--- bibliography: - lib/zotero.bib link-citations: true mainfont: Linux Libertine O monofont: DejaVu Sans Mono sansfont: Linux Biolinum O title: Clear Skies - A Reference Architecture for Resilient Alaskan Microgrid Cyberinfrastructure title-block: false ---

Basic Book Builder

A Pandoc Template for building books and articles

Cover illustration
TitleBasic Book Builder
SubtitleA Pandoc Template for building books and articles
AffiliationAlaska Center for Energy and Power
InstitutionUniversity of Alaska Fairbanks
AuthorJohn Haverlack
Copyright© 2025 Alaska Center for Energy and Power
LicenseCC BY-ND 4.0
Version1.0.0
Date2025-11-13
StateBETA
Sourcehttps://github.com/jehaverlack/basic-book-builder
- [Introduction](#introduction) - [Conventions](#conventions) - [Getting Started](#getting-started) - [Installing Pre-Requisites](#installing-pre-requisites) - [Required](#required) - [Optional](#optional) - [Editing the Configuration](#editing-the-configuration) - [Editing the Book](#editing-the-book) - [Configuration](#configuration) - [FrontMatter Config](#frontmatter-config) - [Editing the Content](#editing-the-content) - [Citations](#citations) - [Usage: Building the Book](#usage-building-the-book) - [Example Content](#example-content) - [SI Conversion Factors](#si-conversion-factors) - [Physical Constants](#physical-constants) - [Fine Structure Constant](#fine-structure-constant) - [Newton’s Law of Gravity](#newtons-law-of-gravity) - [Relativistic Energy Momentum Relation](#relativistic-energy-momentum-relation) - [Planck’s Constant](#plancks-constant) - [Planck Length](#planck-length) - [Fine Structure Constant](#fine-structure-constant-1) - [Sage Code](#sage-code) - [Terminology](#terminology) - [Citations](#citations-1) # Introduction This is a basic book (or article) builder template based on a Pandoc build process in conjunction with a number of other tools to generate PDF, ODT, HTML, LaTex, Markdown, and Epub book output formats from Markdown source content , which can optionally be edited as an Obsidian vault. This book builder template has been curated by John Haverlack.([“John Haverlack ACEP” n.d.](#ref-JohnHaverlackACEP)) ## Conventions A few callout box styles have been added to easily highlight content.
**Established Concept** Einsteins Relativistic Dynamics Equations *E*2 = (*m*0⋅*c*2)2 + (*p*⋅*c*)2
**Proposed Concept** With the speed of light, *c* = 1: *E*2 = *m*02 + *p*2
**Speculative Concept** With the speed of light, *c* = 1: *E*2 = *m*02 + *p*2
**Caution Note** Beware of this section.
**Warning Note** Beware of this section.
**Alerts** Extreme Highlight
# Getting Started ## Installing Pre-Requisites For Debian / ZorinOS and likely Ubuntu based systems.
**TODO** It would be nice to roll a setup script to take care of this.
### Required #### Pandoc - https://pandoc.org/ - [Download](https://github.com/jgm/pandoc/releases/tag/3.8.2.1) sudo apt install https://github.com/jgm/pandoc/releases/download/3.8.2.1/pandoc-3.8.2.1-1-amd64.deb #### Code Editor
**Code Editor** [VSCodium](https://vscodium.com/) is recommend for privacy (telemetry/tracking) reasons - https://vscodium.com/
But any text editor will work. \#### make sudo apt install make #### jq and yq sudo apt install jq yq #### texlive sudo apt install texlive texlive-xetex texlive-latex-extra texlive-fonts-recommended texlive-fonts-extra #### MathJax - https://www.mathjax.org/ wget https://registry.npmjs.org/mathjax/-/mathjax-3.2.2.tgz tar xzf mathjax-3.2.2.tgz mv package/es5/* lib/mathjax rm -rf package mathjax-3.2.2.tgz
**TODO** This need to be rolled into a setup script.
### Optional The following are not strictly requires to use this book builder template. #### Obsidian
**Highly Recommended** Editing book chapter content in Obsidian is a very productive means for editing Markdown source content.
