|
| 1 | +{ |
| 2 | + "cells": [ |
| 3 | + { |
| 4 | + "cell_type": "markdown", |
| 5 | + "metadata": {}, |
| 6 | + "source": [ |
| 7 | + "# Happy Pi Day!\n", |
| 8 | + "\n", |
| 9 | + "### Two Ways to Calculate Pi: \n", |
| 10 | + "Real pi = 3.14159265359\n", |
| 11 | + "\n", |
| 12 | + "### 1. percentage of unit square random points that lie in unit circle\n", |
| 13 | + "This method is only as good as our random number generator. And with number of iterations the accuracy improves, up to about 1 million." |
| 14 | + ] |
| 15 | + }, |
| 16 | + { |
| 17 | + "cell_type": "code", |
| 18 | + "execution_count": 9, |
| 19 | + "metadata": {}, |
| 20 | + "outputs": [ |
| 21 | + { |
| 22 | + "name": "stdout", |
| 23 | + "output_type": "stream", |
| 24 | + "text": [ |
| 25 | + "3.1419916\n" |
| 26 | + ] |
| 27 | + } |
| 28 | + ], |
| 29 | + "source": [ |
| 30 | + "import random\n", |
| 31 | + "in_square = in_circle = pi = 0\n", |
| 32 | + "\n", |
| 33 | + "for i in range(10000000):\n", |
| 34 | + " x = random.random()\n", |
| 35 | + " y = random.random()\n", |
| 36 | + " dist = (x*x + y*y) ** 0.5\n", |
| 37 | + "\n", |
| 38 | + " in_square += 1\n", |
| 39 | + " if dist <= 1.0:\n", |
| 40 | + " in_circle += 1\n", |
| 41 | + " \n", |
| 42 | + "pi = 4 * in_circle / in_square\n", |
| 43 | + "print(pi)" |
| 44 | + ] |
| 45 | + }, |
| 46 | + { |
| 47 | + "cell_type": "markdown", |
| 48 | + "metadata": {}, |
| 49 | + "source": [ |
| 50 | + "### 2. using series addition\n", |
| 51 | + "pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + 4/13 - 4/15 ... \n", |
| 52 | + "This method is the more accurate of the two, and is faster. Its accuracy only depends on the size of n." |
| 53 | + ] |
| 54 | + }, |
| 55 | + { |
| 56 | + "cell_type": "code", |
| 57 | + "execution_count": 10, |
| 58 | + "metadata": {}, |
| 59 | + "outputs": [ |
| 60 | + { |
| 61 | + "name": "stdout", |
| 62 | + "output_type": "stream", |
| 63 | + "text": [ |
| 64 | + "3.1415924535897797\n" |
| 65 | + ] |
| 66 | + } |
| 67 | + ], |
| 68 | + "source": [ |
| 69 | + "pi = 0.0\n", |
| 70 | + "for i in range(1, 10000000, 4):\n", |
| 71 | + " pi += 4/i\n", |
| 72 | + " pi -= 4/(i+2)\n", |
| 73 | + "print(pi)" |
| 74 | + ] |
| 75 | + }, |
| 76 | + { |
| 77 | + "cell_type": "code", |
| 78 | + "execution_count": null, |
| 79 | + "metadata": {}, |
| 80 | + "outputs": [], |
| 81 | + "source": [] |
| 82 | + } |
| 83 | + ], |
| 84 | + "metadata": { |
| 85 | + "kernelspec": { |
| 86 | + "display_name": "Python 3", |
| 87 | + "language": "python", |
| 88 | + "name": "python3" |
| 89 | + }, |
| 90 | + "language_info": { |
| 91 | + "codemirror_mode": { |
| 92 | + "name": "ipython", |
| 93 | + "version": 3 |
| 94 | + }, |
| 95 | + "file_extension": ".py", |
| 96 | + "mimetype": "text/x-python", |
| 97 | + "name": "python", |
| 98 | + "nbconvert_exporter": "python", |
| 99 | + "pygments_lexer": "ipython3", |
| 100 | + "version": "3.7.0" |
| 101 | + } |
| 102 | + }, |
| 103 | + "nbformat": 4, |
| 104 | + "nbformat_minor": 2 |
| 105 | +} |
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