pi_monte_carlo.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7a86f242-c2e9-41ed-96b8-e8cdb11ecb4c",
   "metadata": {},
   "source": [
    "The cell below will be all the libraries I will be importing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c6f9d528-393f-45bb-b62f-661aafaf7ad2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.patches import Rectangle\n",
    "import random as rn\n",
    "from numpy.random import randint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "ba729bd2-d118-4ffd-ad14-be6674d42689",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "value of pi is:  3.130346813718837\n"
     ]
    },
    {
     "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": [
    "figure, axes = plt.subplots()\n",
    "draw_circle = plt.Circle((0, 0), 3,fill=False)\n",
    "\n",
    "##############____Begin random dots____##############\n",
    "n = 100 #number of times that my simulation will be run\n",
    "val1=np.zeros(n)\n",
    "error_g = np.zeros(1000000)\n",
    "time = np.zeros(1000000)\n",
    "for w in range(n):\n",
    "    circ_counter = 0\n",
    "    sqr_counter = 0\n",
    "    x_arr = randint(-10.0, 10.0, 1000000)\n",
    "    y_arr = randint(-10.0, 10.0, 1000000)\n",
    "    for i in range(1000000):\n",
    "       # x_arr[i] = rn.randint(-10,10)\n",
    "       # y_arr[i] = rn.randint(-10,10)\n",
    "        val = x_arr[i]**2 + y_arr[i]**2\n",
    "        if(val < 9):\n",
    "            circ_counter = circ_counter+1\n",
    "        elif((x_arr[i]< -4) and (x_arr[i]>-7 )and (y_arr[i]>3) and (y_arr[i]<6)):\n",
    "            sqr_counter = sqr_counter+1\n",
    "        if(sqr_counter!=0):\n",
    "            error_g[i] = (circ_counter/sqr_counter)/2\n",
    "            time[i]=i\n",
    "    val2 = circ_counter/sqr_counter\n",
    "    val1[w]= val2/2\n",
    "pi = (np.sum(val1))/n\n",
    "print(\"value of pi is: \", pi)\n",
    "#for i in range(1000):\n",
    "    \n",
    "##############____end random dots_____##############\n",
    "\n",
    "##############____Begin Square____##############\n",
    "point1 = [-4, 3]\n",
    "point2 = [-7, 3]\n",
    "point3 = [-4,6]\n",
    "point4 = [-7, 6]\n",
    "\n",
    "#first line\n",
    "x1_values = [point1[0], point2[0]]\n",
    "y1_values = [point1[1], point2[1]]\n",
    "\n",
    "#second line\n",
    "x2_values = [point1[0], point3[0]]\n",
    "y2_values = [point1[1], point3[1]]\n",
    "\n",
    "#third line\n",
    "x3_values = [point2[0], point4[0]]\n",
    "y3_values = [point2[1], point4[1]]\n",
    "\n",
    "#fourth line\n",
    "x4_values = [point3[0], point4[0]]\n",
    "y4_values = [point3[1], point4[1]]\n",
    "##############____end Square____##############\n",
    "\n",
    "##############____begin random point plot____##############\n",
    "plt.scatter(x_arr,y_arr)\n",
    "##############____end of random point plot____##############\n",
    "\n",
    "\n",
    "plt.plot(x1_values, y1_values)\n",
    "plt.plot(x2_values, y2_values)\n",
    "plt.plot(x3_values, y3_values)\n",
    "plt.plot(x4_values, y4_values)\n",
    "plt.ylim(-10, 10) \n",
    "#corresponding function for the x-axis\n",
    "plt.xlim(-15, 15)\n",
    "\n",
    "axes.set_aspect(1)\n",
    "axes.add_artist(draw_circle)\n",
    "plt.title('Circle')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "id": "e6ef054e-1bcd-4e8d-8740-b58e0e23744a",
   "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.axhline(y=np.pi, color='r', linestyle='-')\n",
    "#error_g[:]/2\n",
    "plt.plot(error_g)\n",
    "plt.ylim(2.5, 4) \n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2d553e54-fe09-4d84-8a11-ddaa6f3160ee",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}