- https://obsidian.md/ - [Deb Package](https://github.com/obsidianmd/obsidian-releases/releases/download/v1.9.14/obsidian_1.9.14_amd64.deb) sudo apt install https://github.com/obsidianmd/obsidian-releases/releases/download/v1.9.14/obsidian_1.9.14_amd64.deb #### Zotero
**Highly Recommended** If you need to managed citations and references, Zotero integration is highly recommended.
- https://www.zotero.org/ sudo cp ./scripts/deps/zotero.list /etc/apt/sources.list.d/ sudo apt update sudo apt install zotero ##### Better BibTex for Zotero Install the Better BibTex Plugin for Zotero - Zotero \> Tool \> Plugins ##### Export citations.bib - Zotero \> File \> Export Library \> Format: Better BibTeX - [ ] Keep Updated - [ ] Save to: \~/Documents/Lib/zotero.bib - [ ] Symlink your \~/Documents/Lib/Citations.bib to basic-book-builder/lib/zotero.bib ##### Zotero Connector Browser Plugin - https://chromewebstore.google.com/detail/zotero-connector/ekhagklcjbdpajgpjgmbionohlpdbjgc Provides you the ability to auto add Web resources to your Zotero citation database. #### lmodern sudo apt install lmodern #### epubcheck sudo apt install epubcheck #### foliate An EPub Reader - https://johnfactotum.github.io/foliate/ sudo apt install https://github.com/johnfactotum/foliate/releases/download/2.6.4/com.github.johnfactotum.foliate_2.6.4_all.deb #### calibre An EPub Reader - https://calibre-ebook.com sudo apt install calibre ## Editing the Configuration # Editing the Book ### Configuration There are a number of other config files for each format: conf/ ├── epub-metadata.xml ├── epub_template.html ├── epub.yaml ├── frontmatter_epub.md ├── frontmatter_epub.xhtml ├── frontmatter.html ├── frontmatter.tex ├── header.tex ├── html.yaml ├── latex.yaml ├── markdown.yaml ├── metadata.yaml ├── pandoc.yaml ├── pdf.yaml ├── style.css └── style_epub.css #### Main Config Files - metadata.yaml - Set Title, etc - pandoc.yaml - Main Pandoc Config \#### Per format Configs - `pdf.yaml` - `html.yaml` - `latex.yaml` - `epub.yaml` ### FrontMatter Config There are 2 Version of the FrontMatter for PDF, and HTML bases formats that set the Title, Author, Verizon, Copyright, etc… - `frontmatter.tex` - `frontmatter.html` - `frontmatter_epub.*` - Work in Progress > There is probably a better way to do this. ## Editing the Content To edit the book open the `basic-book-builder` directory as an Obsidian Vault. - Edit the Markdown content in the `chapters` directory. ### Citations > Note: the Zotero database needs configured to export automatically to > `lib/citations.bib` To insert a Zotero Citation - Ensure the Zotero App and DB are running on you system. - Alt + I (to insert citation) - Search for and select citation reference ## Usage: Building the Book #### PDF make pdf #### HTML make html #### LaTex make latex #### Markdown make markdown #### EPub > Note: This ePub configuration still needs tuning. make epub # Example Content In *R**ν* the [Planck Length](https://en.wikipedia.org/wiki/Planck_units#Planck_length) is the universal unit for