diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index 8c88c1bd93c507541bce2bed07d8a829172a5927..2d534e4d0b424e5b0934e162938027b1411b82f7 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,7 +4,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1 On the computation of π\n", + "## 1 On the computation of $\\pi$\n", "\n", "### 1.1 Asking the maths library\n", "\n", @@ -13,7 +13,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 20, "metadata": {}, "outputs": [ { @@ -40,7 +40,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 21, "metadata": {}, "outputs": [ { @@ -49,7 +49,7 @@ "3.128911138923655" ] }, - "execution_count": 15, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -69,14 +69,12 @@ "source": [ "### 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[X² + Y² ≤ 1] = π/4 (see \"Monte Carlo method\" on Wikipedia). \n", - "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:" ] }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 22, "metadata": {}, "outputs": [ { @@ -116,7 +114,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -125,7 +123,7 @@ "3.112" ] }, - "execution_count": 19, + "execution_count": 23, "metadata": {}, "output_type": "execute_result" }