diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index 03ff4bc425b6c83e4014f017f2bf96b70a3ed6c5..03a662615405639d8065959f91a14e26e8c2c9a9 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,21 +4,15 @@ "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" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "My computer tells me that $\\pi$ is approximatively" + "## Asking the maths library\n", + "My computer tells me that $\\pi$ is *approximatively*" ] }, { @@ -43,14 +37,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1.2 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" + "## Buffon's needle\n", + "Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the __approximation__" ] }, { @@ -82,14 +70,8 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1.3 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 $X ∼ U(0, 1)$ and $Y ∼ U(0, 1)$, then $P[X^2 + Y^2 ≤ 1] = π/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method). The following code uses this approach:" + "## 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 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:" ] }, {