Appendix B. Variable List
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# Appendix B. Variable List

## Basic Constants

Table B.1. Variables: Basic Constants

Title | Names | Value
--- | --- | ---
Apery's Constant | apery | zeta(3)
Archimedes' Constant (pi) | π / pi | 3.1415926535897932385 (variable precision)
Base of Natural Logarithms (e) | e | 2.7182818284590452354 (variable precision)
Catalan's Constant | catalan | 0.91596559417721901505 (variable precision)
Euler's Constant | γ / euler | 0.57721566490153286061 (variable precision)
Golden Ratio | golden / φ / phi | (1 + √(5)) ∕ 2
Omega Constant | omega | lambertw(1)
Plastic Number | plastic / ρ / rho | cbrt((9 + √(69)) ∕ 18) + cbrt((9 − √(69)) ∕ 18)
Pythagoras' Constant (sqrt 2) | pythagoras | √(2)
Tau (2pi) | τ / tau | 2π

## Date & Time

Table B.2. Variables: Date & Time

Title | Names | Value
--- | --- | ---
Now (date and time) | now | current date and time
Today | today | current date
Tomorrow | tomorrow | tomorrow's date
Yesterday | yesterday | yesterday's date

## Large Numbers

Table B.3. Variables: Large Numbers

Title | Names | Value
--- | --- | ---
Billion | billion | 109
Centillion | centillion | 10303
Decillion | decillion | 1033
Duodecillion | duodecillion | 1039
Googol | googol | 10100
Googolplex | googolplex | 10^(10^100)
Hundred | hundred | 100
Million | million | 106
Nonillion | nonillion | 1030
Novemdecillion | novemdecillion | 1060
Octillion | octillion | 1027
Octodecillion | octodecillion | 1057
Quadrillion | quadrillion | 1015
Quattuordecillion | quattuordecillion | 1045
Quindecillion | quindecillion | 1048
Quintillion | quintillion | 1018
Septendecillion | septendecillion | 1054
Septillion | septillion | 1024
Sexdecillion | sexdecillion | 1051
Sextillion | sextillion | 1021
Thousand | thousand | 1000
Tredecillion | tredecillion | 1042
Trillion | trillion | 1012
Undecillion | undecillion | 1036
Vigintillion | vigintillion | 1063

## Matrices & Vectors

Table B.4. Variables: Matrices & Vectors

Title | Names | Value
--- | --- | ---
Pauli Matrix 0 | Pauli0 / σ_0 | [1 0; 0 1]
Pauli Matrix 1 | Pauli1 / σ_1 | [0 1; 1 0]
Pauli Matrix 2 | Pauli2 / σ_2 | [0 −i; i 0]
Pauli Matrix 3 | Pauli3 / σ_3 | [1 0; 0 −1]

## Physical Constants

### Atomic and Nuclear Constants

Table B.5. Variables: Atomic and Nuclear Constants

Title | Names | Value
--- | --- | ---
Bohr Radius | BohrRadius / a_0 | ℏ ∕ (c × me × α)
Classical Electron Radius | ClassicalElectronRadius / r_e | qe2 ∕ (4c2 × me × ε0 × π)
Fermi Coupling Constant | FermiCoupling | 0.0000116637870(60) GeV−2
Fine-Structure Constant | FineStructure / α / alpha | 0.0072973525643(12)
Hartree Energy (constant) | HartreeConstant / Ha_constant | 2c × R∞ × ℎ
Quantum of Circulation | QuantumCirculation | ℎ ∕ (2 me)
Quantum of Circulation times 2 | QuantumCirculation2 | 2 QuantumCirculation
Rydberg Constant | rydberg / R_∞ | 1.0973731568157(12) × 107 m−1
Thomson cross section | ThomsonCrossSection / σ_t / sigma_t | (re2 (8π)) ∕ 3
W to Z Mass Ratio | w_z_ratio | 0.88145(13)
Weak Mixing Angle (sin²θw) | WeakMixingAngle / sin2θ_W / weinberg / sin2_theta_W | 1 − w_z_ratio2

