [\"Monte Carlo method\"\n",
+    "## Using a surface fraction argument\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 $X \\sim U(0, 1)$ and $Y \\sim U(0, 1)$, then $P[X^2 + Y^2 \\leq 1] = \\pi/4$ (see [\"Monte Carlo method\"\n",
     "on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
    ]
   },
@@ -117,7 +108,7 @@
    "metadata": {},
    "source": [
     "\n",
-    "It is then straightforward to obtain a (not really good) approximation to $π$ by counting how\n",
+    "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how\n",
     "many times, on average, $X^2 + Y^2$\n",
     "is smaller than 1:"
    ]