From e18a46cf9c8489c7954f91532de21e31795a1c5f Mon Sep 17 00:00:00 2001 From: ef8766fce5f06e5c105a6af29adae07c Date: Thu, 21 Sep 2023 14:03:09 +0000 Subject: [PATCH] Some changes --- module2/exo1/toy_notebook_en.ipynb | 19 ++++++++++--------- 1 file changed, 10 insertions(+), 9 deletions(-) diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index d948907..c003f68 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,8 +4,13 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "# On the computation of $\\pi$\n", - "\n", + "# On the computation of $\\pi$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "## Asking the maths library\n", "\n", "My computer tells me that $\\pi$ is *approximatively*" @@ -34,8 +39,7 @@ "metadata": {}, "source": [ "## Buffon’s needle\n", - "\n", - "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__" ] }, { @@ -68,9 +72,7 @@ "metadata": {}, "source": [ "## 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 fact that 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\"\n", - "on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). 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 $P[X^2 + Y^2 \\le 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:" ] }, { @@ -113,8 +115,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how\n", - "many times, on average, $X^2 + Y^2$ is smaller than 1:" + "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:" ] }, { -- 2.18.1