diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index cb38e538bb187e8d6fb5a4505865bae4a5803974..6b2de2bde5a87d4bb4f29347ae084c5bb8935309 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,18 +4,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "#
toy_notebook_en
\n", - "\n", - "
March 28, 2019
" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# 1 On the computation of $π$\n", - "## 1.1 Asking the maths library\n", - "My computer tells me that $π$ is *approximatively*" + "# On the computation of $π$\n", + "## Asking the maths library\n", + "My computer tells me that $\\pi$ is *approximatively*" ] }, { @@ -40,7 +31,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 1.2 Buffon’s needle\n", + "## Buffon’s needle\n", "Applying the method of [Buffon’s needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the **approximation**" ] }, @@ -73,9 +64,9 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## 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\n", - "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\"\n", + "## 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\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:" ] }, @@ -117,7 +108,7 @@ "metadata": {}, "source": [ "\n", - "It is then straightforward to obtain a (not really good) approximation to $π$ by counting how\n", + "It is then straightforward to obtain a (not really good) approximation to $\\pi$ by counting how\n", "many times, on average, $X^2 + Y^2$\n", "is smaller than 1:" ]