bnaul/Riddler_8_19_2016.ipynb

## Riddler_8_19_2016.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HmbFpBtOSpzFn2xw61evEgNYD+GvPv1L/yvpexxPxJZW8hNTeY3v5YtMXTEua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\nRHzs/wP/0qAcNIst5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d32b0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
    "\n",
    "dt = 1e-6\n",
    "t = np.arange(0., 1., step=dt)\n",
    "N = len(t)\n",
    "c = np.pi / 2.0\n",
    "\n",
    "me = np.c_[np.ones(N), t]\n",
    "ram = np.zeros((N, 2))\n",
    "for i in range(1, N):\n",
    "    v = me[i - 1] - ram[i - 1]\n",
    "    v /= np.linalg.norm(v)\n",
    "    ram[i] = ram[i - 1] + c * v * dt\n",
    "\n",
    "plt.plot(me[:, 0], me[:, 1], 'o')\n",
    "plt.plot(ram[:, 0], ram[:, 1], '-')\n",
    "\n",
    "any(ram[:, 0] >= 1 - np.sqrt(dt))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 36,
	"metadata": {
	"collapsed": false
	},
	"outputs": [
	{
	"data": {
	"text/plain": [
	"True"
	]
	},
	"execution_count": 36,
	"metadata": {},
	"output_type": "execute_result"
	},
	{
	"data": {
	"image/png": 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HmbFpBtOSpzFn2xw61evEgNYD+GvPv1L/yvpexxPxJZW8hNTeY3v5YtMXTEua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\nRHzs/wP/0qAcNIst5QAAAABJRU5ErkJggg==\n",
	"text/plain": [
	"<matplotlib.figure.Figure at 0x10d32b0f0>"
	]
	},
	"metadata": {},
	"output_type": "display_data"
	}
	],
	"source": [
	"import numpy as np\n",
	"import matplotlib.pyplot as plt\n",
	"%matplotlib inline\n",
	"plt.rcParams[\"figure.figsize\"] = (6, 6)\n",
	"\n",
	"dt = 1e-6\n",
	"t = np.arange(0., 1., step=dt)\n",
	"N = len(t)\n",
	"c = np.pi / 2.0\n",
	"\n",
	"me = np.c_[np.ones(N), t]\n",
	"ram = np.zeros((N, 2))\n",
	"for i in range(1, N):\n",
	" v = me[i - 1] - ram[i - 1]\n",
	" v /= np.linalg.norm(v)\n",
	" ram[i] = ram[i - 1] + c * v * dt\n",
	"\n",
	"plt.plot(me[:, 0], me[:, 1], 'o')\n",
	"plt.plot(ram[:, 0], ram[:, 1], '-')\n",
	"\n",
	"any(ram[:, 0] >= 1 - np.sqrt(dt))"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.5.2"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 0
	}