jupyter/pi.ipynb

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    "# Happy Pi Day!\n",
    "\n",
    "### Two Ways to Calculate Pi: \n",
    "Real pi = 3.14159265359\n",
    "\n",
    "### 1. percentage of unit square random points that lie in unit circle\n",
    "This method is only as good as our random number generator. And with number of iterations the accuracy improves, up to about 1 million."
   ]
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  {
   "cell_type": "code",
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     "name": "stdout",
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     "text": [
      "3.1417076\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "in_square = in_circle = pi = 0\n",
    "\n",
    "for i in range(10000000):\n",
    "    x = random.random()\n",
    "    y = random.random()\n",
    "    dist = (x*x + y*y) ** 0.5\n",
    "\n",
    "    in_square += 1\n",
    "    if dist <= 1.0:\n",
    "        in_circle += 1\n",
    "            \n",
    "pi = 4 * in_circle / in_square\n",
    "print(pi)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. using series addition\n",
    "pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 ...  \n",
    "This method is the more accurate of the two, and is faster. Its accuracy only depends on the size of n."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.1415924535897797\n"
     ]
    }
   ],
   "source": [
    "pi = 0.0\n",
    "for i in range(1, 10000000, 4):\n",
    "    pi += 4/i\n",
    "    pi -= 4/(i+2)\n",
    "print(pi)"
   ]
  }
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