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 | 3.1415927 (variable precision)
Base of Natural Logarithms (e) | e | 2.7182818 (variable precision)
Catalan's Constant | catalan | 0.91596559 (variable precision)
Euler's Constant | γ / euler | 0.57721566 (variable precision)
Golden Ratio | golden / φ / phi | (1+sqrt(5))/2
Omega Constant | omega | lambertw(1)
Plastic Number | plastic / ρ / rho | cbrt((9+sqrt(69))/18)+cbrt((9−sqrt(69))/18)
Pythagoras' Constant (sqrt 2) | pythagoras | sqrt(2)
Tau (2pi) | τ / tau | 2×pi

## 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 | 1E9
Centillion | centillion | 1E303
Decillion | decillion | 1E33
Duodecillion | duodecillion | 1E39
Googol | googol | 10^100
Googolplex | googolplex | 10^(10^100)
Hundred | hundred | 1E2
Million | million | 1E6
Nonillion | nonillion | 1E30
Novemdecillion | novemdecillion | 1E60
Octillion | octillion | 1E27
Octodecillion | octodecillion | 1E57
Quadrillion | quadrillion | 1E15
Quattuordecillion | quattuordecillion | 1E45
Quindecillion | quindecillion | 1E48
Quintillion | quintillion | 1E18
Septendecillion | septendecillion | 1E54
Septillion | septillion | 1E24
Sexdecillion | sexdecillion | 1E51
Sextillion | sextillion | 1E21
Thousand | thousand | 1E3
Tredecillion | tredecillion | 1E42
Trillion | trillion | 1E12
Undecillion | undecillion | 1E36
Vigintillion | vigintillion | 1E63

## Matrices & Vectors

Table B.4. Variables: Matrices & Vectors

Title | Names | Value
--- | --- | ---
Pauli Matrix 0 | pauli_0 / σ_0 | [1 0; 0 1]
Pauli Matrix 1 | pauli_1 / σ_1 | [0 1; 1 0]
Pauli Matrix 2 | pauli_2 / σ_2 | [0 −i; i 0]
Pauli Matrix 3 | pauli_3 / 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 | bohr_radius / a_0 | planck2pi/(fine_structure×electron_mass×c)
Classical Electron Radius | classical_electron_radius / r_e | elementary_charge2/(4×pi×electric_constant×electron_mass×c2)
Fermi Coupling Constant | fermi_coupling | 1.1663787E−5±6E−12 GeV^(-2)
Fine-Structure Constant | fine_structure / α / alpha | 7.2973525693E−3±1.1E−12
Hartree Energy (constant) | hartree_constant / Ha_constant | 2×rydberg×planck×c
Quantum of Circulation | quantum_circulation | planck/(2×electron_mass)
Quantum of Circulation times 2 | quantum_circulation_2 | quantum_circulation×2
Rydberg Constant | rydberg / R_∞ | 10973731.568160±0.000021 m^(-1)
Thomson cross section | thomson_cross_section / σ_t / sigma_t | (8×pi/3)×classical_electron_radius2
W to Z Mass Ratio | w_z_ratio | 0.88153±0.00017
Weak Mixing Angle (Weinberg Angle) | weinberg / weak_mixing_angle / θ_W / theta_W | 0.22290±0.00030

### Conversion factors for energy equivalents

Table B.6. Variables: Conversion factors for energy equivalents

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

### Electromagnetic Constants

Table B.7. Variables: Electromagnetic Constants

Title | Names | Value
--- | --- | ---
Bohr Magneton | bohr_magneton / μ_B / µ_0 / mu_B | (elementary_charge×planck)/(4×electron_mass×pi)
Conductance Quantum | conductance_quantum / G_0 | 2×elementary_charge2/planck
Coulomb's Constant (Electric Force Constant) | coulombs_constant / k_e | (magnetic_constant×c2)/(4pi)
Elementary Charge | elementary_charge / q_e / e_charge | 1.602176634E−19 C
Inverse of Conductance Quantum | inverse_conductance_quantum | planck/(2×elementary_charge2)
Josephson Constant | josephson / K_J | 2×elementary_charge/planck
Josephson Constant (conventional value) | josephson_conventional / K_J90 | 4.835979E14 Hz*V^(-1)
Magnetic Flux Quantum | magnetic_flux_quantum / Φ_0 / phi_0 | planck/(2×elementary_charge)
Nuclear Magneton | nuclear_magneton / μ_N / µ_N / mu_N | elementary_charge×planck2pi/(2×proton_mass)
von Klitzing Constant | klitzing / R_K | planck/elementary_charge2
von Klitzing Constant (conventional value) | klitzing_conventional / R_K90 | 25812.807 ohm