### Compton Wavelength

Table B.6. Variables: Compton Wavelength

Title | Names | Value
--- | --- | ---
Compton Wavelength (electron) | ComptonWavelength / λ_C / lambda_C | ℎ ∕ (c × me)
Muon Compton Wavelength | MuonComptonWavelength / λ_Cμ | ℎ ∕ (c × mμ)
Neutron Compton Wavelength | NeutronComptonWavelength / λ_Cn | ℎ ∕ (c × mn)
Proton Compton Wavelength | ProtonComptonWavelength / λ_Cp | ℎ ∕ (c × mp)
Reduced Compton Wavelength (electron) | ComptonWavelength2pi / ƛ_C | ℏ ∕ (c × me)
Reduced Muon Compton Wavelength | MuonComptonWavelength2pi / ƛ_Cμ | ℏ ∕ (c × mμ)
Reduced Neutron Compton Wavelength | NeutronComptonWavelength2pi / ƛ_Cn | ℏ ∕ (c × mn)
Reduced Proton Compton Wavelength | ProtonComptonWavelength2pi / ƛ_Cp | ℏ ∕ (c × mp)
Reduced Tau Compton Wavelength | TauComptonWavelength2pi / ƛ_Cτ | ℏ ∕ (c × mτ)
Tau Compton Wavelength | TauComptonWavelength / λ_Cτ | ℎ ∕ (c × mτ)

### Conversion factors for energy equivalents

Table B.7. Variables: Conversion factors for energy equivalents

Title | Names | Value
--- | --- | ---
Hertz - Inverse Meter Relationship | Hz_to_m | 1 ∕ c
Hertz - Joule Relationship | Hz_to_J | ℎ
Hertz - Kelvin Relationship | Hz_to_K | ℎ ∕ kB
Hertz - Kilogram Relationship | Hz_to_kg | ℎ ∕ c2
Inverse Meter - Hertz Relationship | m_to_Hz | c
Inverse Meter - Joule Relationship | m_to_J | cℎ
Inverse Meter - Kelvin Relationship | m_to_K | (cℎ) ∕ kB
Inverse Meter - Kilogram Relationship | m_to_kg | ℎ ∕ c
Joule - Hertz Relationship | J_to_Hz | 1 ∕ ℎ
Joule - Inverse Meter Relationship | J_to_m | 1 ∕ (cℎ)
Joule - Kelvin Relationship | J_to_K | 1 ∕ kB
Joule - Kilogram Relationship | J_to_kg | 1 ∕ c2
Kelvin - Hertz Relationship | K_to_Hz | kB ∕ ℎ
Kelvin - Inverse Meter Relationship | K_to_m | kB ∕ (cℎ)
Kelvin - Joule Relationship | K_to_J | kB
Kelvin - Kilogram Relationship | K_to_kg | kB ∕ c2
Kilogram - Hertz Relationship | kg_to_Hz | c2 ∕ ℎ
Kilogram - Inverse Meter Relationship | kg_to_m | c ∕ ℎ
Kilogram - Joule Relationship | kg_to_J | c2
Kilogram - Kelvin Relationship | kg_to_K | c2 ∕ kB

### Electromagnetic Constants

Table B.8. Variables: Electromagnetic Constants

Title | Names | Value
--- | --- | ---
Bohr Magneton | BohrMagneton / μ_B / µ_B / mu_B | (qe × ℎ) ∕ (4 me × π)
Conductance Quantum | ConductanceQuantum / G_0 | (2 qe2) ∕ ℎ
Coulomb's Constant (Electric Force Constant) | CoulombsConstant / k_e | (c2 × μ0) ∕ (4π)
Elementary Charge | ElementaryCharge / q_e / e_charge | 160.2176634 zC
Inverse of Conductance Quantum | InverseConductanceQuantum | ℎ ∕ (2 qe2)
Josephson Constant | josephson / K_J | (2 qe) ∕ ℎ
Josephson Constant (conventional value) | JosephsonConventional / K_J90 | 483.5979 THz ∕ V
Magnetic Flux Quantum | MagneticFluxQuantum / Φ_0 / phi_0 | ℎ ∕ (2 qe)
Nuclear Magneton | NuclearMagneton / μ_N / µ_N / mu_N | (qe × ℏ) ∕ (2 mp)
von Klitzing Constant | klitzing / R_K | ℎ ∕ qe2
von Klitzing Constant (conventional value) | KlitzingConventional / R_K90 | 25.812807 kΩ

### Particle Mass in MeV*c^(-2)

Table B.9. Variables: Particle Mass in MeV*c^(-2)

