There is no historical evidence that William the Conqueror "began to build square keep castles" as a new innovation. Square stone keeps (donjons) existed in France before 1066 (e.g., Loches, Langeais). William and his successors built keeps of various shapes—square (Tower of London, Colchester), rectangular, and later polygonal and round—throughout the 11th–12th centuries. The choice depended on terrain, materials, and evolving military engineering, not a single royal decree.