Here are some known ancient Mayan inventions.
Calendar and Astronomy
Maya specifically created, or rather invented, a 260 day cycle in order to allow them to accurately track the occurrence of successive conjunctions involving the Earth and Venus, over a full 2000 year grand cycle.
Astronomy is another field that the Mayans. Again, the Mayans are not as well known as other ancient civilizations for their astronomy, but data suggests they were surprisingly advanced in their findings. They are thought to be the only pre-telescopic society that realized the Orion Nebula is fuzzy.
Among their other accomplishments, the ancient Mayas invented a calendar of remarkable accuracy and complexity. The Maya calendar was adopted by the other Mesoamerican nations, such as the Aztecs and the Toltec. The Maya calendar uses three different dating systems in parallel, the Long Count, the Tzolkin (divine calendar), and theHaab (civil calendar).
Ancient Mayan Number System
The Mayans were very intelligent as evidenced by their books, calendars, study of astronomy, and number system. The Mayan's number system was based on the number 20. Every number was expressed with combinations of lines, points, and zero marks, using system of place values. The modern marks divide figures into tens, thus the value increased from right to left.
Mayans counted in twenties and the value increased from bottom to top in vertical columns; at the lowest point of the column, unit marks were ones, but on top were four-hundreds place (like 20*20). However, the Mayans could not express fractions.
We can thank Mexico for introducing chocolate to the world. Chocolate was highly valued in the Mayan culture - it was actually used as currency. The Mayans, for one, discovered that they could take the thick milky liquid from the sapodilla tree (an evergreen) and harden it into gum. The liquid was "chicle", a word you can still hear on street corners in Mexico from vendors selling chewing gum.
The mayan's invented the ball game. The Mayans were great sportsmen and build huge ballcourts to play their games. The Great Ballcourt of Chichén Itzá is 545 feet long and 225 feet wide overall. It has no vault, no discontinuity between the walls and is totally open to the sky.
The ancient Mayan written language is a complex system of sound, pictures and logograms. A logogram is a written character that represents a meaning or a word. Some of the hieroglyphs represent individual syllables, some are pictures that represent a word or idea, and some represent a spoken word or phrase.
The Maya were noted as well for elaborate and highly decorated ceremonial architecture, including temple-pyramids, palaces and observatories, all built without metal tools. They were also skilled farmers, clearing large sections of tropical rain forest and, where groundwater was scarce, building sizeable underground reservoirs for the storage of rainwater.
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