Distribution of One Million Digits of Pi

pi_dec_1m_digits_dist.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Distribution of One Million Digits of Pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import collections\n",
    "import string\n",
    "import urllib.request\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('./pi_dec_1m.txt', <http.client.HTTPMessage at 0x19c426cd8d0>)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "url = 'https://www.pi2e.ch/blog/wp-content/uploads/2017/03/pi_dec_1m.txt'\n",
    "urllib.request.urlretrieve(url, './pi_dec_1m.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Counter({'3': 100230,\n",
       "         '1': 99758,\n",
       "         '4': 100230,\n",
       "         '5': 100359,\n",
       "         '9': 100106,\n",
       "         '2': 100026,\n",
       "         '6': 99548,\n",
       "         '8': 99985,\n",
       "         '7': 99800,\n",
       "         '0': 99959})"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digitCounts = collections.Counter()\n",
    "with open('pi_dec_1m.txt', \"r\") as ins:\n",
    "    array = []\n",
    "    for line in ins:\n",
    "        digitCounts.update(line.translate(str.maketrans('', '', string.punctuation)))\n",
    "digitCounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sortedDigitCounts = sorted(digitCounts.items())\n",
    "digits = [digit[0] for digit in sortedDigitCounts]\n",
    "counts = [digit[1] for digit in sortedDigitCounts]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.bar(digits, counts, align='center', alpha=0.5)\n",
    "plt.xticks(digits, digits)\n",
    "plt.ylabel('count')\n",
    "axes = plt.gca()\n",
    "axes.set_ylim([99400, 100400])\n",
    "plt.title('Distribution of One Million Digits of Pi')\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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