{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Archimedes Method for PI\n",
    "# FB - 200912082\n",
    "# Revised by Bjorn.madsen AT operationsresearchgroup.com for Python3.3\n",
    "# BHM - 20130302\n",
    "\n",
    "import decimal\n",
    "\n",
    "def ArchPi(precision=99):\n",
    "    # x: circumference of the circumscribed (outside) regular polygon\n",
    "    # y: circumference of the inscribed (inside) regular polygon\n",
    "\n",
    "    decimal.getcontext().prec = precision+1\n",
    "    D=decimal.Decimal\n",
    "    \n",
    "    # max error allowed\n",
    "    eps = D(1)/D(10**precision)\n",
    "    \n",
    "    # initialize w/ square\n",
    "    x = D(4)\n",
    "    y = D(2)*D(2).sqrt()\n",
    "\n",
    "    ctr = D(0)\n",
    "    while x-y > eps:\n",
    "        xnew = 2*x*y/(x+y)\n",
    "        y = D(xnew*y).sqrt()\n",
    "        x = xnew\n",
    "        ctr += 1\n",
    "        \n",
    "\n",
    "    return str((x+y)/D(2))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pi = 3.14159265358979323848\n"
     ]
    }
   ],
   "source": [
    "PiA=ArchPi(20)\n",
    "print(\"pi =\",PiA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068\n"
     ]
    }
   ],
   "source": [
    "print(ArchPi(99))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "64a7e88ebd0abc50aba166b172778bcdfbfd193da8f8e02bffc3c5f026b0d38a"
  },
  "kernelspec": {
   "display_name": "Python 3.7.10",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.10"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}