"My computer tells me that $\\pi$ is *approximatively*"
]
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@@ -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**"
]
},
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@@ -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:"