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"source": [
"# On the computation of $\\pi$ \n",
"## Asking the maths library \n",
"\n",
"My computer tells me that $\\pi$ is *approximatively*"
]
},
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"metadata": {},
"source": [
"## Using a surface fraction argument\n",
"A method that is easier to understand and doest not make use of the sin function is based on the fact that if $X \\sim U(0,1)$ $Y \\sim U(0,1)$, 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:"
"A method that is easier to understand and does not make use of the sin function is based on the fact that if $X \\sim U(0,1)$ $Y \\sim U(0,1)$, 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:"
]
},
{
......@@ -106,7 +107,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"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:"
"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:"
]
},
{
......
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