{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>P</th>\n",
       "      <th>Q</th>\n",
       "      <th>slope of secant</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(2.0, 7.38905609893065)</td>\n",
       "      <td>4.670774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(1.5, 4.4816890703380645)</td>\n",
       "      <td>3.526814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(1.25, 3.4903429574618414)</td>\n",
       "      <td>3.088245</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(1.125, 3.080216848918031)</td>\n",
       "      <td>2.895480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(1.0625, 2.893595944171761)</td>\n",
       "      <td>2.805026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(0.9375, 2.553589458062927)</td>\n",
       "      <td>2.635078</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(0.875, 2.398875293967098)</td>\n",
       "      <td>2.555252</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(0.75, 2.117000016612675)</td>\n",
       "      <td>2.405127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(0.5, 1.6487212707001282)</td>\n",
       "      <td>2.139121</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>(1, 2.718281828459045)</td>\n",
       "      <td>(0.0, 1.0)</td>\n",
       "      <td>1.718282</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ]
     },
     "execution_count": 1,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "f = np.exp  # The function\n",
    "x_0 = 1       # The x loc of P\n",
    "y_0 = f(x_0)  # The y loc of P\n",
    "\n",
    "\n",
    "increments = [1,1/2,1/4,1/8,1/16]\n",
    "\n",
    "a_pos = x_0 + np.array(increments)\n",
    "a_neg = np.flip(x_0 - np.array(increments),axis=0)\n",
    "a = np.concatenate((a_pos,a_neg))\n",
    "\n",
    "\n",
    "Q = [(_a,f(_a)) for _a in a]\n",
    "\n",
    "import pandas as pd\n",
    "\n",
    "data = {'P':[(x_0,y_0)]*len(a),'Q':Q,'slope of secant':(f(a)-y_0)/(a-x_0)}\n",
    "df = pd.DataFrame(data=data)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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     },
     "execution_count": 2,
     "metadata": {
      "image/png": {
       "height": 617,
       "width": 1068
      }
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "fig = plt.gcf()\n",
    "fig.set_size_inches(18.5, 10.5)\n",
    "\n",
    "\n",
    "Qx = [q[0] for q in Q]\n",
    "Qy = [q[1] for q in Q]\n",
    "x = np.arange(min(Qx),1.3*max(Qx),0.1)\n",
    "plt.plot(x,f(x))\n",
    "plt.scatter(Qx,Qy)\n",
    "plt.title(r\"Secant approximations of the tangent line\")\n",
    "for index, row in df.iterrows():\n",
    "   plt.plot([row['P'][0], row['Q'][0]],[row['P'][1], row['Q'][1]])\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "fig.savefig('secants_arctan.png', dpi=100)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 0,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
   ]
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3 (Ubuntu Linux)",
   "language": "python",
   "name": "python3"
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   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  },
  "name": "",
  "signature": "sha256:60e9ad759cf98636e12fd3a340a1f37053e02d8927a1f7cc3d07ad79c9001339"
 },
 "nbformat": 4,
 "nbformat_minor": 0
}