diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index bf7b71af5a04b3a43f8fe112b068fc096148fe86..a5ff17ec3cb0f7bef8fb1c9193555a70b2ecc4c6 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,9 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1 On the computation of $\\pi$\n", + "# 1 On the computation of $\\pi$\n", "\n", - "### 1.1 Asking the maths library\n", + "## 1.1 Asking the maths library\n", "\n", "My computer tells me that $\\pi$ is *approximatively*" ] @@ -33,7 +33,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 1.2 Buffon’s needle\n", + "## 1.2 Buffon’s needle\n", "Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the **approximation**" ] }, @@ -66,9 +66,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "### 1.3 Using a surface fraction argument\n", + "## 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 fact that \n", - "if *X* $\\sim$ *U*(0, 1) and *Y* $\\sim$ *U*(0, 1), then *P*[$X^2$ + $Y^2$ $\\le$1] $=$ $\\pi$/4 (see [\"Monte Carlo method\"on Wikipedia)](https://en.wikipedia.org/wiki/Monte_Carlo_method). The following code uses this approach:" + "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:" ] }, {