Final answer:
Ancient Greek geometry deeply influenced their art and architecture, as they searched for perfect proportions using mathematical rules to create lifelike sculptures and harmoniously balanced structures like the Parthenon.
Step-by-step explanation:
The use of geometry in Ancient Greece significantly influenced art and architecture, which is evident in the work of the Greek sculptor Polykleitos and the architectural grandeur of structures like the Parthenon.
Greeks applied mathematical principles, such as the golden ratio, to achieve perfect proportions in sculpture and architecture, believing that these proportions were inherently pleasing to the eye.
The perfection seen in Greek art is a result of mathematical precision and an understanding of human perception, allowing the Greeks to create the visual impression of perfection.
Artists like Polykleitos found beauty in lifelike proportions, which they achieved by adhering to strict mathematical rules when sculpting. This method of incorporating mathematics into art reached its zenith in classical Greek architecture, illustrated by the mathematical scale used in all temples, following specific ratios for harmony and balance.