diff --git a/module2/exo1/toy_notebook_en.ipynb b/module2/exo1/toy_notebook_en.ipynb index ead7508f9301cd72fc5deec01796a1f4f55a89e9..e498ae5ae83b1d4ec02d26c5c2ce4ee976eb53fa 100644 --- a/module2/exo1/toy_notebook_en.ipynb +++ b/module2/exo1/toy_notebook_en.ipynb @@ -4,16 +4,14 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "##
toy_notebook_en\n", - "
March 28, 2019" + "# 1 On the computation of $\\pi$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "### **1 On the computation of** $\\pi$\n", - "**1.1 Asking the math library**" + "## 1.1 Asking the maths library" ] }, { @@ -45,7 +43,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "**1.2 Buffon's needle**" + "## 1.2 Buffon's needle" ] }, { @@ -77,21 +75,21 @@ "N = 10000\n", "x = np.random.uniform(size=N, low=0, high=1)\n", "theta = np.random.uniform(size=N, low=0, high=pi/2)\n", - "2/(sum((x+np.sin(theta))>1)/N)\n" + "2/(sum((x+np.sin(theta))>1)/N)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "**1.3 Using a surface fraction argument**" + "## 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 $X\\sim U(0,1)$ 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:" + "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:" ] }, {