"My computer tells me that $\\pi$ is *approximatively*"
"My computer tells me that $\\pi$ is *approximatively*"
]
]
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"### 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**"
"Applying the method of [Buffon's needle](https://en.wikipedia.org/wiki/Buffon%27s_needle_problem), we get the **approximation**"
]
]
},
},
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"### 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",
"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:"