Title | Names | Value
--- | --- | ---
Alpha Particle Mass (in MeV/c^2) | AlphaParticleEV | nounit((10−6c2 × mα) ∕ eV) × MeV ∕ c2
Bottom Quark Mass (in MeV/c^2) | quark_b | 4180(40) MeV ∕ c2
Charm Quark Mass (in MeV/c^2) | quark_c | 1270(20) MeV ∕ c2
Down Quark Mass (in MeV/c^2) | quark_d | 4.70(50) MeV ∕ c2
Electron Mass (in MeV/c^2) | ElectronEV | nounit((10−6c2 × me) ∕ eV) × MeV ∕ c2
Higgs Boson Mass (in MeV/c^2) | HiggsBoson | 125110±110 MeV ∕ c2
Muon Mass (in MeV/c^2) | MuonEV | nounit((10−6c2 × mμ) ∕ eV) × MeV ∕ c2
Neutron Mass (in MeV/c^2) | NeutronEV | nounit((10−6c2 × mn) ∕ eV) × MeV ∕ c2
Proton Mass (in MeV/c^2) | ProtonEV | nounit((10−6c2 × mp) ∕ eV) × MeV ∕ c2
Strange Quark Mass (in MeV/c^2) | quark_s | 95.0(90) MeV ∕ c2
Tau Mass (in MeV/c^2) | TauEV | nounit((10−6c2 × mτ) ∕ eV) × MeV ∕ c2
Top Quark Mass (in MeV/c^2) | quark_t | 172760±300 MeV ∕ c2
Up Quark Mass (in MeV/c^2) | quark_u | 2.20(50) MeV ∕ c2
W Boson Mass (in MeV/c^2) | w_boson | 80379(12) MeV ∕ c2
Z Boson Mass (in MeV/c^2) | z_boson | 91187.6(21) MeV ∕ c2

### Particle Mass in kg

Table B.10. Variables: Particle Mass in kg

Title | Names | Value
--- | --- | ---
Alpha Particle Mass | AlphaParticleMass / m_α / m_alpha | mu × nounit(AlphaParticleu)
Deuteron Mass | DeuteronMass | mu × nounit(deuteronu)
Electron Mass | ElectronMass / m_e | (2 R∞ × ℎ) ∕ (cα2)
Helion Mass | HelionMass / m_h | mu × nounit(helionu)
Muon Mass | MuonMass / m_μ / m_µ / m_mu | mu × nounit(muonu)
Neutron Mass | NeutronMass / m_n | mu × nounit(neutronu)
Proton Mass | ProtonMass / m_p | mu × nounit(protonu)
Tau Mass | TauMass / m_τ / m_tau | mu × nounit(tauu)
Triton Mass | TritonMass | mu × nounit(tritonu)

### Particle Mass in u

Table B.11. Variables: Particle Mass in u

Title | Names | Value
--- | --- | ---
Alpha Particle Mass (in u) | alpha_particle_u | 4.001506179129(62) u
Deuteron Mass (in u) | deuteron_u | 2.013553212544(15) u
Electron Mass (in u) | electron_u | 0.0005485799090441(97) u
Helion Mass (in u) | helion_u | 3.014932246932(74) u
Muon Mass (in u) | muon_u | 0.1134289257(25) u
Neutron Mass (in u) | neutron_u | 1.00866491606(40) u
Proton Mass (in u) | proton_u | 1.0072764665789(83) u
Tau Mass (in u) | tau_u | 1.90754(13) u
Triton Mass (in u) | triton_u | 3.01550071597(10) u

