A compendium of quantities that happen to have nice numbers, for no reason
Fine structure constant
Defined as \alpha := e^2/ (4\pi \varepsilon_0 \hbar c ) .\alpha \approx \frac{1}{137}.
Intriging, since it seemed for a time that it would be precisely the inverse of an integer number.
Actually,\alpha \approx \frac{1}{137.035999084}
pH of water
The pH scale is logarithmic and inversely indicates the activity of hydrogen ions in the solution:
pH = −\log ( a_{H^+} ) \approx − \log ( [ H^+ ] ) ,
where [H+] is the equilibrium molar concentration (mol/L) of H+ in the solution. At 25 °C, it so turns out that [H+] ≈ 10^(-7) mol / L.
Viscosity of water
It so turns out that, at 20ºC, the dynamic shear viscosity coefficient is \mu \approx 10^{-3} Pa·s. Therefore, the kinematic viscosity coefficient is \nu \approx 10^{-6} m^2/s.
Far away place in general relativity
For a minimal distance R, a uniform acceleration a is given by a = c^2/R . This would be the normal acceleration needed to keep a particle traveling at the speed of light moving on a circle of radius R. If we want a close to g, the gravitational acceleration at the Earth, we would need to go very close to 1 light year. See Susskinds’ lecture on general relativity
| Magnitude | Value |
| Fine structure constant | \alpha \approx \frac{1}{137} |
| pH of water | [H+] \approx 10^{-7} mol / L |
| Viscosity of water | \nu \approx 10^{-6} m²/s. |
| Far away place | a = c^2/R \approx 1 lyr |
