The ground-state binding energy of the exciton in a finite-potential quantu
m disc setting is calculated variationally to study the change in dimension
ality of the exciton within the limiting cases of the quantum well, wire, a
nd dot, as well as the intermediate regime between these limiting geometrie
s. Quantitative comparisons have been made with previous calculations using
different trial wavefunctions to show the superiority of the present trial
wavefunction in the quantum disc setting and to further illustrate the beh
aviour of the exciton in the quantum dot limit. Using the binding energy ob
tained from the present calculations, we further calculated the virial theo
rem number for the exciton in various confinement geometries, to disprove t
he recent claim of the existence of universal-constant virial theorem numbe
rs for the quantum wells and wires. Also, the dimensionality parameter of t
he fractional-dimensionality model for confined excitons in the various con
finement geometries has been calculated to facilitate discussion of its app
licability to these structures, including the quantum dot limit.