### Physico-Chemical Constants

Table B.12. Variables: Physico-Chemical Constants

Title | Names | Value
--- | --- | ---
Atomic Mass Constant | AtomicMassConstant / m_u | (2 R∞ × ℎ) ∕ (cα2 × nounit(electronu))
Avogadro Constant | avogadro / N_A | 6.02214076 × 1023 mol−1
Boltzmann Constant | boltzmann / k_B | 13.80649 yJ ∕ K
Electronvolt (constant) | ElectronvoltConstant / eV_constant | qe J ∕ C
Faraday Constant | faraday / ℱ | NA × qe
First Radiation Constant | FirstRadiation / c_1 | 2c2πℎ
First Radiation Constant for Spectral Radiance | FirstRadiationSr / c_1L | c1 ∕ π
Gas Constant | GasConstant / IdealGas | kB × NA
Lattice Parameter of Silicon | LatticeParameterSi | 543.1020511(89) pm
Lattice Spacing of Ideal Silicon (220) | LatticeSpacingSi220 / d_220 | LatticeParameterSi ∕ √(8)
Loschmidt Constant (273.15 K, 100 kPa) | Loschmidt100 / n_0100 | (2000 ∕ (5463 kB)) kPa ∕ K
Loschmidt Constant (273.15 K, 101.325 kPa) | LoschmidtAtm / loschmidt / n_0 | (4053 ∕ (10926 kB)) kPa ∕ K
Molar Mass Constant | MolarMass / M_u | (2 NA × R∞ × ℎ) ∕ (cα2 × nounit(electronu))
Molar Planck Constant | MolarPlanck | NA × ℎ
Molar Volume of Ideal Gas (273.15 K, 100 kPa) | IdealGasMolar100 / IdealGasMolar / V_m | (5463 ∕ (2 × 106)) × GasConstant K ∕ Pa
Molar Volume of Ideal Gas (273.15 K, 101.325 kPa) | IdealGasMolarAtm / ideal_gas_molar_101 / V_m101 | (5463 ∕ 2026500) × GasConstant K ∕ Pa
Sackur-Tetrode constant (1 K, 100 kPa) | SackurTetrode100 / SackurTetrode | −1.15170753496(47)
Sackur-Tetrode constant (1 K, 101.325 kPa) | SackurTetrodeAtm / sackur_tetrode_101 | −1.16487052149(47)
Second Radiation Constant | SecondRadiation / c_2 | (cℎ) ∕ kB
Stefan-Boltzmann Constant | stefan / σ / sigma | (kB4 (2π5)) ∕ (15c2ℎ3)
Wien frequency displacement law constant | WienFrequency | (kB(3 + lambertw(−3 ∕ e3))) ∕ ℎ
Wien wavelength displacement law constant | WienDisplacement / b_energy | (cℎ) ∕ (kB(5 + lambertw(−5 ∕ e5)))

### Universal Constants

Table B.13. Variables: Universal Constants

Title | Names | Value
--- | --- | ---
Characteristic Impedance of Vacuum | CharacteristicImpedance / Z_0 | (2αℎ) ∕ qe2
Electric Constant (Permittivity of Free Space) | ElectricConstant / ε_0 / VacuumPermittivity / epsilon_0 | qe2 ∕ (2cαℎ)
Magnetic Constant (Permeability of Free Space) | MagneticConstant / μ_0 / µ_0 / VacuumPermeability / mu_0 | (2αℎ) ∕ (c × qe2)
Newtonian Constant of Gravitation | NewtonianConstant / G | 6.67430(15) × 10−11 m3 ∕ (s2·kg)
Planck Constant | planck / ℎ | 6.62607015 × 10−34 J·s
Reduced Planck Constant (Dirac constant) | planck2pi / dirac / ℏ / hbar | ℎ ∕ (2π)
Speed of Light in Vacuum | c / SpeedOfLight | 299792.458 km ∕ s
Standard Acceleration due to Gravity | StandardGravity / g_0 / ɡ_0 / ɡ_n | 9.80665 m ∕ s2

## Small Numbers

Table B.14. Variables: Small Numbers

Title | Names | Value
--- | --- | ---
Per Mille | permille / ‰ | 0.001
Per Myriad | permyriad / ‱ | 0.0001
Percent | % / percent | 0.01

## Special Numbers

Table B.15. Variables: Special Numbers

Title | Names | Value
--- | --- | ---
False | false / no | 0
Imaginary i (sqrt -1) | i | i
Negative Infinity | MinusInfinity | −∞
Positive Infinity | ∞ / PlusInfinity / infinity | +∞
True | true / yes | 1
Undefined | undefined | undefined

## Temporary

Table B.16. Variables: Temporary

Title | Names | Value
--- | --- | ---
Answer 2 | ans2 | a previous result
Answer 3 | ans3 | a previous result
Answer 4 | ans4 | a previous result
Answer 5 | ans5 | a previous result
Last Answer | ans / answer / ans1 | a previous result
Memory | MR / MRC | result of memory operations (MC, MS, M+, M−)

## Traditional Numbers

Table B.17. Variables: Traditional Numbers

Title | Names | Value
--- | --- | ---
Baker's Dozen | BakersDozen | 13
Dozen | dozen / dz / doz | 12
Great Gross | GreatGross | 1728
Gross | gross / gro | 144
Long Hundred | LongHundred / GreatHundred / twelfty | 120
Long Thousand | LongThousand | 1200
Score | score | 20

## Unknowns

Table B.18. Variables: Unknowns

Title | Names | Value
--- | --- | ---
n (integer) | n | integer
x | x | default assumptions
y | y | default assumptions
z | z | default assumptions

## Utilities

Table B.19. Variables: Utilities

Title | Names | Value
--- | --- | ---
Precision | precision | current precision
System Uptime | uptime | current computer uptime

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