measurement of distance, and is defined approximately to be: $$\\boxed{L_P=\\sqrt{\\hbar}=5.72928\\times10^{-35}m=1 L}$$ Where 1 *L*, is 1 Planck Length of distance. ### SI Conversion Factors The following conversion factors can be used to convert observable quantities of measure from the *SI* system of units to *R**ν* to \~6 significant digits. | Conversion Factor | Symbol | Value | |------------------------------|-------------------|--------------------------------------------------------| | meters to Planck Length | *χ**P* | $1.74542\\times10^{34} \\frac{L}{m}$ | | seconds to Planck Length | *τ**p* | $5.23264\\times10^{42} \\frac{L}{s}$ | | mass to Planck Length | *G**P* | $1.62871\\times10^8 \\frac{L}{kg}$ | | energy to Planck Length | *E**P* | $1.81219\\times10^9 \\frac{L}{J}$ | | momentum to Planck Length | *P**P* | $5.43280\\times10^{-1} \\frac{L\\cdot s}{kg \\cdot m}$ | | temperature to Planck Length | *k**P* | $2.501998\\times10^{-14} \\frac{L}{K}$ | | charge to Planck Length | *C**P* | $1.89007\\times10^{18} \\frac{L}{C}$ | ### Physical Constants Applying conversion factors from the table above, we can convert SI values to Reduced Natural Units. For example, performing this analysis on the the speed of light yields a unit-less number with a value of 1: $c = 299792458 \\frac{m}{s} = 299792458 \\frac{m}{s} \\cdot 1.74542\\times10^{34} \\frac{L}{m} \\cdot \\frac{1}{5.23264\\times10^{42} \\frac{L}{s}} = 1.00000$ | Quantity | Symbol | SI | *ν* | |--------------------------------|-------------------|-----------------------------------------------------------------|-----------------------------------------| | Speed of Light | *c* | $299792458 \\frac{m}{s}$ | 1 | | Reduced Gravitational Constant | *G*0 | $8.38659\\times10^{-10} \\frac{m^3}{kg \\cdot s^2}$ | 1 | | Boltzmann’s Constant | *k* | $k=1.380649\\times10^-23 \\frac{J}{K}$ | 1 | | Permittivity of Free Space | *ϵ**o* | $8.854187817620\\times10^{-12} \\frac{C^{2}s^2}{kg \\cdot m^3}$ | 1 | | Permeability of Free Space | *μ**o* | $\\huge{\\frac{1}{\\epsilon\_{o} \\cdot c^{2}}}$ | 1 | | Reduced Planck’s Constant | ℏ | $1.054571726\\times10^-34 \\frac{kg \\cdot m^2}{s}$ | 1*L*2 | | Mass of the Electron | *m**e* | 9.10938 × 10−31*k**g* | 1.48366 × 10−22*L* | | Charge of the Electron | *e*− |  − 1.60218 × 10−19*C* |  − 3.02822 × 10−1*L* | | Unit Cycle | *Θ* | 2*π* = 6.28318... *R**a**d**i**a**n**s* | 1*τ* = 6.28318... *R**a**d**i**a**n**s* | ## Fine Structure Constant As a consistency check, we compute the *[Fine Structure Constant](https://en.wikipedia.org/wiki/Fine-structure_constant)* using Reduced Natural Units which is a unit less ratio that should be independent of our system of units. $\\huge{\\alpha=\\frac{e^2}{4\\pi\\epsilon_o\\hbar c}=\\frac{e^2}{2\\tau}=0.00729735≈\\frac{1}{137}}$ #### Dimensional Analysis The reader should be familiar with high school physics and chemistry [dimensional analysis](https://en.wikipedia.org/wiki/Dimensional_analysis). - 1 *m**e**t**e**r* (*m*) = 100 *c**e**n**t**i**m**e**t**e**r**s* (*c**m*) - 1 *k**i**l**o**m**e**t**e**r* (*k**m*) = 1000 *m**e**t**e**r**s* (*m*) - 1 *m**i**l**e* = 5280 *f**e**e**t* (*f**t* *o**r* ′) - $1\\ foot\\ (ft\\ or\\ ') = 12\\ inches\\ (in\\ or\\ ")$ - $1\\ inch\\ (") = 2.54\\ centimeters\\ (cm)$ How many kilometers are in 1 mile? $1\\ mile = 1\\ mile \\times \\frac{5280\\ ft}{mile} \\times \\frac{12\\ in}{ft} \\times \\frac{2.54\\ cm}{in}\\times \\frac{1\\ m}{100 cm} \\times \\frac{1\\ km}{1000 m} = \\frac{5280 \\times 12 \\times 2.54}{100 \\times 1000}\\ km = \\frac{160934.40}{100000}\\ km = 1.6\\ km$ Note that each unit in the denominator cancels with one if the numerator until we are left with only km. ## Newton’s Law of Gravity The force of gravity (*F**g*) between 2 masses, *m*1 and *m*2 separated by distance *r* is given by [Newton’s Law of Gravity](https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation): $F\_{g} = G \\frac{m\_{1} m\_{2}}{r^{2}}$ Where *G*, is the [Gravitational Constant](http://en.wikipedia.org/wiki/Gravitational_Constant). $G = 6.67430 \\times 10^{-11}\\ N\\frac{m^2}{kg^2}$ The strength of gravitational force follow the inverse square law distributing gravitational flux over the surface area of a sphere (4*π**r*2). #### Inverse Square Law Any source of a signal strength (*S*0) that radiates isotropically in 3-dimensional space will distribute that signal strength (*S*0) over the surface area of a sphere (*S**A* = 4*π**r*) of radius (*r*). Such that the intensity (*I*) at distance (*r*) is: $$I(r) = \\frac{S_0}{4 \\pi r^{2}}=\\frac{S_0}{2 \\tau r^{2}}$$ ![inverse square law](lib/img/Inverse_square_law.svg.png) \#### *R**ν* Reduced Gravitational Constant In this version of Newton’s Law of Gravity we introduce a new constant *G*0, the reduced gravitational constant to accommodate for the factor of 4*π* = 2*τ* which is has been integrated in the SI version of the gravitational constant. $F_g =G \\frac{m\_{1} m\_{2}}{r^{2}}= G_0 \\frac{m\_{1} m\_{2}}{4 \\pi r^{2}}=G_0 \\frac{m\_{1} m\_{2}}{2 \\tau r^{2}}$ Where: $G = \\frac{G\_{0}}{2\\tau} = 6.67384 \\times 10^{-11} \\frac{N \\cdot m^2}{kg^2}$ Analyzing the units: $$\\frac{N \\cdot m^2}{kg^2} = \\left( \\frac{\\left( kg \\cdot \\frac{m}{s^2} \\right) \\cdot m^2}{kg^2} \\right)=\\frac{m^3}{s^2 kg}$$ Converting seconds to meters with the SI speed of light as a conversion factor: $$\\frac{m^3}{s^2 kg}\\cdot\\frac{1}{c^2}=\\frac{m^3}{s^2 kg}\\cdot\\frac{s^2}{m^2}=\\frac{m}{kg}$$ Thus where space and time are measured in units of meters, the reduced gravitational constant, is: $$\\boxed{G_0=\\frac{2\\tau G}{c^2}=\\frac{2\\tau \\cdot 6.67384 \\times 10^{-11}}{299792458^2} \\frac{m}{kg} = 9.33135 \\times 10^-27 \\frac{m}{kg}}$$ > Observation This implies that not only can space an time be measure in > units of meters, but so can mass. ### Relativistic Energy Momentum Relation Einsteins [Relativistic Energy Momentum](https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation) relationship shows a Pythagorean relation between the total energy (*E*), rest mass (*m*0) and momentum (*p*) of a system. *E*2 = (*m*0⋅*c*2)2 + (*p*⋅*c*)2 Where space and time are both measure in units of meters, c=1. *E*2 = (*m*0)2 + (*p*)2 From this we can see that Energy, Momentum and Mass have equivalent units. > *While we do not really know what energy, mass and momentum are we > know that they are fundamentally “made” out of the same stuff because > they have the same units.