These are some of accomplishments of ancient Mayans in various fields.
Ancient Mayan Accomplishments in Art
It particularly evolved during the pre-classical period but flourished in the Classical period. Mayan art had survived until the 16th century. The Olmecs, Toltecs and Teotihuacan influenced Mayan art.
Painting and description was drawn on paper. Other art form like carving was made on wood, stone and clay.Things like pottery, ceramics and some buildings with murals have survived. The artists used Maya Blue to paint their work. The Mayan artists marked their work by writing their name.
Ancient Mayan Calendar
Mayans developed three dating systems-the Long Count(Kins, Winals, Tuns, K'atuns and Bak'tuns),Tzolki'in (260 day calendar comprising of 13 numbers are paired with 20 day names) and Haab,

365 days cycle, consisting of 19 months, namely Pop, Uo, Zip, Zotz, Tzec, Xul, Yaxkin, Mol, Chen, Yax, Zac, Keh, Mac, Kankin, Muwan, Pax, Kayab, Kumku and Wayeb. Year Bearers calendar had characteristics- Ik, Eb', Kaban and Manik.
Ancient Mayan Contribution in Agriculture
Farming was done by men. Corn was the staple food of the people. Mayas were the first civilization to cultivate cacao plant and used to make chocolate drink from cacao beans. Mayan agriculture was carried on permanent raised fields and forest gardens. Other methods included terracing, wild harvesting, slash and burn.
Ancient Mayan Legacy in Architecture

Mayan Structures
Structures were built without using metal tools. Materials like limestone, cement and plaster were used for construction. The structures covered with lime stucco were trademark of Mayan architecture. Houses, temples, courtyards and stepped pyramids are great examples of Mayan architectural design. At the top of some pyramids, temples were placed to honor a deity. Mayans used corbel arch, a type of false arch.

The arch was developed by stepping each block from the other side closer to the center and was capped at the peak. Temple of the Cross at Palenque is an example where corbel vault was used. Temples and pyramids were rebuilt every 52 years according to Maya Long Calendar Count but it's likely that rebuilding may have taken place at the behest of a new ruler for political reasons.
The topography of an area played a crucial role in building a structure. Cities having flat plains had vast municipalities while higher ground surface was used to build high-rise temples and towers. Mayans gave importance to the availability of water.
New structures were placed on top of a platform sub-structure whose height varied from 1 meter to 45 meters. Steep stone steps were placed on one side of the platform. Platforms were made of a cut and stucco stone and filled with gravel. Stucco was used as a filling to level any imperfection.
Ancient Mayan Achievement in Mathematics

Mayans used three symbols to represent numbers- dot(.), dash(-) and shell( ). Mayans were the first civilization to develop and use the concept of 'zero'. They also used a base 20 and base 5 numbering system. This system was based on the number of fingers and toes and number of digits on one hand or foot of a person. The numbers were written vertically, the lowest denomination being at the bottom. Mayans made precise astronomical observations by using mathematical calculations.
Ancient Mayan Achievement in Astronomy

Mayan Mythology
Mayan mythology lays emphasis on astronomy. Mayas believed that the celestial objects had a direct impact on their lives. Time was calculated by observing the sky. Mayans observed the sky to predict events like harvest season, famines and floods. They were probably the first civilization to know about the Orion Nebula.

Mayan Astronomy
Astronomy was considered to be crucial even in case of religion. Astronomers had the ability to predict future events. They would record the movements in the sky with naked eyes. The moon, sun, Venus and certain stars were given importance. Significance was given on Zenial passage.
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