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The Buckingham PI theorem, created by Edgar Buckingham, states that n dimensional variables in a dimensionally homogeneous equation can be grouped into K dimensionless groups. These dimensionless groups, called pi, have relationships written as functions of each other. This method, also known as the method of repeating variables, helps in understanding relationships, as demonstrated in the case of drag force on a smooth sphere by listing parameters like diameter, velocity, density, and viscosity.