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    "Fibonacci numbers\n",
    "-----------------\n",
    "\n",
    "The Fibonacci numbers is the number of the following sequence $$f_0 = f_1 = 1 \\qquad f_{n+2} = f_{n+1} + f_n.$$ We will see two loops to generate Fibonacci numbers:\n",
    "- the first one builds the list of Fibonacci numbers\n",
    "- the second one only computes two consecutive terms $(f_n, f_{n+1})$\n",
    "\n",
    "Depending on the problem you are considering you might want loop of the first kind or of the second one."
   ]
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     "text": [
      "[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]\n"
     ]
    }
   ],
   "source": [
    "# this loop generates the list of Fibonacci numbers\n",
    "L = [1, 1]\n",
    "for i in range(10):\n",
    "    L.append(L[-1] + L[-2])\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
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   "outputs": [],
   "source": []
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   "execution_count": 3,
   "metadata": {
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "144\n"
     ]
    }
   ],
   "source": [
    "# this loop go through the fibonacci numbers\n",
    "# (below we only print the last term)\n",
    "f0 = f1 = 1\n",
    "for i in range(10):\n",
    "    tmp = f0 + f1\n",
    "    f0 = f1\n",
    "    f1 = tmp\n",
    "print(f1)"
   ]
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