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   "source": [
    "In [1]: from math import *\n",
    "print(pi)\n",
    "\n",
    "In [2]: import numpy as np\n",
    "np.random.seed(seed=42)\n",
    "N = 10000\n",
    "x = np.random.uniform(size=N, low=0, high=1)\n",
    "theta = np.random.uniform(size=N, low=0, high=pi/2)\n",
    "2/(sum((x+np.sin(theta))>1)/N)\n",
    "Out[2]: 3.1289111389236548\n",
    "    \n",
    "In [3]: %matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "np.random.seed(seed=42)\n",
    "N = 1000\n",
    "x = np.random.uniform(size=N, low=0, high=1)\n",
    "y = np.random.uniform(size=N, low=0, high=1)\n",
    "1\n",
    "accept = (x*x+y*y) <= 1\n",
    "reject = np.logical_not(accept)\n",
    "fig, ax = plt.subplots(1)\n",
    "ax.scatter(x[accept], y[accept], c='b', alpha=0.2, edgecolor=None)\n",
    "ax.scatter(x[reject], y[reject], c='r', alpha=0.2, edgecolor=None)\n",
    "ax.set_aspect('equal')\n",
    "\n",
    "In [4]: 4*np.mean(accept)\n",
    "Out[4]: 3.1120000000000001"
   ]
  }
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