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So why are wafers round and not rectangular? Especially since the CPU and GPU bare die we see are rectangular,wafer tester wouldn't it be better if the wafers were not round but rectangular so that they could theoretically be cut into small pieces with no waste at all?

This needs to start with the manufacturing process of wafers.

In the silica ore and carbon mixed by heating the redox reaction can be obtained after the crude silicon, but this time to get the crude silicon purity can not be used to make integrated circuits. Next, the crude silicon by hydrochloric acid chlorination and distillation can be further obtained by a higher purity of polycrystalline silicon, and then next there is a very important access to single-crystal material crystal growth method, it is known as Chaikolaski method, is currently the main access to single-crystal material crystal growth method, the use of which can be polycrystalline silicon into monocrystalline silicon.

The method consists of melting the previously obtained polysilicon, placing a crystal seed (or "seed crystal") at the end of a precisely oriented rod, and immersing the end in the molten state of silicon. The rod is then slowly lifted upwards and rotated at the same time. The temperature gradient of the rod,wafer probe testing the rate of lifting, and the rate of rotation are precisely controlled, and a large, cylindrical (rather like the shape of a pencil with the ends sharpened) single crystal silicon rod can be obtained at the end of the rod.

Silicon rods and then after slicing, grinding, polishing, that is, the basic raw material for integrated circuit chips - silicon wafers, is the "wafer". It is sliced by the cylinder, so it is round.

Wafer is round mainly because the integrated circuit chip needs single crystal silicon, and the realization of single crystal silicon mainly rely on the Chaikolasky method, we can remember the name of this method,vibration isolation table it is named after the Polish scientist Jan Chaikolasky, he was in 1916 when the study of the rate of crystallization of metals, the invention of this method. Nowadays, the Chaikolasky method has evolved into one of the standard processes in steel mills.