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"cell_type": "markdown",
"metadata": {},
"source": [
"# On the computation of $\\pi$"
"# On the computation of $\\pi$"
]
},
{
......@@ -57,7 +57,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"## Buffons needle"
"## Buffon's needle"
]
},
{
......@@ -96,16 +96,14 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"### 1.3 Using a surface fraction argument"
"## 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\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:"
"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:"
]
},
{
......
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