Final answer:
The best summary of the Greek definition of 'symmetry' is 'proportional relationships between the parts and the whole', reflecting the Greeks' pursuit of perfection and balance, as seen in the mathematical and architectural refinements such as the golden ratio and symmetrical balance.
Step-by-step explanation:
When considering the Greek definition of "symmetry" as transmitted by Vitruvius, the phrase that best summarizes it is the proportional relationships between the parts and the whole. This is evidenced in the Greek pursuit of perfection and balance in architecture, such as the use of the golden ratio which was applied in the construction of the Parthenon. The Greeks aimed to create a harmonious design known as symmetria, achieving a visual perfection that incorporates subtle distortions to correct for imperfections of human sight. These distortions, such as the entasis seen in Greek Doric columns, create the illusion of perfection and stability.
Furthermore, the mathematical formula of 'twice the number of columns across the front of the temple plus one equals the number of columns down each side' (2x + 1 = y) reflects the Greek endeavor for symmetrical balance in their temple architecture. In examining ancient Greek temples such as the Temple of Artemis at Corfu, one can observe the rigid symmetry imposed in these structures, echoing the Greek admiration for aesthetic dimensions and balance.