  A manifestation of the Pauli Exclusion Principle is observed when fermions
are trapped in the ground state of a 2D harmonic oscillator trap at very low
temperatures. This non-interaction of fermions results in the formation of
Pauli crystals. This work introduces a statistical mechanical interpretation of
the principles that led to the observation of Pauli crystals by calculating the
energy, radius and other parameters of the non-interacting arrangement of
ultra-cold fermions. This model approaches the problem from two different
directions, namely fermion degeneracy and harmonic oscillator treatment.
Unifying the two different approaches gives a more comprehensive and robust
description of the various parameters of Pauli crystals.
