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The term fundamental physical constant is sometimes used to refer to some universal dimensionless constants. Perhaps the best-known example is the fine-structure constant, α, which has an approximate value of 1 / 137.036 . [2]
This is a list of well-known dimensionless quantities illustrating their variety of forms and applications. The tables also include pure numbers, dimensionless ratios, or dimensionless physical constants; these topics are discussed in the article.
In differential geometry, the use of dimensionless parameters is evident in geometric relationships and transformations. Physics relies on dimensionless numbers like the Reynolds number in fluid dynamics, [6] the fine-structure constant in quantum mechanics, [7] and the Lorentz factor in relativity. [8]
These include the Boltzmann constant, which gives the correspondence of the dimension temperature to the dimension of energy per degree of freedom, and the Avogadro constant, which gives the correspondence of the dimension of amount of substance with the dimension of count of entities (the latter formally regarded in the SI as being dimensionless).
It is a dimensionless quantity (dimensionless physical constant), independent of the system of units used, which is related to the strength of the coupling of an elementary charge e with the electromagnetic field, by the formula 4πε 0 ħcα = e 2.
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The fine-structure constant α is the best known dimensionless fundamental physical constant. It is the value of the elementary charge squared expressed in Planck units . This value has become a standard example when discussing the derivability or non-derivability of physical constants.
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]