* ##### Objects of mass at rest For an object at rest with no momentum (*p* = 0) we see Einstein’s famous equations: *E* = *m*0 ⋅ *c*2 Or, with *c* = 1, this is much simpler to understand. Energy = Mass *E* = *m*0 ##### Zero mass objects moving at the speed of light And for objects with no mass, like photos, (*m*0 = 0): *E* = *p**c* Or, with *c* = 1, this is much simpler to understand. Energy = Momentum *E* = *p* ## Planck’s Constant The [Reduced Planck constant](https://en.wikipedia.org/wiki/Planck_constant) , ħ, represents a conversion factor for relating the frequency, *ω* (in 2*π* radians per second), of a photon to the energy of that photon. This can easily be seen from the simple but profound relationship: *E* = ℏ*ω* Where: ℏ = 1.054571726 × 10−34*J* ⋅ *s* and $J \\cdot s = {kg}\\cdot\\frac{m^2}{s}$ > Reduced Planck’s Constant > $\\hbar = \\frac{h}{2\\pi} = \\frac{h}{\\tau}$ Simplifying our units by converting time and mass to units of meters: $$\\boxed{\\hbar=1.054571726 \\times 10^{−34} {kg}\\cdot\\frac{m^2}{s}\\cdot\\frac{G_0}{c}=3.282462\\times10^{-69}m^2}$$ Which suggest that the Plank constant can be interpreted as an areas for which the square root of is suspiciously close to the Plank length: $$\\boxed{\\sqrt{\\hbar}=\\sqrt{3.282462\\times10^{-69}m^2}=5.72928\\times10^{-35}m}$$ #### Planck Area The [Planck Area](https://en.wikipedia.org/wiki/Planck_units#Derived_units) is the square of the [Planck Length](https://en.wikipedia.org/wiki/Planck_units#Planck_length). $l\_{P}= \\sqrt{\\frac{\\hbar G}{c^3}}$ and $l\_{P}^{2}= \\frac{\\hbar G}{c^3}$ In *R**ν* units both *c* and *G**o* are 1. $l\_{P} = \\sqrt{\\hbar}$ and *l**P*2 = ℏ \## Bekenstein’s Bound After having recently read *Three Roads to Quantum Gravity* by Lee Smolin, I now suspect the meaning of this areas is related to the [Bekensteins Law](https://en.wikipedia.org/wiki/Bekenstein_bound) as applied to a surface areas surrounding a mass. Where the [thermodynamic entropy](https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)), *S*, is proportional to the the enclosed surface area, *A*. $S=\\frac{1}{4}\\cdot\\frac{A}{G\\hbar}$ $S=\\frac{k c^{3} A}{4 G \\hbar}$ $S \\le \\frac{2\\pi k R E}{\\hbar c} = \\frac{\\tau R k E}{\\hbar c}$ From our new values for *G*0and ℏ we can likely rewrite this: $S=\\frac{\\pi\\cdot A}{\\hbar G_0}$ With the limiting case being at the Plank scale. $S=\\frac{\\pi\\cdot \\sqrt{\\hbar}}{\\hbar G_0}$ ## Planck Length https://en.wikipedia.org/wiki/Planck_length The concept of the Planck Length comes from exploring the limits of Quantum Mechanics and General Relativity. The limits of General Relativity can be seen a the event