{
"cells": [
{
"cell_type": "markdown",
"id": "b2c494fa-bf65-450e-99b8-07c997b1d846",
"metadata": {},
"source": [
"[Oregon Curriculum Network](http://4dsolutions.net/ocn/)
\n",
"[School of Tomorrow](School_of_Tomorrow.ipynb)\n",
"\n",
"\n",
"## The TetraBook and S3\n",
"\n",
"A Jupyter Notebook for the School of Tomorrow.\n",
"\n",
"With thanks to Alan Michelson on Synergeo, for circling back to it, and to David Koski, for the TetraBook meme in the first place.\n",
"\n",
"[View in nbviewer](https://nbviewer.org/github/4dsolutions/School_of_Tomorrow/blob/master/TetraBook.ipynb)"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "fda9e374-30aa-4ce0-a2ca-12724db39940",
"metadata": {},
"outputs": [],
"source": [
"from IPython.display import YouTubeVideo"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1960684d-cb7e-4a90-b462-7fab4ed09f8d",
"metadata": {},
"outputs": [
{
"data": {
"image/jpeg": "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",
"text/html": [
"\n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"YouTubeVideo(\"WKrGmuXW-RQ\")"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "71f41d58-cca6-4994-bc7a-822b4322e808",
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import pandas as pd"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "4c392a18-9d2b-4f16-96d3-2fdd88a712be",
"metadata": {},
"outputs": [],
"source": [
"import math"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "bef4b5c4-bf9d-409b-a403-636f20252999",
"metadata": {},
"outputs": [],
"source": [
"root3 = math.sqrt(3)\n",
"S3 = math.sqrt(9/8)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "559103cb-46af-4114-b476-d4d86ab7f859",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.4641016151377544"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"2 * root3 # book cover tip to book cover tip"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "0c752872-11a9-46b5-a2ff-9e616e065ca1",
"metadata": {},
"outputs": [],
"source": [
"theta_deg = np.arange(0, 181) # degrees"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "3efad524-6e9b-4828-b206-f77d996ce174",
"metadata": {},
"outputs": [],
"source": [
"front_cover_tip = (-root3, 0.0) # left\n",
"back_cover_tip = ( root3, 0.0) # right"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "5dc80f09-4d97-4612-a56d-d9a82355fab7",
"metadata": {},
"outputs": [],
"source": [
"page_tip_deg = lambda deg: (-root3 * np.cos(np.radians(deg)), root3 * (np.sin(np.radians(deg))))\n",
"page_tip_rad = lambda rad: (-root3 * np.cos(rad), root3 * np.sin(rad))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "9f3a2f62-1885-4bc3-ba25-d452efd0c8c0",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(-1.0605752387249068e-16, 1.7320508075688772)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"page_tip_rad(math.pi/2)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "d3450655-e0c8-470d-a08d-618465e4073b",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"70.52877936550931"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"dihedral_angle_of_reg_tet = math.acos(1/3)\n",
"math.degrees(dihedral_angle_of_reg_tet)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "985838f7-0366-4ff7-86ab-49535aa7998d",
"metadata": {},
"outputs": [],
"source": [
"def distance(a, b):\n",
" return np.sqrt((a[0] - b[0])**2 + (a[1] - b[1])**2)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "bfaa4d07-0a3a-4d9f-b536-e1ad1f0872dd",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.4641016151377544"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"distance(front_cover_tip, back_cover_tip)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "05dabb6f-aa23-44d8-9405-0b1e6255c003",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"2.449489742783178"
]
},
"execution_count": 14,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"distance(front_cover_tip, page_tip_deg(90))"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "534c901e-dcd0-4eaf-9f88-3654246cb0e2",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.4641016151377544"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"distance(front_cover_tip, page_tip_deg(180))"
]
},
{
"cell_type": "markdown",
"id": "a2a00560-9a3c-4c79-87f2-d53d8d5fa6b4",
"metadata": {},
"source": [
"![\"tetrabook2\"](\"https://live.staticflickr.com/4850/46149255411_31eb8869cf.jpg\")
"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "d686c0f1-e3bc-4d87-bf1e-13d909163ab5",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/var/folders/z2/2d18w70j4yj5hqyn50kt8cn40000gn/T/ipykernel_27093/713651319.py:1: DeprecationWarning: the imp module is deprecated in favour of importlib and slated for removal in Python 3.12; see the module's documentation for alternative uses\n",
