The Nature of Glass

Glass is a totally brittle substance. It will bend a very small amount, but has no capacity like most metals to deform. It will bend to a point and then break. It is this bending stress that is the focus for calculating the thickness.
Glass also has a wide variability in strength. Testing samples of uniform manufacture has proved this (see specifications for glass, - Tensile Strength 19.3 to 28.4MPa).

Glass is weak in tension, is elastic up to its breaking point, and has no ductility. It is not capable of being permanently deformed, and does not give any pre-warning of impending failure by showing a permanent set after an excessive load has been removed.
An important characteristic is its ability to carry an impulse load approximately twice its rated load (i.e. banging the aquarium with your hand quite hard). This is inevitably what saves many aquariums when they are accidentally knocked.
The variability of the strength of glass due to limitations of the manufacturing process means a suitable safety factor must be used when calculating glass thickness. The factor commonly used is 3.8. While not a perfect guarantee, it will remove all risk bar that of damaged or very poor quality glass. The main damage that will cause failures is scratches and chips. Also a point load on the glass surface will cause it to fail. For this reason a soft packer like polystyrene is used under aquariums to stop the point loading of dirt and grit.
Also when manufacturing an aquarium, the joining compound (commonly silicone) must have a minimum thickness (0.5-1mm) to allow for irregularities along the glass edge. When glass is cut it is not flat along its edge unless it has been specially ground.
It is possible to use a lower safety factor if the glass is of excellent quality and has no internal stress. It is at the designers risk however to lower the safety factor.