"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:"
"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 $P[X^2+Y^2 \\leq 1] = \\pi /4$ (see [\"Monte Carlo method\" on Wikipedia](https://en.wikipedia.org/wiki/Monte_Carlo_method)). The following code uses this approach:"
]
},
{
...
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@@ -107,7 +107,7 @@
"cell_type": "markdown",
"metadata": {},
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"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:"