horizon of a black hole, described by the Schwarzschild Radius. And the limits of Quantum Mechanics can be found in the Compton Wavelength for a given quanta. The [Schwarzschild Radius](https://simple.wikipedia.org/wiki/Schwarzschild_radius) is defined as the distance at which light cannot escape from the gravitational field of a mass (m): Classic Derivation. $r_S=\\frac{2G m}{c^2}$ The reduced [Compton Wavelength](https://en.wikipedia.org/wiki/Compton_wavelength) represents a lower limit on the wavelength for quanta that can interact with a quantum particle with mass (m): $\\lambda_C=\\frac{h}{m c}$ $\\bar{\\lambda_C}=\\frac{2\\pi\\hbar}{m c}=\\frac{\\tau\\hbar}{m c}$ And set the Schwarzschild Radius equal to the Compton Wavelength: *r**S* = *λ**C* $\\frac{2Gm}{c^{2}}=\\frac{h}{m c}$ $m^{2}= \\frac{hc}{2G}$ $m = \\sqrt{\\frac{hc}{2G}}$ $l_P=\\frac{2G\\sqrt{\\frac{hc}{2G}}}{c^2}$ $l_P=\\frac{2G\\sqrt{\\frac{hc}{2G}}}{c^{2}}= \\sqrt{\\frac{2Gh}{c^2}}$ With reduced Compton Wavelength $r_S=\\bar{\\lambda_C}$ $\\frac{2Gm}{c^{2}}=\\frac{\\tau\\hbar}{m c}$ $m^2=\\frac{\\tau\\ \\hbar\\ c}{2G}$ $m = \\sqrt{\\frac{\\tau\\ \\hbar\\ c}{2G}}$ $l_P=\\frac{2G\\sqrt{\\frac{\\tau\\ \\hbar\\ c}{2G}}}{c^2}$ $l_P=\\frac{2G\\sqrt{\\frac{\\tau\\ \\hbar\\ c}{2G}}}{c^{2}}=\\sqrt{\\frac{4\\ \\tau\\ G\\ \\hbar}{c^3}}$ If we reduce the units in these equation to those of mass and time measured in meters. $l_P=\\sqrt{4\\tau\\hbar G\_{o}}$ and $\\lambda_C=\\frac{\\hbar}{m}$ $m=R_s=\\lambda_C=\\frac{\\hbar}{m}$ This is known as the Planck Mass, *M**P*. $M_P=m=\\sqrt{\\hbar}$ Solving the Compton Wavelength for distance we find the classic Plank Length: $\\lambda_C=\\frac{\\hbar}{\\sqrt{\\hbar}}=\\frac{\\sqrt{\\hbar}}{\\sqrt{\\hbar}}\\cdot\\frac{\\hbar}{\\sqrt{\\hbar}}=\\sqrt{\\hbar}=L_P$ Which is in precise agreement with the value we found in above. Thus the Plank Length is: $L_P=\\sqrt{\\hbar}=5.72928\\times10^{-35}m$ When we measure distance, time, and mass in units of distance, c=1, and the Plank Time, *T**P*, is equal to Plank Length, *L**P*, which is equal to the Plank Mass, *M**P*: $$\\boxed{L_P=T_P=M_P}$$ | Conversion Factor | Symbol | Value | |------------------------------|-------------------|--------------------------------------------------------| | meters to Planck Length | *χ**P* | $1.74542\\times10^{34} \\frac{L}{m}$ | | seconds to Planck Length | *τ**p* | $5.23264\\times10^{42} \\frac{L}{s}$ | | mass to Planck Length | *G**P* | $1.62871\\times10^8 \\frac{L}{kg}$ | | energy to Planck Length | *E**P* | $1.81219\\times10^9 \\frac{L}{J}$ | | momentum to Planck Length | *P**P* | $5.43280\\times10^{-1} \\frac{L\\cdot s}{kg \\cdot m}$ | | temperature to Planck Length | *k**P* | $2.501998\\times10^{-14} \\frac{L}{K}$ | | charge to Planck Length | *C**P* | $1.89007\\times10^{18} \\frac{L}{C}$ | Applying conversion factors from the table above, we can convert SI values to Reduced Natural Units. $c=\\frac{1}{\\sqrt{\\epsilon_o \\mu_o}}$ | Quantity | Symbol | SI | *ν* | |----------------------------|-------------------|-----------------------------------------------------------------|---------------------------------| | Speed of Light | *c* | $299792458 \\frac{m}{s}$ | 1 | | Gravitational Constant | *G*0 | $8.38659\\times10^{-10} \\frac{m^3}{kg \\cdot s^2}$ | 1 | | Boltzmann’s Constant | *k* | $k=1.380649\\times10^-23 \\frac{J}{K}$ | 1 | | Permittivity of Free Space | *ϵ**o* | $8.854187817620\\times10^{-12} \\frac{C^{2}s^2}{kg \\cdot m^3}$ | 1 | | Permeability of Free Space | *μ**o* | $\\huge{\\frac{1}{\\epsilon\_{o} \\cdot c^{2}}}$ | 1 | | Planck’s Constant | ℏ | $1.054571726\\times10^-34 \\frac{kg \\cdot m^2}{s}$ | 1*L*2 | | Mass of the Electron | *m**e* | 9.10938 × 10−31*k**g* | 1.48366 × 10−22*L* | | Charge of the Electron | *e*− |  − 1.60218 × 10−19*C* |  − 3.02822 × 10−1*L* | ## Fine Structure Constant https://en.wikipedia.org/wiki/Fine-structure_constant As a consistency check, we compute the *Fine Structure Constant* using Reduced Natural Units which is a unit less ratio that should be independent of our system of units. $\\huge{\\alpha=\\frac{e^2}{4\\pi\\epsilon_o\\hbar c}=\\frac{e^2}{4\\pi}=0.00729735≈\\frac{1}{137}}$ This check confirms that our system of Reduced Natural Units has internally consistent values for *c*, *ϵ**o*, ℏ and *e*−. And also *G**o* which was used to computer prior values is also consistent. ## Sage Code Unit Analysis computations have been performed with [Sage Math](https://www.sagemath.org/). ``` bash # Define constance one = 1.n(digits=6) pi = pi.n(digits=6) tau = 2 * pi t = tau # Define the units meters = var('m') m = one*meters seconds = var('s') s = seconds kilograms = var('kg') kg = kilograms newtons = kg * m / s^2 N = newtons joules = N * m J = joules print("pi =", pi) print("tau =", t) # Speed of light in meters/second speed_of_light = 299792458 * meters/seconds sol = speed_of_light c = sol print("si c =", c) rnu_c = c / c print("R\u03BD c =", rnu_c) # Gravitational Constant gravitational_constant = 6.67384e-11 * N*(m^2/kg^2) G = gravitational_constant print("si G =", G) rnu_G = 4*pi*G/c^2 Go = rnu_G print("R\u03BD Go =", Go) # Planck's Constant reduced_plancks_constant = 1.054571726e-34 * J*s h_bar = reduced_plancks_constant print("si \u210F =", h_bar) rnu_h_bar = h_bar * Go / c print("R\u03BD "u"\u210F =", rnu_h_bar) # Planck Length rnu_h_bar_str = str(rnu_h_bar) numerical_part_str = rnu_h_bar_str.split('*')[0] numerical_part_str = numerical_part_str.strip('()') numerical_part = float(numerical_part_str) rnu_sqrt_h_bar = numerical_part^(1/2) # ^ Sage cannot process sqrt on units... Lame. lP = rnu_sqrt_h_bar * m print("R\u03BD \u221A\u210F =", lP) ``` #### Output pi = 3.14159 tau = 6.28319 si c = 299792458*m/s Rν c = 1 si G = (6.67384e-11)*m^3/(kg*s^2) Rν Go = (9.33135e-27)*m/kg si ℏ = (1.05457e-34)*kg*m^2/s Rν ℏ = (3.28246e-69)*m^2 Rν √ℏ = (5.72928e-35)*m si lP = (1.61620e-35)*sqrt(m^2) Rν lP = (2.77455e-47)*sqrt(m^3/kg) # Terminology # Citations
“John Haverlack ACEP.” n.d. https://www.uaf.edu/acep/about/our-team/john-haverlack.php. Accessed September 30, 2025.