Created
March 9, 2019 11:23
-
-
Save vlad-bezden/1565aa472c5a089abd664c615244f2cb to your computer and use it in GitHub Desktop.
Calculating pi using Leibniz formula
This file contains hidden or bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
{ | |
"cells": [ | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"# Calculating pi" | |
] | |
}, | |
{ | |
"cell_type": "markdown", | |
"metadata": {}, | |
"source": [ | |
"The mathematically significant number pi (π or 3.14159…) can be derived using many formulas. One of the simplest is the Leibniz formula. It posits that the convergence of the following infinite series is equal to pi:\n", | |
"π = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11..." | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 1, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"%matplotlib inline\n", | |
"import matplotlib.pyplot as plt" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 2, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"def calc_pi(n):\n", | |
" pi = 0\n", | |
" points = []\n", | |
" sign = 1\n", | |
" for i in range (0, n):\n", | |
" pi += 4/(i * 2 + 1) * sign\n", | |
" points.append(pi)\n", | |
" sign *= -1\n", | |
" return points" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 3, | |
"metadata": {}, | |
"outputs": [], | |
"source": [ | |
"times = 100\n", | |
"points = calc_pi(times)" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 19, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"data": { | |
"image/png": "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\n", | |
"text/plain": [ | |
"<Figure size 1152x720 with 1 Axes>" | |
] | |
}, | |
"metadata": { | |
"needs_background": "light" | |
}, | |
"output_type": "display_data" | |
} | |
], | |
"source": [ | |
"plt.figure(figsize=(16, 10))\n", | |
"plt.plot(range(len(points)), points)\n", | |
"plt.xlabel(\"Times\")\n", | |
"plt.ylabel(\"Pi\");" | |
] | |
}, | |
{ | |
"cell_type": "code", | |
"execution_count": 5, | |
"metadata": {}, | |
"outputs": [ | |
{ | |
"name": "stdout", | |
"output_type": "stream", | |
"text": [ | |
" 0 4.000000\n", | |
" 10 3.232316\n", | |
" 20 3.189185\n", | |
" 30 3.173842\n", | |
" 40 3.165979\n", | |
" 50 3.161199\n", | |
" 60 3.157985\n", | |
" 70 3.155676\n", | |
" 80 3.153938\n", | |
" 90 3.152581\n" | |
] | |
} | |
], | |
"source": [ | |
"for i, p in enumerate(points):\n", | |
" if not i % 10:\n", | |
" print(f\"{i:>3} {p:>12.6f}\")" | |
] | |
} | |
], | |
"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": "3.7.2" | |
} | |
}, | |
"nbformat": 4, | |
"nbformat_minor": 2 | |
} |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment