1. Pi (π): The ratio of a circle's circumference to its diameter, π is a fundamental dimensionless constant that appears in various mathematical and physical contexts, including geometry, trigonometry, and calculus.

2. Euler's Number (e): Euler's number is the base of the natural logarithm and appears in exponential growth and decay processes, as well as in various areas of mathematics and physics.

3. Golden Ratio (φ): The golden ratio is a dimensionless constant that appears in art, architecture, and nature. It is often associated with aesthetic beauty and is approximately equal to 1.6180339887.

4. Fine-Structure Constant (α): In quantum electrodynamics, the fine-structure constant characterizes the strength of the electromagnetic interaction between elementary charged particles. It is approximately 1/137.

5. Reynolds Number (Re): In fluid dynamics, the Reynolds number is a dimensionless quantity that characterizes the flow of a fluid. It determines whether a flow is laminar or turbulent and plays a crucial role in understanding fluid behavior.

6. Mach Number (Ma): In fluid dynamics, the Mach number is a dimensionless quantity that represents the ratio of an object's speed to the speed of sound in the surrounding medium. It is used to describe supersonic and subsonic flows.

7. Prandtl Number (Pr): In heat transfer, the Prandtl number is a dimensionless quantity that relates the momentum diffusivity to the thermal diffusivity. It plays a role in convection and fluid flow.

8. Archimedes Number (Ar): In fluid dynamics, the Archimedes number relates buoyancy forces to viscous forces and is used to analyze the behavior of floating or sinking objects.

9. Péclet Number (Pe): In heat and mass transfer, the Péclet number relates convective transport to diffusive transport and is used to characterize the dominant mode of heat or mass transfer.

10. Weber Number (We): In fluid dynamics, the Weber number relates inertial forces to surface tension forces and is used to predict the behavior of fluid flows.

These are just a few examples of non-dimensional constants, and there are many more that appear in different scientific disciplines. Non-dimensional constants are valuable tools for simplifying and analyzing complex physical phenomena, as they provide insight into the underlying relationships between various physical quantities.