{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "afcfc049",
   "metadata": {},
   "outputs": [],
   "source": [
    "import re\n",
    "\n",
    "orbits = \"\"\"\n",
    "Mercury: 88 days.\n",
    "Venus: 225 days.\n",
    "Earth: 365 days.\n",
    "Mars: 687 days.\n",
    "Jupiter: 4333 days.\n",
    "Saturn: 10759 days.\n",
    "Uranus: 30687 days.\n",
    "Neptune: 60190 days.\n",
    "\"\"\".splitlines()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "c0665887",
   "metadata": {},
   "outputs": [],
   "source": [
    "ratios = [int((re.findall(r'\\d+', x)[0:1] or [0])[0])/88 for x in orbits][1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "56eb1e3f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 6.307132459970888,\n",
       " 15.660844250363901,\n",
       " 44.66812227074236,\n",
       " 87.61280931586609]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x / ratios[3] for x in ratios[3:]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "8401b303",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 1.5990053726670783,\n",
       " 2.036596983383623,\n",
       " 2.794068392473273,\n",
       " 7.017024751533684,\n",
       " 11.0571860632063,\n",
       " 18.67393662543892,\n",
       " 26.152959158138735]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "[math.sqrt(x) for x in ratios]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "85f986fc",
   "metadata": {},
   "outputs": [],
   "source": [
    "dist = \"\"\"The distance from the Sun to Mercury is 0.39 AU, to Venus is 0.72 AU, to Earth is 1.00 AU, to Mars is 1.52 AU, to Jupiter is 5.20 AU, to Saturn is 9.54 AU, to Uranus is 19.22 AU, and to Neptune is 30.06 AU.\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "id": "7c321d05",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5.875871902123325,\n",
       " 15.072438995419457,\n",
       " 20.0,\n",
       " 26.280655022872775,\n",
       " 44.729879383810726,\n",
       " 53.83240228190293,\n",
       " 64.3392710531322,\n",
       " 71.04793076487243]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[20 + 1.5 * math.log(float(x))*10 for x in re.findall(r'[0-9]+.\\d+', dist)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "36ce6b46",
   "metadata": {},
   "outputs": [],
   "source": [
    "planets = [\n",
    "    ('mercury', 1.0, 50),\n",
    "    ('venus', 1.6, 130),\n",
    "    ('earth', 2.0, 200),\n",
    "    ('mars', 2.8, 270),\n",
    "    ('jupiter', 7.0, 450),\n",
    "    ('saturn', 11, 540),\n",
    "    ('uranus', 18, 640),\n",
    "    ('neptune', 26, 710),\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "6a36fcb8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def b():\n",
    "    prevp = 1.0\n",
    "    for n, p, d in planets:\n",
    "        yield p / prevp\n",
    "        prevp = p\n",
    "        \n",
    "ratios = list(b())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "5f6e6b6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "scale = 5\n",
    "\n",
    "tooth_width = 0.8;\n",
    "tooth_crop = 0.5;\n",
    "tooth_thickness = 0.6;\n",
    "\n",
    "def gear_base_radius(n):\n",
    "    perimeter = tooth_width * (1 + 0.8*(1-tooth_crop)) * n\n",
    "    return perimeter / math.pi / 2;\n",
    "\n",
    "def gear_wheel_radius(n):\n",
    "    return math.sqrt(gear_base_radius(n)**2 + (tooth_width/2)**2);\n",
    "\n",
    "def gear_radius(n):\n",
    "    return scale * (gear_wheel_radius(n) + gear_base_radius(n) + tooth_crop)/2;\n",
    "\n",
    "def dcenter(n1, n2):\n",
    "    return gear_radius(n1) + gear_radius(n2)\n",
    "\n",
    "def search():\n",
    "    for n1 in range(11, 39):\n",
    "        n2 = 50 - n1\n",
    "        yield (n1, n2, n2 / n1, dcenter(n1, n2))\n",
    "        \n",
    "rr = list(search())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "b64daa46",
   "metadata": {},
   "outputs": [],
   "source": [
    "def found():\n",
    "    for r in ratios:\n",
    "        for n1, n2, tr, _ in rr:\n",
    "            if tr < r:\n",
    "                yield (n1, n2, r, tr)\n",
    "                break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "c587ff67",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(26, 24, 1.0, 0.9230769230769231),\n",
       " (20, 30, 1.6, 1.5),\n",
       " (23, 27, 1.25, 1.173913043478261),\n",
       " (21, 29, 1.4, 1.380952380952381),\n",
       " (15, 35, 2.5, 2.3333333333333335),\n",
       " (20, 30, 1.5714285714285714, 1.5),\n",
       " (19, 31, 1.6363636363636365, 1.631578947368421),\n",
       " (21, 29, 1.4444444444444444, 1.380952380952381)]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "list(found())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "id": "2d7d6f8b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(11, 39, 3.5454545454545454, 47.19308954151068),\n",
       " (12, 38, 3.1666666666666665, 47.18558098978421),\n",
       " (13, 37, 2.8461538461538463, 47.179354476011646),\n",
       " (14, 36, 2.5714285714285716, 47.17415487784531),\n",
       " (15, 35, 2.3333333333333335, 47.16979419516311),\n",
       " (16, 34, 2.125, 47.166131477877656),\n",
       " (17, 33, 1.9411764705882353, 47.16305960247725),\n",
       " (18, 32, 1.7777777777777777, 47.16049634511566),\n",
       " (19, 31, 1.631578947368421, 47.158378230688704),\n",
       " (20, 30, 1.5, 47.15665622507779),\n",
       " (21, 29, 1.380952380952381, 47.15529268372393),\n",
       " (22, 28, 1.2727272727272727, 47.154259179645024),\n",
       " (23, 27, 1.173913043478261, 47.15353496521375),\n",
       " (24, 26, 1.0833333333333333, 47.15310590655676),\n",
       " (25, 25, 1.0, 47.15296378588499),\n",
       " (26, 24, 0.9230769230769231, 47.15310590655676),\n",
       " (27, 23, 0.8518518518518519, 47.15353496521375),\n",
       " (28, 22, 0.7857142857142857, 47.154259179645024),\n",
       " (29, 21, 0.7241379310344828, 47.15529268372393),\n",
       " (30, 20, 0.6666666666666666, 47.15665622507779),\n",
       " (31, 19, 0.6129032258064516, 47.158378230688704),\n",
       " (32, 18, 0.5625, 47.16049634511566),\n",
       " (33, 17, 0.5151515151515151, 47.16305960247725),\n",
       " (34, 16, 0.47058823529411764, 47.166131477877656),\n",
       " (35, 15, 0.42857142857142855, 47.16979419516311),\n",
       " (36, 14, 0.3888888888888889, 47.17415487784531),\n",
       " (37, 13, 0.35135135135135137, 47.179354476011646),\n",
       " (38, 12, 0.3157894736842105, 47.18558098978421)]"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8c2dca2a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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