Dimensionless quantities are quantities that do not have units associated with them. They often arise in various fields of science, engineering, and mathematics. Here's a list of some common dimensionless quantities:

1. Pure Numbers:

   • Any counting number (1, 2, 3, ...), including integers and fractions.
   • Mathematical constants like π (pi), e (Euler's number), and φ (phi).

2. Ratios and Fractions:

   • Ratios of similar quantities such as aspect ratios, concentration ratios, and fractions of any kind.

3. Trigonometric Functions:

   • Sine, cosine, tangent, secant, cosecant, and cotangent functions, and their inverses.

4. Logarithmic Functions:

   • Logarithms of any base. For instance, the common logarithm (base 10), natural logarithm (base e), and logarithms to any other base.

5. Physical Constants and Parameters:

   • Reynolds number (in fluid dynamics).
   • Mach number (in fluid dynamics).
   • Prandtl number (in fluid mechanics and heat transfer).
   • Froude number (in fluid mechanics).
   • Péclet number (in heat and mass transfer).
   • Schmidt number (in fluid mechanics and mass transfer).
   • Grashof number (in fluid mechanics and heat transfer).
   • Nusselt number (in heat transfer).
   • Biot number (in heat transfer).
   • Strouhal number (in fluid dynamics and aerodynamics).
   • Euler number (in fluid dynamics).
   • Weber number (in fluid dynamics).
   • Bond number (in fluid dynamics and heat transfer).

6. Unitless Quantities in Mathematics:

   • Mathematical constants, like those in trigonometry and calculus.
   • Unitless quantities arising from algebraic manipulations.
   • Fractal dimensions (e.g., Hausdorff dimension).