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

Table B.8. Variables: Particle Mass in MeV*c^(-2)

Title | Names | Value
--- | --- | ---
Alpha Particle Mass (in MeV/c^2) | alpha_particle_eV | alpha_particle_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Bottom Quark Mass (in MeV/c^2) | quark_b | 4180±40 MeV*c_unit^(-2)
Charm Quark Mass (in MeV/c^2) | quark_c | 1275±35 MeV*c_unit^(-2)
Down Quark Mass (in MeV/c^2) | quark_d | 4.7±0.5 MeV*c_unit^(-2)
Electron Mass (in MeV/c^2) | electron_eV | electron_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Higgs Boson Mass (in MeV/c^2) | higgs_boson | 125180±160 MeV*c_unit^(-2)
Muon Mass (in MeV/c^2) | muon_eV | muon_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Neutron Mass (in MeV/c^2) | neutron_eV | neutron_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Proton Mass (in MeV/c^2) | proton_eV | proton_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Strange Quark Mass (in MeV/c^2) | quark_s | 95±9 MeV*c_unit^(-2)
Tau Mass (in MeV/c^2) | tau_eV | tau_mass×c2/electronvolt_constant×1E−6 MeV*c_unit^(-2)
Top Quark Mass (in MeV/c^2) | quark_t | 173210±510 MeV*c_unit^(-2)
Up Quark Mass (in MeV/c^2) | quark_u | 2.2±0.5 MeV*c_unit^(-2)
W Boson Mass (in MeV/c^2) | w_boson | 80379±12 MeV*c_unit^(-2)
Z Boson Mass (in MeV/c^2) | z_boson | 91187.6±2.1 MeV*c_unit^(-2)

### Particle Mass in kg

Table B.9. Variables: Particle Mass in kg

Title | Names | Value
--- | --- | ---
Alpha Particle Mass | alpha_particle_mass / m_α / m_alpha | nounit(alpha_particle_u)×atomic_mass_constant
Deuteron Mass | deuteron_mass | nounit(deuteron_u)×atomic_mass_constant
Electron Mass | electron_mass / m_e | (2×rydberg×planck)/(c×fine_structure2)
Helion Mass | helion_mass / m_h | nounit(helion_u)×atomic_mass_constant
Muon Mass | muon_mass / m_μ / m_µ / m_mu | nounit(muon_u)×atomic_mass_constant
Neutron Mass | neutron_mass / m_n | nounit(neutron_u)×atomic_mass_constant
Proton Mass | proton_mass / m_p | nounit(proton_u)×atomic_mass_constant
Tau Mass | tau_mass / m_τ / m_tau | nounit(tau_u)×atomic_mass_constant
Triton Mass | triton_mass | nounit(triton_u)×atomic_mass_constant

### Particle Mass in u

Table B.10. Variables: Particle Mass in u

Title | Names | Value
--- | --- | ---
Alpha Particle Mass (in u) | alpha_particle_u | 4.001506179127±6.3E−11 u
Deuteron Mass (in u) | deuteron_u | 2.013553212745±4.0E−11 u
Electron Mass (in u) | electron_u | 5.48579909065E−4±1.6E−14 u
Helion Mass (in u) | helion_u | 3.014932247175±9.7E−11 u
Muon Mass (in u) | muon_u | 0.1134289259±2.5E−9 u
Neutron Mass (in u) | neutron_u | 1.00866491595±4.9E−10 u
Proton Mass (in u) | proton_u | 1.007276466621±5.3E−11 u
Tau Mass (in u) | tau_u | 1.90754±1.3E−4 u
Triton Mass (in u) | triton_u | 3.01550071621±1.2E−10 u

