{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Oregon Curriculum Network](http://4dsolutions.net/ocn/)\n",
    "\n",
    "[Home](School_of_Tomorrow.ipynb)\n",
    "\n",
    "\n",
    "# The Density of the CCP Using Tetravolumes\n",
    "\n",
    "See the Youtube at the end for more of an explanation.\n",
    "\n",
    "<a data-flickr-embed=\"true\"  href=\"https://www.flickr.com/photos/kirbyurner/9530922237/in/album-72157624750749042/\" title=\"Regular and Right Tetrahedrons Compared\"><img src=\"https://live.staticflickr.com/3790/9530922237_dcc672a68a_z.jpg\" width=\"640\" height=\"480\" alt=\"Regular and Right Tetrahedrons Compared\"></a><script async src=\"//embedr.flickr.com/assets/client-code.js\" charset=\"utf-8\"></script>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "S3 = 1.060660171779821   \n",
      "\n"
     ]
    }
   ],
   "source": [
    "root2 = pow(2,1/2)\n",
    "xyz_cube = root2 ** 3\n",
    "ivm_cube = 3\n",
    "S3 = ivm_cube/xyz_cube\n",
    "print(\"\"\"\n",
    "S3 = {}   \n",
    "\"\"\".format(S3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.1887902047863905"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from math import pi\n",
    "xyz_ball = (4/3)*pi\n",
    "xyz_ball"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7404804896930607"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(xyz_ball*S3)/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/ZCoYzZBn-kI\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x1131884a8>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from IPython.display import YouTubeVideo\n",
    "YouTubeVideo(\"ZCoYzZBn-kI\") # https://youtu.be/ZCoYzZBn-kI"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Don't see the Youtube?  Check it out [on nbviewer](https://nbviewer.jupyter.org/github/4dsolutions/School_of_Tomorrow/blob/master/HoneyComb_Density.ipynb)."
   ]
  }
 ],
 "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": "3.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}