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   "cell_type": "markdown",
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   "source": [
    "Thanks to unicode, we may use Greek letters directly in our code.  \n",
    "\n",
    "In this Jupyter Notebook, lets use θ (theta), π (pi) and τ (tau) with τ = 2 * π.  \n",
    "\n",
    "Then we'll plot the graph of Euler's Formula, e to the i θ over the range 0 to τ.\n",
    "\n",
    "In Python we signify i, the root of -1, as 1j for readability, so lets bind i to 1j as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.00000\n"
     ]
    }
   ],
   "source": [
    "from math import e, pi as π\n",
    "τ = 2 * π\n",
    "i = 1j\n",
    "result = e ** (i * τ)\n",
    "print (\"{:1.5f}\".format(result.real))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Below we import some industrial grade tools used for plotting with Python.  The same greek letter names remain active and guide the construction of a domain t and range s.  Then we label the graph and generate a picture.  plt.show(), if used, produces a plot in its own window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "t = np.arange(0.0, τ, 0.01)\n",
    "s = np.array([(np.e ** (i * θ)).real for θ in t])\n",
    "plt.plot(t, s)\n",
    "plt.xlabel('radians')\n",
    "plt.ylabel('real part')\n",
    "plt.title('Euler\\'s Formula from 0 to tau')\n",
    "plt.grid(True)\n",
    "plt.savefig(\"euler_test.png\") # uploaded to Flickr for display below"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![euler_test.png](https://c2.staticflickr.com/2/1562/26157050065_392d24fb62_z.jpg \"euler_test.png\")"
   ]
  }
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