" import imp\n"
]
}
],
"source": [
"import imp"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "b75c66a0-511a-4371-8da6-5cef878f57a7",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 17,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import tetravolume\n",
"imp.reload(tetravolume)"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "a4cb182d-560c-4afc-8600-79cd9bd596ce",
"metadata": {},
"outputs": [],
"source": [
"import tetravolume as tv\n",
"from tetravolume import Tetrahedron"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "1d4a6a24-5b74-4422-abcb-1c1caffb071d",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1$"
],
"text/plain": [
"1"
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tv.D"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "ed4c62a1-5cb5-4746-9054-2a229744538e",
"metadata": {},
"outputs": [],
"source": [
"test_tet = Tetrahedron(1,1,1,1,1,1)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "5254f86b-22dc-4c22-9613-1e018e15961f",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1.0$"
],
"text/plain": [
"1.00000000000000"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"test_tet.ivm_volume()"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "cc0e7a45-ef5c-4c8f-a32e-bf820abe1bcd",
"metadata": {},
"outputs": [],
"source": [
"def get_volume_rad(theta):\n",
" return Tetrahedron(1,1,1,1,1, distance(back_cover_tip, page_tip_rad(theta))/2).ivm_volume()"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "d399e4ab-47ab-44ac-957b-581d592ff40e",
"metadata": {},
"outputs": [],
"source": [
"get_vol = np.vectorize(get_volume_rad)"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "a62b6789-169a-44ac-bdc8-67adbe76ba33",
"metadata": {},
"outputs": [],
"source": [
"table = pd.DataFrame({\"theta_deg\":theta_deg, \"theta_rad\":np.radians(theta_deg)})"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "b8172027-099e-4b42-adf3-f38aa95c4ec8",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" theta_deg | \n",
" theta_rad | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.000000 | \n",
"
\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 0.017453 | \n",
"
\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 0.034907 | \n",
"
\n",
" \n",
" | 3 | \n",
" 3 | \n",
" 0.052360 | \n",
"
\n",
" \n",
" | 4 | \n",
" 4 | \n",
" 0.069813 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" theta_deg | \n",
" theta_rad | \n",
" alt | \n",
" tvs | \n",
" x | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.000000 | \n",
" 0.000000e+00 | \n",
" 2.10734242554470e-8 | \n",
" 1.732051 | \n",
"
\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 0.017453 | \n",
" 3.022845e-02 | \n",
" 0.0185110724097577 | \n",
" 1.731787 | \n",
"
\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 0.034907 | \n",
" 6.044770e-02 | \n",
" 0.0370165061675079 | \n",
" 1.730996 | \n",
"
\n",
" \n",
" | 3 | \n",
" 3 | \n",
" 0.052360 | \n",
" 9.064854e-02 | \n",
" 0.0555106643389176 | \n",
" 1.729677 | \n",
"
\n",
" \n",
" | 4 | \n",
" 4 | \n",
" 0.069813 | \n",
" 1.208218e-01 | \n",
" 0.0739879134242018 | \n",
" 1.727832 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 176 | \n",
" 176 | \n",
" 3.071779 | \n",
" 1.208218e-01 | \n",
" 0.0739879134242003 | \n",
" -1.727832 | \n",
"
\n",
" \n",
" | 177 | \n",
" 177 | \n",
" 3.089233 | \n",
" 9.064854e-02 | \n",
" 0.0555106643389016 | \n",
" -1.729677 | \n",
"
\n",
" \n",
" | 178 | \n",
" 178 | \n",
" 3.106686 | \n",
" 6.044770e-02 | \n",
" 0.0370165061675049 | \n",
" -1.730996 | \n",
"
\n",
" \n",
" | 179 | \n",
" 179 | \n",
" 3.124139 | \n",
" 3.022845e-02 | \n",
" 0.0185110724097397 | \n",
" -1.731787 | \n",
"
\n",
" \n",
" | 180 | \n",
" 180 | \n",
" 3.141593 | \n",
" 2.121150e-16 | \n",
" 0 | \n",
" -1.732051 | \n",
"
\n",
" \n",
"
\n",
"
181 rows × 5 columns
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" theta_deg | \n",
" theta_rad | \n",
" x | \n",
" alt | \n",
" tvs | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.000000 | \n",
" 1.732051 | \n",
" 0.000000e+00 | \n",
" 2.10734242554470e-8 | \n",
"
\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 0.017453 | \n",
" 1.731787 | \n",
" 3.022845e-02 | \n",
" 0.0185110724097577 | \n",
"
\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 0.034907 | \n",
" 1.730996 | \n",
" 6.044770e-02 | \n",
" 0.0370165061675079 | \n",
"
\n",
" \n",
" | 3 | \n",
" 3 | \n",
" 0.052360 | \n",
" 1.729677 | \n",
" 9.064854e-02 | \n",
" 0.0555106643389176 | \n",
"
\n",
" \n",
" | 4 | \n",
" 4 | \n",
