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@kwinkunks
Last active August 29, 2015 14:09
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Heights of mountains, compared to the centre of the earth. View IPython Notebook... http://nbviewer.ipython.org/gist/kwinkunks/a449bff4c8c35952e6ce
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"metadata": {
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"signature": "sha256:749323cc65f5e4f91dd0b5b2e0733bdd24765dd719ac2bea84f483987d08413d"
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Radius of earth\n",
"\n",
"We have a formula [from Wikipedia](https://en.wikipedia.org/wiki/Earth_radius#Location-dependent_radii):\n",
"\n",
"$$ R=R(\\varphi)=\\sqrt{\\frac{(a^2\\cos\\varphi)^2+(b^2\\sin\\varphi)^2}{(a\\cos\\varphi)^2+(b\\sin\\varphi)^2}} $$\n",
"\n",
"and some data for the equatorial radius *a* and the polar radius *b*:\n",
"\n",
"$$ a = 6,378.1370\\ \\mathrm{km} $$\n",
"$$ b = 6,356.7523\\ \\mathrm{km} $$\n",
"\n",
"So we can make a chart, then add some mountains. But first some prelims... "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"%matplotlib inline"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = 6378.1370\n",
"b = 6356.7523\n",
"\n",
"lat = np.linspace(0,90,90)\n",
"latr = np.radians(lat)\n",
"\n",
"denom = (a * np.cos(latr))**2. + (b * np.sin(latr))**2.\n",
"numer = (a**2. * np.cos(latr))**2. + (b**2. * np.sin(latr))**2.\n",
"\n",
"R = np.sqrt(numer/denom)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.plot(lat, R)\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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KMM9b90NMX2L/MQO5jmsqNgof7N+wkg9iylUC+A/W6HEZUz3sHmVpb/3fWMcU\nlzE1wfJTGSxvLgLOcxxTkV0KLAhYH0let9Fwq8eJiT8DqOG9rknedBSuzMVusvslrnLYPaALfRBT\nHeA94HLyWvyuYwJL/Gfl2+YyrkpYQsvPD78rgC7Ah95rlzFVxRpaVbCT43xsqhmXMd2ATaGT6yEs\n4fvl365QbsAGh+Xqy8m7e4ZDPU5M/AcDXsflWw+3esBXQAXcx1UCuzI7jLU28EFMr2NXbB3JS/yu\nYwJLsquxDg53eNtcxtUcK9VNIW9gZqLjmAJNJm+6F9cx/QH7G88CpvkgpsbYyagq1uj6BHi2sDH5\nZXbOHNcBBCm3z6wL5bEeVPdy4pQZ4Cau41gCqQN0wFrZLmPqgf3nXM2pe4y5+ve7DDshdQfuwUqK\ngcId1+kGZrqKKVcprLv36yfZF+6YzgOGYQ2u2tj/wb6OY8oAnsDq+O9gja/swsbkl8T/NVbPy5UE\n7HYUS377sEsngFpYcgm3kljSn4aVevwSF9hNuLeBlo5jagf0xMoqM4FO2O/LD7+n/3hf9wNzgNaO\n49rtLSu89VnYCWCvw5hydce6gu/31l3+nlphLepvsHnK3sDK0q5/T5O92DpiLfutFPL35JfE/zk2\n2Ksedsa/ibybc67Nw27o4H2de5pji0McMAnreTHOJ3FVI6/XQFms7rnacUwPYA2G+sDNwGJsWhDX\n/37lsNIcWDmlC1ZKdBlX4MBMyBuYOd9hTLn6YCfuXC5/TxlAW+xvPA77PW3C/e8pd9xUXWzs1Azc\n/50XWXesdrUd60LlwkxsvqFfsP8YA7Fa2nu46ybVHiurrCGvq1s3x3FdhNWG12DdFId7213/rnJ1\nJK/h4Dqm+tjvaQ3W/S73b9t1XPkHZlbyQUyJ2Oj+CgHbXMc0grzunFOxq2/XMX3gxbSGvBKr65hE\nRERERERERERERERERERERERERERERERERATg/wEcdj5Xu2P2lgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x107701250>"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This list is [from Wikipedia](http://en.wikipedia.org/wiki/List_of_mountains#Summits_farthest_from_Earth.27s_centre)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mountains = \"\"\"\n",
"Summit, Distance from center, Elevation above sea level, Latitude, Country\n",
"Chimborazo, 6384.4, 6268.2, -1.469167, Ecuador\n",
"Huascaran, 6384.4, 6748, -9.121389, Peru\n",
"Kilimanjaro, 6383, 5895, -3.075833, Tanzania\n",
"Everest, 6382.3, 8848, 27.988056, Nepal\n",
"\"\"\""
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"m = filter(None, mountains.split('\\n'))\n",
"\n",
"# Start the plot.\n",
"plt.figure(figsize=(12,12))\n",
"ax = plt.subplot(111)\n",
"ax.plot(lat[:40], R[:40])\n",
"\n",
"# Iterate over the mountains, skipping the first.\n",
"for row in m[1:]:\n",
" \n",
" # Make a list out of each row.\n",
" data = row.split(',')\n",
" \n",
" # Extract data we can use.\n",
" deg = np.abs(np.round(float(data[3]),0))\n",
" ht = float(data[2])/1000.\n",
" \n",
" # Add to the plot.\n",
" ax.axhline(R[deg]+ht, color=\"lightgray\")\n",
" ax.vlines(np.abs(float(data[3])), R[deg], R[deg]+ht)\n",
" ax.text(deg+0.5, R[deg]-1, data[0], fontsize=12, rotation=90, horizontalalignment='right')\n",
" ax.text(deg+0.5, 1.0004*(R[deg]+ht), str(np.round(R[deg]+ht,3))+\" km\" , fontsize=10, rotation=90, horizontalalignment='right')\n",
" \n",
"# Adjust and show the plot.\n",
"ax.set_xlim(-5, 45)\n",
"ax.set_ylim(6370, 6390)\n",
