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@konsbn
Created May 26, 2015 11:07
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"metadata": {
"name": "Untitled0"
},
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"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "#Beautiful (and Nerdy) Polar Graphs\n-----------------------------------------------"
},
{
"cell_type": "markdown",
"metadata": {},
"source": ">This is a short notebook on plotting some beautiful polar graphs in python using very simple functions and code. This something that can be taken as an exercise as well as a piece of art to admire and to learn.\n"
},
{
"cell_type": "markdown",
"metadata": {},
"source": "##Cardioid\nThis is one of the first curves I discovered when I was reading a book on differential calculus. It was an old book and was full of curve tracing. \nCardioid as you might have guessed has it's roots in the greek word for heart.\nThe equation is \n>## $$r = a + b*cos(\\theta)$$ \n\nwhere\n\n> ## $$\\theta \\in [\\ 0, 2 \\pi]\\ $$\n \n\nOf course it is plotted as a Polar Graph. If you wanna read up more on Cardioid and I suggest you should head over to the [wikipedia page]\n[wikipedia page]:http://en.wikipedia.org/wiki/Cardioid\n\n"
},
{
"cell_type": "markdown",
"metadata": {},
"source": "##Getting Started you'll need to start the Ipython Shell and import these\n"
},
{
"cell_type": "code",
"collapsed": false,
"input": "%matplotlib inline\nimport matplotlib.pyplot as plt\nfrom numpy import *",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Now that you have the basic setup let's start with plotting the cardioid.\nstarting with setting up values of \n## $$\\theta$$"
},
{
"cell_type": "code",
"collapsed": false,
"input": "theta = arange(0.0, 2*pi , 0.1)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": "now for the \n>## $$a \\& b$$"
},
{
"cell_type": "code",
"collapsed": false,
"input": "a = 1.0 \nb = 1.0",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": "## $$r = $$"
},
{
"cell_type": "code",
"collapsed": false,
"input": "r = map(lambda x:a + b*cos(x),theta)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": ">Now we plot it as a polar plot"
},
{
"cell_type": "code",
"collapsed": false,
"input": "plt.polar(theta, r)",
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": "[<matplotlib.lines.Line2D at 0x7fc3ce0bb050>]"
},
{
"metadata": {},
"output_type": "display_data",
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fP/30U0yePBnDhg1Ddna2wJqxyysxMiksLMTw4cMxcuRIrF27Vqd8JA8fPkRsbCx8fHyE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\nIYRfSJgIIfziT0cNrpWj0SK0AAAAAElFTkSuQmCC\n",
"text": "<matplotlib.figure.Figure at 0x7fc3d54682d0>"
}
],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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