" 0.069813 | \n",
" 1.727832 | \n",
" 1.208218e-01 | \n",
" 0.0739879134242018 | \n",
"
\n",
" \n",
" | ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
" ... | \n",
"
\n",
" \n",
" | 176 | \n",
" 176 | \n",
" 3.071779 | \n",
" -1.727832 | \n",
" 1.208218e-01 | \n",
" 0.0739879134242003 | \n",
"
\n",
" \n",
" | 177 | \n",
" 177 | \n",
" 3.089233 | \n",
" -1.729677 | \n",
" 9.064854e-02 | \n",
" 0.0555106643389016 | \n",
"
\n",
" \n",
" | 178 | \n",
" 178 | \n",
" 3.106686 | \n",
" -1.730996 | \n",
" 6.044770e-02 | \n",
" 0.0370165061675049 | \n",
"
\n",
" \n",
" | 179 | \n",
" 179 | \n",
" 3.124139 | \n",
" -1.731787 | \n",
" 3.022845e-02 | \n",
" 0.0185110724097397 | \n",
"
\n",
" \n",
" | 180 | \n",
" 180 | \n",
" 3.141593 | \n",
" -1.732051 | \n",
" 2.121150e-16 | \n",
" 0 | \n",
"
\n",
" \n",
"
\n",
"
181 rows × 5 columns
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" theta_deg | \n",
" theta_rad | \n",
" x | \n",
" alt | \n",
" tvs | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.000 | \n",
" 1.732 | \n",
" 0.000 | \n",
" 2.10734242554470e-8 | \n",
"
\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 0.017 | \n",
" 1.732 | \n",
" 0.030 | \n",
" 0.0185110724097577 | \n",
"
\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 0.035 | \n",
" 1.731 | \n",
" 0.060 | \n",
" 0.0370165061675079 | \n",
"
\n",
" \n",
" | 3 | \n",
" 3 | \n",
" 0.052 | \n",
" 1.730 | \n",
" 0.091 | \n",
" 0.0555106643389176 | \n",
"
\n",
" \n",
" | 4 | \n",
" 4 | \n",
" 0.070 | \n",
" 1.728 | \n",
" 0.121 | \n",
" 0.0739879134242018 | \n",
"
\n",
" \n",
"
\n",
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" theta_deg | \n",
" theta_rad | \n",
" x | \n",
" alt | \n",
" tvs | \n",
" cus | \n",
"
\n",
" \n",
" \n",
" \n",
" | 0 | \n",
" 0 | \n",
" 0.000 | \n",
" 1.732 | \n",
" 0.000 | \n",
" 2.10734242554470e-8 | \n",
" 1.98682149251302e-8 | \n",
"
\n",
" \n",
" | 1 | \n",
" 1 | \n",
" 0.017 | \n",
" 1.732 | \n",
" 0.030 | \n",
" 0.0185110724097577 | \n",
" 0.0174524064372998 | \n",
"
\n",
" \n",
" | 2 | \n",
" 2 | \n",
" 0.035 | \n",
" 1.731 | \n",
" 0.060 | \n",
" 0.0370165061675079 | \n",
" 0.0348994967025047 | \n",
"
\n",
" \n",
" | 3 | \n",
" 3 | \n",
" 0.052 | \n",
" 1.730 | \n",
" 0.091 | \n",
" 0.0555106643389176 | \n",
" 0.0523359562429586 | \n",
"
\n",
" \n",
" | 4 | \n",
" 4 | \n",
" 0.070 | \n",
" 1.728 | \n",
" 0.121 | \n",
" 0.0739879134242018 | \n",
" 0.0697564737441284 | \n",
"
\n",
" \n",
"
\n",
"
![\"Triangular](\"https://live.staticflickr.com/7450/9533679790_b916fba31f_w.jpg\")
\n"
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "0b495c15-ada0-4443-bf09-63a0b64e24f7",
"metadata": {},
"outputs": [],
"source": [
"from math import sqrt as rt2\n",
"import sympy as sym\n",
"from sympy import Eq, Number"
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "b60652d9-6926-490c-969a-d2252fe58cd4",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\sqrt{3}}{2}$"
],
"text/plain": [
"sqrt(3)/2"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"book_edge = sym.symbols([\"book_edge\", \"altitude\"])\n",
"book_edge = Number(1)\n",
"altitude = sym.sqrt(book_edge**2 - (book_edge/2)**2)\n",
"altitude"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "db98984d-0f4f-4a5a-bb9f-e16f11465412",
"metadata": {},
"outputs": [],
"source": [
"right_tet_hyp = sym.sqrt(2 * altitude**2)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "23135026-13e1-4f93-9a75-5a9f03c42a51",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{\\sqrt{6}}{2}$"
],
"text/plain": [
"sqrt(6)/2"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"right_tet_hyp"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "2fc89b32-a87e-4a85-af28-6f3a85c1da8a",
"metadata": {},
"outputs": [],
"source": [
"tv = Tetrahedron(1,1,1,1,1,right_tet_hyp)"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "c084204f-443b-496e-b3ec-d6817cafcd94",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle 1$"
],
"text/plain": [
"1"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tv.xyz_volume()"
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "e0b27fed-6c59-461b-b8ad-5ab91dab62ed",
"metadata": {},
"outputs": [
{
"data": {
"text/latex": [
"$\\displaystyle \\frac{3 \\sqrt{2}}{4}$"
],
"text/plain": [
"3*sqrt(2)/4"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tv.ivm_volume()"
]
},
{
"cell_type": "markdown",
"id": "99fbb5e9-22a9-46c6-9ed1-f0fb67e36073",
"metadata": {},
"source": [
"[Another Notebook on the TetraBook](https://github.com/4dsolutions/m4w/blob/main/Tetrabook.ipynb) (M4W repo)"
]
}
],
"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
}