Final answer:
The greatest accomplishments of the Greeks are evident in their contributions to philosophy, advancements in art and architecture exemplified by the use of the golden ratio, and the creation of democracy in Athens which set a precedent for future political systems.
Step-by-step explanation:
Some of the greatest accomplishments of the Greeks can be witnessed in their philosophy, art, and democratic government. The period known as Classical Greece marked a time of significant intellectual advancement, where Greek thinkers made groundbreaking contributions to philosophy, breaking with supernatural explanations and instead seeking to understand the world through reason and human capacities. Greek philosophers, like Socrates, Plato, and Aristotle, were not only influential in their ethical and moral codes but were also involved in mathematics and science.
Another remarkable achievement is evident in Greek art and architecture, which celebrated perfection and balance. The use of the golden ratio in buildings, like the Parthenon, created aesthetically pleasing forms that are admired to this day. The Greeks' belief in humanistic principles was also reflected in their art, depicting the human body in its ideal state and striving for symmetry and balance.
Moreover, the Athenian invention of democracy was a significant political innovation that heavily influenced future generations. The focus on civic engagement and the empowerment of citizens to participate in government set a model that resonates in modern political systems. These cultural achievements, alongside the rise of dramatic forms like comedy and tragedy and the development of historical research and writing, highlight the enduring legacy of ancient Greece.