Spacerat/e.ipynb

## e.ipynb
{
 "metadata": {
  "name": "Eeeeee"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%pylab inline",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "Populating the interactive namespace from numpy and matplotlib\n"
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "def bestn(targ):\n    '''Try dividing 'targ' by all integers between 0 and targ\n    targ/k = n\n    find the k and n giving the largest value of k^n'''\n    \n    t = arange(1, targ)\n    n = float(targ) / t\n    p = n**t\n    argm = argmax(p)\n    return (targ, t[argm], float(targ) / t[argm])\n    \n    \n# Plot n for all targ between 2 and 80\ntests = linspace(1.1, 80, 500)\nresults = array([bestn(x) for x in tests])\nplot(tests, results[:,2])\n\n# Plot e\nplot((0, 80), (e, e), 'k')\nprint results[:22]\n",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": "[[ 1.1         1.          1.1       ]\n [ 1.25811623  1.          1.25811623]\n [ 1.41623246  1.          1.41623246]\n [ 1.5743487   1.          1.5743487 ]\n [ 1.73246493  1.          1.73246493]\n [ 1.89058116  1.          1.89058116]\n [ 2.04869739  1.          2.04869739]\n [ 2.20681363  1.          2.20681363]\n [ 2.36492986  1.          2.36492986]\n [ 2.52304609  1.          2.52304609]\n [ 2.68116232  1.          2.68116232]\n [ 2.83927856  1.          2.83927856]\n [ 2.99739479  1.          2.99739479]\n [ 3.15551102  1.          3.15551102]\n [ 3.31362725  1.          3.31362725]\n [ 3.47174349  1.          3.47174349]\n [ 3.62985972  1.          3.62985972]\n [ 3.78797595  1.          3.78797595]\n [ 3.94609218  1.          3.94609218]\n [ 4.10420842  2.          2.05210421]\n [ 4.26232465  2.          2.13116232]\n [ 4.42044088  2.          2.21022044]]\n"
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SpZRSlZWVKikpSW3bts1xc9QsXbpU/eIXv1ATJ05USjnz937JJZeo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\nEYY6EVEzwlAnImpGGOpERM3I/wOr44qZrElbswAAAABJRU5ErkJggg==\n",
       "text": "<matplotlib.figure.Figure at 0x1068af550>"
      }
     ],
     "prompt_number": 178
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}
	{
	"metadata": {
	"name": "Eeeeee"
	},
	"nbformat": 3,
	"nbformat_minor": 0,
	"worksheets": [
	{
	"cells": [
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "%pylab inline",
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": "Populating the interactive namespace from numpy and matplotlib\n"
	}
	],
	"prompt_number": 15
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "def bestn(targ):\n '''Try dividing 'targ' by all integers between 0 and targ\n targ/k = n\n find the k and n giving the largest value of k^n'''\n \n t = arange(1, targ)\n n = float(targ) / t\n p = n**t\n argm = argmax(p)\n return (targ, t[argm], float(targ) / t[argm])\n \n \n# Plot n for all targ between 2 and 80\ntests = linspace(1.1, 80, 500)\nresults = array([bestn(x) for x in tests])\nplot(tests, results[:,2])\n\n# Plot e\nplot((0, 80), (e, e), 'k')\nprint results[:22]\n",
	"language": "python",
	"metadata": {},
	"outputs": [
	{
	"output_type": "stream",
	"stream": "stdout",
	"text": "[[ 1.1 1. 1.1 ]\n [ 1.25811623 1. 1.25811623]\n [ 1.41623246 1. 1.41623246]\n [ 1.5743487 1. 1.5743487 ]\n [ 1.73246493 1. 1.73246493]\n [ 1.89058116 1. 1.89058116]\n [ 2.04869739 1. 2.04869739]\n [ 2.20681363 1. 2.20681363]\n [ 2.36492986 1. 2.36492986]\n [ 2.52304609 1. 2.52304609]\n [ 2.68116232 1. 2.68116232]\n [ 2.83927856 1. 2.83927856]\n [ 2.99739479 1. 2.99739479]\n [ 3.15551102 1. 3.15551102]\n [ 3.31362725 1. 3.31362725]\n [ 3.47174349 1. 3.47174349]\n [ 3.62985972 1. 3.62985972]\n [ 3.78797595 1. 3.78797595]\n [ 3.94609218 1. 3.94609218]\n [ 4.10420842 2. 2.05210421]\n [ 4.26232465 2. 2.13116232]\n [ 4.42044088 2. 2.21022044]]\n"
	},
	{
	"metadata": {},
	"output_type": "display_data",
	"png": 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SpZRSlZWVKikpSW3bts1xc9QsXbpU/eIXv1ATJ05USjnz937JJZeo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\nEYY6EVEzwlAnImpGGOpERM3I/wOr44qZrElbswAAAABJRU5ErkJggg==\n",
	"text": "<matplotlib.figure.Figure at 0x1068af550>"
	}
	],
	"prompt_number": 178
	},
	{
	"cell_type": "code",
	"collapsed": false,
	"input": "",
	"language": "python",
	"metadata": {},
	"outputs": []
	}
	],
	"metadata": {}
	}
	]
	}