toy_notebook_en

module2/exo1/toy_notebook_en.ipynb

@@ -18,21 +18,21 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## 1   On the computation of $\\pi$"
+    "#   On the computation of $\\pi$"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 1.1 Asking the maths library"
+    "## Asking the maths library"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "My computer tells me that $\\pi$ is approximatively"
+    "My computer tells me that $\\pi$ is *approximatively*"
    ]
   },
   {
@@ -57,14 +57,14 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 1.2 Buffon’s needle"
+    "## Buffon’s needle"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the approximation"
+    "Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__"
    ]
   },
   {
@@ -104,7 +104,7 @@
    "metadata": {},
    "source": [
     "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 $P[X^2 + Y^2 ≤ 1] = \\pi/4$ (see [\"Monte Carlo method\"\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:"
    ]
   },
@@ -142,9 +142,16 @@
     "ax.set_aspect('equal')"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how many times, on average, $X^2 + Y^2$ is smaller than 1:"
+   ]
+  },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -153,7 +160,7 @@
        "3.112"
       ]
      },
-     "execution_count": 4,
+     "execution_count": 5,
      "metadata": {},
      "output_type": "execute_result"
     }