### Physico-Chemical Constants

Table B.11. Variables: Physico-Chemical Constants

Title | Names | Value
--- | --- | ---
Atomic Mass Constant | atomic_mass_constant / m_u | (2×rydberg×planck)/(c×fine_structure2×nounit(electron_u))
Avogadro Constant | avogadro / N_A | 6.02214076E23 mol^(-1)
Boltzmann Constant | boltzmann / k_B | 1.380649E−23 J*K^(-1)
Compton Wavelength | compton_wavelength / λ_C / lambda_C | planck/(electron_mass×c)
Electronvolt (constant) | electronvolt_constant / eV_constant | elementary_charge/C×J
Faraday Constant | faraday / ℱ | avogadro×elementary_charge
First Radiation Constant | first_radiation / c_1 | 2×pi×planck×c2
First Radiation Constant for Spectral Radiance | first_radiation_sr / c_1L | first_radiation/pi
Gas Constant | gas_constant / ideal_gas | boltzmann×avogadro
Lattice Parameter of Silicon | lattice_parameter_Si | 543.1020511E−12±8.9E−18 m
Lattice Spacing of Ideal Silicon (220) | lattice_spacing_Si220 / d_220 | lattice_parameter_Si/sqrt(8)
Loschmidt Constant (273.15 K, 100 kPa) | loschmidt_100 | (100000×Pa)/(boltzmann×273.15×K)
Loschmidt Constant (273.15 K, 101.325 kPa) | loschmidt / n_0 | (101325×Pa)/(boltzmann×273.15×K)
Molar Mass Constant | molar_mass / M_u | (2×planck×rydberg×avogadro)/(c×fine_structure2×nounit(electron_u))
Molar Planck Constant | molar_planck | avogadro×planck
Molar Volume of Ideal Gas (273.15 K, 100 kPa) | ideal_gas_molar / V_m | (gas_constant×273.15×K)/(100000×Pa)
Molar Volume of Ideal Gas (273.15 K, 101.325 kPa) | ideal_gas_molar_101 / V_m101 | (gas_constant×273.15×K)/(101325×Pa)
Reduced Compton Wavelength | compton_wavelength_2pi | compton_wavelength/(2×pi)
Sackur-Tetrode constant (1 K, 100 kPa) | sackur_tetrode | −1.15170753706±4.5E−10
Sackur-Tetrode constant (1 K, 101.325 kPa) | sackur_tetrode_101 | −1.16487052358±4.5E−10
Second Radiation Constant | second_radiation / c_2 | planck×c/boltzmann
Stefan-Boltzmann Constant | stefan / σ / sigma | (2pi5×boltzmann4)/(15×planck3×c2)
Wien frequency displacement law constant | wien_frequency | (k_B/planck)×(lambertw(−3/e3)+3)
Wien wavelength displacement law constant | wien_displacement / b_energy | (planck×c/k_B)/(lambertw(−5/e5)+5)

### Universal Constants

Table B.12. Variables: Universal Constants

Title | Names | Value
--- | --- | ---
Characteristic Impedance of Vacuum | characteristic_impedance / Z_0 | (2×planck×fine_structure)/(elementary_charge2)
Electric Constant (Permittivity of Free Space) | electric_constant / ε_0 / vacuum_permittivity / epsilon_0 | elementary_charge2/(2×planck×fine_structure×c)
Magnetic Constant (Permeability of Free Space) | magnetic_constant / μ_0 / µ_0 / vacuum_permeability / mu_0 | (2×planck×fine_structure)/(c×elementary_charge2)
Newtonian Constant of Gravitation | newtonian_constant / G | 6.67430E−11±1.5E−15 m^3*kg^(-1)*s^(-2)
Planck Constant | planck / ℎ | 6.62607015E−34 J*s
Reduced Planck Constant (Dirac constant) | planck2pi / dirac / ℏ / hbar | planck/(2×pi)
Speed of Light in Vacuum | c / speed_of_light | 299792458 m*s^(-1)
Standard Acceleration due to Gravity | standard_gravity / g_0 / ɡ_0 / ɡ_n | 9.80665 m s^(-2)

## Small Numbers

Table B.13. Variables: Small Numbers

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

## Special Numbers

Table B.14. Variables: Special Numbers

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

## Temporary

Table B.15. 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.16. Variables: Traditional Numbers

Title | Names | Value
--- | --- | ---
Baker's Dozen | bakers_dozen | 13
Dozen | dozen / dz / doz | 12
Great Gross | great_gross | 1728
Gross | gross / gro | 144
Long Hundred | long_hundred / great_hundred / twelfty | 120
Long Thousand | long_thousand | 1200
Score | score | 20

## Unknowns

Table B.17. Variables: Unknowns

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

## Utilities

Table B.18. Variables: Utilities

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

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