Discuss three important achievements of ancient Maya. Write your answer in English.

1. Architecture and Urban Planning: The ancient Maya were skilled architects and urban planners, creating intricate and impressive cities like Tikal, Palenque, and Chichen Itza. Their construction techniques and innovations included the use of the corbel arch, platform-and-mound complexes, and carved stone monuments. Many of their structures were built for religious or ritualistic purposes, such as pyramids, temples, and observatories. The Maya cities were also designed with a grid-like pattern, which reflects their advanced knowledge of geometry and spatial organization.

2. Writing System and Mathematics: The Maya developed a sophisticated writing system known as the Maya Hieroglyphics or Maya Script. This system combined both logographic and syllabic elements, enabling the Maya to record their history, knowledge, and myths in inscriptions on monuments, pottery, and bark paper books. The Maya also had an advanced understanding of mathematics, having devised a numeral system that used the concept of zero, which was relatively rare among ancient civilizations. Their numerals were based on a vigesimal (base-20) counting system, which they used for purposes such as recording dates, calculations, and astronomical observations.

3. Astronomy and Calendar Systems: The Maya had a deep understanding of astronomy and were able to accurately observe and track the movements of celestial bodies like the sun, moon, and planets. This understanding enabled them to create advanced calendar systems, such as the Tzolk'in (a 260-day sacred calendar) and the Haab' (a 365-day solar calendar). They also developed the Long Count calendar, which allowed them to record dates over a period of thousands of years. They used these calendars to plan agricultural activities, ceremonies, and other important events, as well as to make accurate predictions of solar and lunar eclipses. Their expertise in astronomy also led to the construction of observatories at sites like Chichen Itza and Uxmal, where they could study the night sky and make observations.