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The Mayan and other Mesoamerican cultures used a vigesimal number system based on base 20, (and, to some extent, base 5), probably originally developed from counting on fingers and toes. The numerals consisted of only three symbols: zero, represented as a shell shape; one, a dot; and five, a bar.

Maya numbers are based around the number 20, so in Maya numbers , 20 is a 1 and a 0. So write a dot for the 1 and leave a gap below it. Then below the gap, draw a clamshell – the Mayan symbol for zero. To write numbers from 21–39, think of them as 20 plus something.

The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal (base-20) positional numeral system. The numerals are made up of three symbols; zero (shell shape, with the plastron uppermost), one (a dot) and five (a bar).

A unit of the third position is worth 400 (20 x 20), so to write 401 a dot goes in the first position, a zero in the second and a dot in the third.

The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.

The Maya used the following names for their powers of twenty: kal (20), bak (400), pic (8,000), calab (160,000), kinchil (3,200,000) and alau (64,000,000).

Similar to the number system we use today , the Mayan system operated with place values. To achieve this place value system they developed the idea of a zero placeholder. The Mayan system is in base 20 (vigesimal) rather than base 10 (decimal). This system also uses a different digit representation.

The Maya counting system required only three symbols: a dot representing a value of one, a bar representing five, and a shell representing zero . That the Maya understood the value of zero is remarkable – most of the world’s civilizations had no concept of zero at that time.

The Babylonian cuneiform method of recording quantities, approximately 5000 years old, is among the oldest numeral systems in existence. They developed a base-60 (sexidecimal) system with numbers less than sixty represented in base-ten.

vigesimal

There is no Maya alphabet . Maya writing is difficult to interpret for a number of reasons. First, glyphs do not represent just sounds or ideas, they can represent both, making it difficult to know how each glyph or cartouche should be read.

So where we learn to count on our fingers, Maya children counted on their fingers and toes. The numbers above nineteen are indicated on the basis of their vertical position. The Maya used a vigesimal ( Base – 20 ) system, so each position is a power of twenty .

Of all the ancient calendar systems, the Maya and other Mesoamerican systems are the most complex and intricate. They used 20-day months, and had two calendar years: the 260-day Sacred Round, or tzolkin , and the 365-day Vague Year, or haab . These two calendars coincided every 52 years.

Pyramids were used not only as temples and focal points for Maya religious practices where offerings were made to the gods but also as gigantic tombs for deceased rulers, their partners, sacrificial victims, and precious goods.

Two thousand years ago, the ancient Maya developed one of the most advanced civilizations in the Americas. They developed a written language of hieroglyphs and invented the mathematical concept of zero. With their expertise in astronomy and mathematics, the Maya developed a complex and accurate calendar system.

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