Why can coaxial cables of different diameters have the same characteristic impedance?

The characteristic impedance of a coaxial cable is governed mathematically by the ratio of the inner shield diameter to the outer diameter of the centre conductor, combined with the dielectric constant of the insulator between them. As long as this specific mathematical ratio is maintained, the overall physical size of the cable can be scaled up or down without changing the impedance. This principle explains why a thick cable like RG-8 and a much thinner cable like RG-58 can both perfectly maintain a 50-ohm characteristic impedance.