{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sympy import init_printing,plot,limit,oo\n",
    "init_printing(pretty_print=True)\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sympy.abc import a,n\n",
    "from sympy import tan,pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "expr = n / (4*tan(pi/n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAEAAAAAfCAYAAABXscv8AAAABHNCSVQICAgIfAhkiAAAAxVJREFU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\nRU5ErkJggg==\n",
      "text/latex": [
       "$$\\frac{n}{4 \\tan{\\left (\\frac{\\pi}{n} \\right )}}$$"
      ],
      "text/plain": [
       "   n    \n",
       "────────\n",
       "     ⎛π⎞\n",
       "4⋅tan⎜─⎟\n",
       "     ⎝n⎠"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MLD9qM9vMGpTf2UkmKygIW0g0bAhvvAHjx4dpuyuuUEISiUsm/NV7FOi8V2wg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\nEZGMoaQkIiIZQ0lJREQyxv8DqElJw1mP9V0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b2ecc5e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f6b2ed4cc10>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(expr, (n,0,1000))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAABUAAAANCAYAAABGkiVgAAAABHNCSVQICAgIfAhkiAAAAP5JREFU\nOI3l0r8rhlEYxvEP5cebd3gQw5vBYCEpZTIoxfJSBovRZiR/gkUGg7IZDH5EJiVZlJTBZLFYhFHJ\nZHvFcM7wdDyP0eLaznW+57rv7vvwB8qwjWe84BBjBdwAdnGLc2yhqyiwDZdYwhBmcYcGVnPcDO5R\nz3n92Ed7GrqCycTrwBW+YvBwLFQraGoQy6m5WdQ+OvGATzxitISDdWjOGR8l4Dvm4n0Wz2VqpKEt\nv8BNMSzDKaolXDUNfRXmkqobB1jAGkZwjNaEm8ZT+riCI/TlvHFhMfM5b0NY3DUmIr+IG+EH/VAv\ndnAWoRNh46mmcCGM5A176CkK/If6BtVcLQZPV0fcAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\infty$$"
      ],
      "text/plain": [
       "∞"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(expr, n, oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "expr = n*tan(pi/n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAANCAYAAACZ3F9/AAAABHNCSVQICAgIfAhkiAAAALBJREFU\nKJHN0KGKglEUBOBPd4MIikGDb+BLaDAsiG3bItjsgu/iAxi2iMlosLmCad9ADFuNK8KqwQP+yC8a\nDDtwuXMH5sycyxNQwCd+cbxxDqhDJkwZTPCNJd6xwhp9DLHHDosYALpoJdLHeAk+Tav3GvcooZVC\n/0MelTRjNkXr4Ct4LQY8ZOxhHryKcprxGg1sXfb7cP7l3L3EAWaJej9hat5LXOMt8S5ig/Yjdf8p\nTmMXIaGE71oKAAAAAElFTkSuQmCC\n",
      "text/latex": [
       "$$\\pi$$"
      ],
      "text/plain": [
       "π"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit(expr, n, oo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAD7CAYAAACIYvgKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n5aNb/B1csQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6b2de164d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<sympy.plotting.plot.Plot at 0x7f6b2dfb1d90>"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(expr, pi, (n,0,5), ylim=(3,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAFoAAAAZCAYAAACxZDnAAAAABHNCSVQICAgIfAhkiAAABAxJREFU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\nMMIItfIv68/Qt86bqXgAAAAASUVORK5CYII=\n",
      "text/latex": [
       "$$n \\tan{\\left (\\frac{\\pi}{n} \\right )}$$"
      ],
      "text/plain": [
       "     ⎛π⎞\n",
       "n⋅tan⎜─⎟\n",
       "     ⎝n⎠"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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   "language": "python",
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   "file_extension": ".py",
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