{
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    "cell_type": "markdown",
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    "source": [
      "# À propos de pi"
    ]
  },
  {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
      "Some mathematical formulas:\n",
      "$\\pi = \\frac{C}{D}$\n",
      "$$ \\pi \\approx 3.14 $$"
    ]
  },
  {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
      "import math\n",
      "print(math.pi)"
    ]
  },
  {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
      "Learn more here: [Aiguilles de Buffon](https://fr.wikipedia.org/wiki/Aiguille_de_Buffon)"
    ]
  },
  {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
      "import random\n",
      "import math\n\n",
      "def buffon_needle(n):\n",
      "    count = 0\n",
      "    for _ in range(n):\n",
      "        x = random.uniform(0, 1)\n",
      "        theta = random.uniform(0, math.pi / 2)\n",
      "        if x <= math.sin(theta):\n",
      "            count += 1\n",
      "    return (2 * n) / count\n\n",
      "print(buffon_needle(100000))"
    ]
  },
  {
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
      "import matplotlib.pyplot as plt\n",
      "import numpy as np\n\n",
      "x = np.linspace(0, 2 * np.pi, 100)\n",
      "y = np.sin(x)\n\n",
      "plt.plot(x, y)\n",
      "plt.title(\"Sine Wave\")\n",
      "plt.xlabel(\"x\")\n",
      "plt.ylabel(\"sin(x)\")\n",
      "plt.grid(True)\n",
      "plt.show()"
    ]
  }
]
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