"plt.xlabel('Absolute latitude in degrees')\n",
"plt.ylabel(\"Distance from Earth's centre\")\n",
"plt.show()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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6MGPGjGSXKKUsh4VIklTF7Ny5k5o1awLQqFEjJk6cyIYNG7jooovYvn17kquT\ndCCGa0mSIqht27a89957pa8zMjIYN24cnTp1Yv78+UmsTFJFHBaiSjksJJo8hlL1tnnzZtLS0sjM\nzCz33ooVK8jJyUlCVZLAYSGSJFU5devW5euvv6awsBCAgoICnn/+eebOnWuwliLMcC1JUgSNGjWK\n73znO5x44omMHTuWc845h0mTJnHxxRczZsyYZJcn6QAcFqJKOSwkmjyGUvV27LHHMn36dDZt2kTr\n1q0pKCggOzubTZs20atXL+bNm5fsEqWUVdGwkIzDW4okSYpHRkYGmZmZ1KpVi7p169KkSRMA6tWr\nR3q6//AsRZU916qUPdfR5DGUqreBAwcCsGnTJho2bMiWLVs4//zzeeedd9i+fTsTJkxIcoVS6qqo\n59pwrUoZrqPJYyhVb1u3buWZZ56hefPmnHXWWUyYMIGPPvqITp06cfXVV1O7du1klyilLMO1Donh\nOpo8hpIkJYdT8UmSVMUsX76cK6+8kuHDh1NYWMiQIUPo0qULgwcPZvXq1ckuT9IBGK4lSYqgyy+/\nnNzcXLKysujduzcdO3bk9ddfp1evXlx77bXJLk/SATgsRJVyWEg0eQyl6q179+7MnDkTgFatWrFs\n2bL9vifp8HNYiCRJVUzZi+fBgwfv9d7OnTsPdzmS4mS4liQpggYMGEBRUREAd955Z+n+hQsX0rFj\nx2SVJakSDgtRpRwWEk0eQ0mSksNhIZIkVTEff/wx69evB2Dz5s3cfvvtnHfeefzyl78s3S8pegzX\nkiRF0JAhQ6hXrx4Aw4YNY8OGDQwfPpzMzEyGDBmS5OokHUhGsguQJEnllZSUkJER/JqePn06+fn5\nAPTt25fc3NxkliapAvZcS5IUQZ07d2bcuHEA5ObmMm3aNAAWLFhArVq1klmapAp4Q6Mq5Q2N0eQx\nlKq3wsJChg0bxpQpU8jOziY/P5+cnBxatmzJ/fffb++1lEQV3dBouFalDNfR5DGUUsP69espKCig\nuLiYnJwcmjVrluySpJRnuNYhMVxHk8dQkqTkcCo+SZIk6TAwXEuSJEkhMVxLkiRJITFcS5IkSSEx\nXEuSJEkhMVxLkiRJITFcS5IkSSExXEuSJEkhMVxLkiRJITFcS5IkSSExXEuSJEkhMVxLkiRJITFc\nS5IkSSExXEuSJEkhMVxLkiRJITFcS5IkSSExXEuSJEkhMVxLkiRJITFcS5IkSSExXEuSJEkhMVxL\nkiRJITGzymM0AAAgAElEQVRcS5IkSSExXEuSJEkhMVxLkiRJITFcS5IkSSExXEuSJEkhSUt2ASEq\nmTNnTrJrkCRJUjXXtWtXOECOrlbhuqSkJNk1VEtpaWmEfWwT8Z2pxmMopRbPeSk60tLS4AA52mEh\nkiRJUkjiCdfpwGDg9tjrVkCvhFUkSZIkVVHxhOs/AycBg2KvN8b2SZIkSSojI47PnAgcB8yIvf4G\nqJmwiiRJkqQqKp6e6+1AjTKvs4FdiSlHkiRJqrriCdf3A38DvgX8L/Ah8H+JLEqSJEmqiiqbii+d\nYLz1N8AZsX1vA/MTWdRBciq+BHEqvmjyGEqpxXNeio6KpuKLZ57rmUD3MAtKEMN1ghiuo8ljKKUW\nz3kpOg51nuu3gAsP9AWSJEmSAvEE5o1AXWAnsDW2rwRomKiiDpI91wliz3U0eQyl1OI5L0VHRT3X\n8UzFVz/UaiRJkqRqKp5hIW/HuU+SJElKaRX1XGcSDAfJBpqU2d8QaJHIoiRJkqSqqKJwfTUwDDgK\nmF5mfxHwQCKLkiRJkqqieG5o/DlwX6ILCYE3NCaINzRGk8dQSi2e81J0HOo81wB9gNbs3dM9/pCq\nCp/hOkEM19HkMZRSi+e8FB2HOlvIBKAtwWIyO8vsj1q4liRJkpIqnnB9PHAswdzWkiRJkg4gnqn4\n5gLNE12IJEmSVNXF03OdDXwKTAW2xfaVAAMSVZQkSZJUFcUTru+IPZawZ+C2Q0QkSZKkfcQ7W0hr\noD3wFsHCMhnAhgTVdLCcLSRBnC0kmjyGUmrxnJeio6LZQuIZc30V8DzwUOx1DvC3UCqTJEmSqpF4\nwvV1QF/29FQvAL6VsIokSZKkKiqecL2NPTcyQjAkxH+XkiRJkvYRT7h+D7iNYKz1mQRDRCYmsihJ\nkiSpKornhsYawBXA92Kv3wDGEr3ea29oTBBvaIwmj6GUWjznpeio6IbGeMJ1PWAre5Y+rwHUBjaH\nUVyIDNcJYriOJo+hlFo856XoONTZQt4BMsu8rkswJZ8kSZKkMuIJ17WBjWVeFxEEbEmSJEllxBOu\nNwHHl3ndE9iSmHIkSZKkqiue5c+vB54DVsVeNwcuTlhFkiRJUhUV7/LntYCOseefA9sTU84h8YbG\nBPGGxmjyGEqpxXNeio5DnS2kqjBcJ4jhOpo8hlJq8ZyXouNQZwuRJEmSFAfDtSRJkhSSeMJ1X6B+\n7Plg4G7g6IRVJEmSJFVR8YTrBwmm48sFbgQWAeMTWZQkSZJUFcUTrouBEiAP+FNsa5DIoiRJkqSq\nKJ55rouAW4FLgFOAGkDNRBYlSZIkVUXx9FxfDGwFhgJfAS2AuxJZlCRJklQVOc+1KuU819HkMZRS\ni+e8FB0VzXNd0bCQgtjjauDEkGuSJEmSqh17rlUpe66jyWMopRbPeSk6DrbnuqwawJH7fH7ZoZUl\nSZIkVS/xhOufASMIhofsLLO/a0IqkiRJkqqoeIaFLAJ6AWsTXMuhclhIgjgsJJo8hlJq8ZyXoqOi\nYSHxTMW3DNgQZkGSJElSdVTRsJCbYo+LgcnAq8D22L4S4O7ElSVJkiRVPRWF6wYEIXoZsByoFdsk\nSZIk7Uc8Y65/CDwXx75kc8x1gjjmOpo8hlJq8ZyXoqOiMdfxhOsZwHFx7Es2w3WCGK6jyWMopRbP\neSk6Dnae63OAc4EWwH1lvqABsCPE+iRJkqRqoaJw/SUwHRgQe0wjGINdBNyQ+NIkSZKkqqWyYSEZ\nwHhg0GGo5VA5LCRBHBYSTR5DKbV4zkvRcSjzXBcDrYDaIdckSZIkVTvxLH9eAHwAvAJsju1znmtJ\nkiRpH/GE60WxLR2oz56x15IkSZLKiGcqvqrCMdcJ4pjraPIYSqnFc16KjoOdim+3bwG/AI4FMmP7\nSoDTwyhOkiRJqi4qu6ER4K/AZ0Bb4A5gCfBJ4kqSJEmSqqZ4hoXkAz2A2UC32L5PgJ6JKuogOSwk\nQRwWEk0eQym1eM5L0XGow0K2xx6/As4jWFymcSiVSZIkSdVIPOH6TqARcBNwP9AQV2iUJEmSynG2\nEFXKYSHR5DGUUovnvBQdB7tC43Nlnv//+7z3z0OsSZIkSap2KgrXHco8/94+72UnoBZJkiSpSotn\nKr5D0Qh4AZgPfAr0Bn4LzAJmAm8DLWOfrQM8TTAryafA8DLfczwwB1gI3JvgmiVJkqSDUlG4ziSY\ngu/4Ms/Lvo7HvcDrwDEE0/jNB+4CcoHuwMvAiNhnfxR77BZr42qgVWzfg8AVBL3pHYCz42xfkiRJ\nOmwqmi3kK2DMfp4DrIrju7OAU4DLYq+LgfX7fKY+sKbMd9YDasQetwMbgOZAA2Bq7HPjgTxgUhw1\nSJIkSYdNReG63yF+dxvga+Axgp7q6cAwYDPB9H6DY897xz7/RmzfKqAucD1QCLQHVpT53pVAi0Os\nTZIkSQpdIsdcZxAMI/lz7HETe8ZR30Yw5ONx4J7YvksIhps0JwjmN8ceJUmSpCohnkVkDtaK2DYt\n9voF9r5JEeApgjHZAH2AvwE7CXq8PyQYe/0BkFPmz+QQ9F6Xc8cdd5Q+79evH/369TuE8iVJkiSY\nPHkykydPjuuziV5E5n3gSmABcAdBz/QjwBex938G9CIYDvJzgpschxKMuZ4KXAzMBT6OvT8VeA24\nj/Jjrl1EJkFcRCaaPIZSavGcl6KjokVk4g3XuUBr9vR0lwAvxfnnxgK1gEUEwXks0JGgh3oRcC2w\nGqgNPBr7M+nAOPbcRHk8wRCSTIKe7p/vpy3DdYIYrqPJYyilFs95KToONVw/BnQF5gG7yuwfcsiV\nhctwnSCG62jyGEqpxXNeio6KwnU8Y65PBDoT9FZLkiRJOoB4ZguZBhyb6EIkSZKkqi6enuvHgH8R\nLCSzLbavhGAlRUmSJEkx8YTrRwnmoJ7L3mOuJUmSJJURT7heDbyS6EIkSZKkqi6ecD2DYLGXicD2\n2L54p+KTJEmSUkY84bouQaj+3j77DdeSJElSGYleofFwcp7rBHGe62jyGEqpxXNeio6K5rmOZyq+\nlsDfgK9j24tATljFSZIkSdVFPOH6MYIbGo+KbRNj+yRJkiSVEc+wkFlAbhz7ks1hIQnisJBo8hhK\nqcVzXoqOQx0WshYYDNQguAHyEmBNWMVJkiRJ1UU84XoI8EOCFRpXARfF9kmSJEkqo7Kp+DKA/wX6\nH4ZaJEmSpCqtsp7rYuBooPZhqEWSJEmq0uJZRKYA+IBgxpDNsX0lwN2JKkqSJEmqiuIJ118Aiwh6\nuesnthxJkiSp6qooXD9JMEvIeuCPh6ccSZIkqeqqaMz18QSLxgwFmuxnkyRJklRGRT3XfwHeBtoC\n0/d5ryS2X5IkSVJMPCs0/gW4JtGFhMAVGhPEFRqjyWMopRbPeSk6KlqhMZ5wXVUYrhPEcB1NHkMp\ntXjOS9FxqMufS5IkSYqD4VqSJEkKSbzhujXw3djzukDDhFQjSZIkVWHxhOurgOeBh2Kvc4C/Jawi\nSZIkqYqKJ1xfB/QFNsReLwC+lbCKJEmSpCoqnnC9LbbtlkEwz7UkSZKkMuIJ1+8BtxGMtT6TYIjI\nxEQWJUmSJFVF8cxzXQO4Avhe7PUbwFii13vtPNcJ4jzX0eQxlFKL57wUHYe6iEw9YCuwM/a6BlAb\n2BxGcSEyXCeI4TqaPIZSavGcl6LjUBeReQfILPO6LvDWoZclSZIkVS/xhOvawMYyr4sIArYkSZKk\nMuIJ15uA48u87glsSUw5kiRJUtWVEcdnrgeeA1bFXjcHLk5YRZIkSVIVFc8NjQC1gI4EM4R8DuxI\nWEUHzxsaE8QbGqPJYyilFs95KToOdbYQgD5AG/ZeQGb8IVcWLsN1ghiuo8ljKKUWz3kpOioK1/EM\nC5kAtAVmsmc6PoheuJYkSZKSKp5wfTxwLNFbNEaSJEmKlHhmC5lLcBOjJEmSpArE03OdDXwKTAW2\nxfaVAAMSVZQkSZJUFcUTru9IdBGSJElSdRDvbCFVgbOFJIizhUSTx1BKLZ7zUnRUNFtIPGOuTwKm\nESyBvgPYBWwIqzhJkiSpuognXD8ADAIWAnWAK4A/J7IoSZIkqSqKJ1xDEKxrEMxz/RhwdsIqkiRJ\nkqqoeG5o3ATUBmYBfwC+onqN1ZYkSZJCEU/P9eDY534KbAZygAsSWZQkSZJUFcUTrvOALcB6gmn5\nbgS+n8CaJEmSpCopnnB9+X72DQm5DkmSJKnKq2jM9UCCWULaABPL7G8ArE1kUZIkSVJVVFG4/ghY\nRbD8+Wj23MS4AZid4LokSZKkKieeWT/qE4y53gl0jG3/IFhQJkpcoTFBXKExmjyGUmrxnJei41BX\naHyPYCq+FsAbBLOHPB5SbZIkSVK1EU+4TieYgu//I1iZ8SKgSyKLkiRJkqqieFdoPAn4MfDaf/nn\nJEmSpJQRT0i+HvgV8DdgHtAOeDeRRUmSJElVUXVaxtwbGoGNG2HNGsjI2LPVrLn36xo1/rvv9IbG\naPIYSqnFc16KjopuaKxoKr57gWHsPcf1biXAgEOuTKGbPBl++lMoLoYdO4LHstuO2BwvZcP27q1e\nPWjQAOrX3/sR7udXvyq/v359yMqC7Gxo2hQaNYK06nS5JkmS9F+qKFyPjz2O2c97XjpH1HnnBVtF\ndu0qH7h37IDNm6GoKOj9Lvv4n/+0pUGD4PlXX+393vr18PXXwbZ1KxxxRBC2992aNt37NWRRUmIY\nlyRJ1Uu80SY79vh1ogoJgcNCkmzbtmBIyu6wXXYru3/1aigo2EatWrVp2ZLSrVUr9nrdsiXUrZvs\n/6ro8p+IpdTiOS9FR0XDQioK12nACOCnwO5RujuB+4GRIdYXFsN1FbN+PSxbBsuX773t3rdiRTD0\nZHfQPvpo6NAh2L797eB1RkX/9lLN+YtWSi2e81J0HGy4vhE4B7gKKIjtawv8BZgE3B1eiaEwXFcz\nJSVBT/fuwL10KSxcCAsWBI9ffQWtW+8J22UfW7SA9Go+YaS/aKXU4jkvRcfBhuuZwJmUHwqSDbwJ\ndA+juBAZrlPM1q2waNHegXv3Y2EhtG8fBO1jj4Vu3YKtffv/fraUqPIXrZRaPOel6DjYcD2XA6/E\nWNF7yWK4VqmiIvjiC/j8c/j0U5g9G+bMCXq7jzlmT9ju1g26dt19k2XV4i9aKbV4zkvRcbDhegZw\n3EG8lyyGa1WqqAjmzg2C9uzZe7bMzD1Bu1s3yM0Nerxr1kx2xQfmL1optXjOS9FxsOF6J7D5AO9l\nUvE0fslguNZBKSkJbp7cHbTnzIGZM4Nx3t27wwknQK9ewda2bXSmD/QXrZRaPOel6DjYcF3VGK4V\nqg0bYPp0mDp1z7Z5856g3atXELy/9a3k1OcvWim1eM5L0WG4lkLy5ZcwbVqwTZ0aPGZl7QnbJ50U\nBO5atRJfi79opdTiOS9Fh+FaSpBdu4IbJ6dOhY8/ho8+CmYsOeEEOPXUYOvdOzGL4fiLVkotnvNS\ndBiupcNo/fogZL//frDNmhXcJLk7bJ98ctDbfaj8RSulFs95KToM11ISbd4c9GrvDttTpwbzb+8O\n26eccnBTAfqLVkotnvNSdBiupQjZvj24UXJ32P7wQ2jTBr73vWA7+WSoU6fy7/EXrZRaPOel6DBc\nSxFWXBz0Zv/zn8E2d24QsHeH7WOP3f/0f/6ilVKL57wUHYZrqQpZtw7efTcI2m+8EfR07w7a3/3u\nniEk/qKVUovnvBQdhmupiiopgUWL9vRqT54M7doFQXvUqFPZseN9MqK2nJOkhDBcS9FhuJaqiR07\ngpsj33gDHn30S7ZvP4pzz4X+/eGss6Bhw2RXKClRDNdSdBiupWpq+XJ49VV45ZXgxsiTToIBA4Kw\n3apVsquTFCbDtRQdhmspBRQVBUNHXnkFXnsNWrYMgvaAAdCjx/5vipRUdRiupegwXEspprgY/vWv\nIGj//e/BXNv9+wdB+4wzDs/y7JLCZbiWosNwLaW4zz8PgvbLL8P8+fCDH8APf2jQlqoSw7UUHYZr\nSaVWrIAXX4TnnoPPPts7aNesmezqJB2I4VqKDsO1pP1avhxeeAGefx4WLIC8vCBon3aaQVuKGsO1\nFB2Ga+3Xjh07+Oijj/jyyy9p0aIFffr0IcNJk1PWsmVB0H7uuWBu7fPPD4J2v344l7YUAYZrKToM\n1yrns88+o3///mzZsoWWLVuyfPly6tSpw8SJEznmmGOSXZ6SbMmSPT3aBQVwwQUweHAw1Z+zjkjJ\nYbiWosNwrXJOO+00zj33XG6++ebS/2GPGTOG1157jXfffTfZ5SlCCgrgmWdg/PhgEZtLL4VLLoG2\nbZNdmZRaDNdSdBiuVU7jxo1Zs2YNNWrUKN23Y8cOsrOzKSwsDLWt7du38/vf/54nn3ySL7/8kqOO\nOorBgwfz61//mlpOVVFllJTAJ5/Ak08GYbtjx6A3+6KLoHHjZFcnVX+Gayk6KgrX6Ye3FEXFUUcd\nxeTJk/faN2XKFFq0aBF6W7/85S95++23eeihh5g1axYPPfQQ77zzDr/4xS9Cb0uJk5YGJ5wA990X\nzDhyyy3w5pvQunUQsCdODHq2JUlKZfZcp6hXXnmFQYMGcd5559GqVSuWLl3Ka6+9xoQJE8jLywu1\nrRYtWjBr1iyaNm1aum/NmjV069aNL7/8MtS2dPitWxeMzR4/Pphx5Ec/Cnq0e/Z0fLYUJnuupeiw\n51rlDBgwgPz8fDp37szGjRvp2rUr+fn5oQdrVX+NG8NVV8EHHwSrQh5xRBCwjz0W7roLVq9OdoWS\nJB0+1alfyZ7r/8L7779Pjx49qF+//l77P/zwQ04++eRQ27r++uuZOnUqt99+O0cffTRLlizh97//\nPT179uTee+8NtS1FQ0kJfPghjB0brAr5ve/B//xPsFBNupf00kGx51qKDm9oVDnp6el06tSJV155\nhfbt25fub9CgAUVFRaG2tfuGxqeeeqr0hsaBAwfy61//mtq1a4falqKnsBD++ld45BHYsAGuvBKG\nDIHmzZNdmVS1GK6l6DBcq5wGDRowZswYfvOb3zB+/HjOOuus0v1hhuvi4mKuuOIKHnroIerUqRPa\n96rq2T3byCOPBGO0+/ULerPPOgvKTFoj6QAM11J0GK5Vzu4Q/cEHH3DxxRdzww03cPPNNyek57p5\n8+YsW7aMmq6nrZiiomA6v0cega++giuugKFDoWXLZFcmRZfhWooOw7XKKRuily9fTl5eHscccwwv\nv/wyGzduDLWtP/zhD6xbt46RI0c6r7XKmTkzCNnPPAO9e8PVV8P3v29vtrQvw7UUHYZrlZObm8us\nWbNKX2/ZsoWhQ4fy7LPPsmvXrlDbysnJ4T//+Q/p6elkZ2fv/oEkLS2NZcuWhdqWqq7Nm4PhIg8+\nGPRm/+QnQY/2EUckuzIpGgzXUnQYrpVU+y5WU1a/fv0OWx2qOqZNgwcegFdegQsugJ/9DHJzk12V\nlFyGayk6DNfar6+++oqpU6eydu3avf6HPXTo0CRWJe2xenUwZOTBB6FtW/jpT+H888Hh+0pFhmsp\nOgzXKufll1/mkksuoUOHDsydO5cuXbowd+5c+vbty7vvvht6ezNmzGDKlCnlgvxvf/vb0NtS9VNc\nHMyXff/9sGgRXHNNMNPIkUcmuzLp8DFcS9HhCo0q57bbbmPcuHHMmDGD+vXrM2PGDB5++GF69OgR\nelsPP/xwaWgfNWoUc+bMYcyYMXzxxReht6XqKSMDLrwQ3nsPXnsNli2DTp2CZdanTk12dZIk7WHP\ndYpq2LAhGzZsAKBx48Z888037Nq1i2bNmvH111+H2la7du147LHHOPXUU2ncuDHr1q3jH//4B08/\n/TTjx48PtS2ljm++gXHj4E9/gm99C264IQjgGRnJrkxKDHuupehwWIjKad++PR988AHNmjXjuOOO\n409/+hNNmzblpJNOYu3ataG2VTbIH3HEEaxevZr09HSaNGnCunXrQm2rOtq2bRuPP/44M2fO3Gua\nxLS0NC9OgJ07g97sMWNg6VK4/vpglpEGDZJdmRQuw7UUHQ4LUTlXXnklH3zwAQA33HADp59+Orm5\nuVx77bWht5WTk0NBQQEAHTp04O9//ztTpkxx6fM4XXbZZdx77700bNiQdu3a0b59e9q1a0e7du2S\nXVok1KgBAwYEQ0aeew7+9S9o0waGD4cvv0x2dZKkVGPPdYrauXMnNcqs0rF06VI2bdrEscceG3pb\njz32GEceeSTnnnsu//jHP7jgggvYvn079913Hz/5yU9Cb6+6adSoEQUFBTRu3DjZpVQZBQXwxz/C\nk0/CD34AN90EXbokuyrp0NhzLUWHw0K0l+LiYho0aEBhYWFSeo+3bdvG9u3baeC/28clNzeXN954\ng2bNmiW7lCrnm2/goYeCWUZyc+Hmm+H00yGtOv2fTynDcC1Fh+Fa5XTr1o1//OMftGjRIiHfX1JS\nUroSY0UrPqanOzKpMmPGjOH555/n5z/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pB6xcp5l//etfjBo1ikGDBm3z3LXXXkvXrl2L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\nSoqeybUkSTHSq1cvAKZOncqll15Kwf1EGRkZ5ObmcvLJJ0c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"text": [
"<matplotlib.figure.Figure at 0x107736990>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
}
],
"metadata": {}
}
]
}
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