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"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# 1. On the computation of $\\pi$\n", "# On the computation of $\\pi$\n",
"## 1.1 Asking the maths library\n", "## Asking the maths library\n",
"My computer tells me that 𝜋 is approximativey" "My computer tells me that 𝜋 is approximativey"
] ]
}, },
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"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 1.2 Buffon’s needle" "## Buffon’s needle"
] ]
}, },
{ {
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"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 1.3 Using a surface fraction argument\n", "## Using a surface fraction argument\n",
"\n", "\n",
"A method that is easier to understand and does not make use of the sin function is based on the fact that if $X ∼ U(0, 1)$ and $Y ∼ U(0, 1)$, then $P[X^2 + Y^2 ≤ 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia)](https://en.wikipedia.org/wiki/Monte_Carlo_method). The following code uses this approach:\n" "A method that is easier to understand and does not make use of the sin function is based on the fact that if $X ∼ U(0, 1)$ and $Y ∼ U(0, 1)$, then $P[X^2 + Y^2 ≤ 1] = \\pi/4$ (see [\"Monte Carlo method\" on Wikipedia)](https://en.wikipedia.org/wiki/Monte_Carlo_method). The following code uses this approach:\n"
] ]
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