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The Babylonians used a base-sixty (sexigesimal) system . In this chapter, we wrap up with a specific example of a civilization that actually used a base system other than 10. The Mayan civilization is generally dated from 1500 BCE to 1700 CE.

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 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.

Any number higher than 19 units in the second position is written using units of the third position. 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 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.

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.

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.

Mysterious Decline of the Maya From the late eighth through the end of the ninth century, something unknown happened to shake the Maya civilization to its foundations. One by one, the Classic cities in the southern lowlands were abandoned, and by A.D. 900, Maya civilization in that region had collapsed.

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.

Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right. Around 300 BC, Euclid introduced the axiomatic method still used in mathematics today, consisting of definition, axiom, theorem, and proof.

Hindu-Arabic numerals, set of 10 symbols— 1 , 2, 3, 4, 5, 6, 7, 8, 9, 0—that represent numbers in the decimal number system. They originated in India in the 6th or 7th century and were introduced to Europe through the writings of Middle Eastern mathematicians, especially al-Khwarizmi and al-Kindi, about the 12th century.

Aryabhata

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).

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.

How to convert Mayan numbers ? Converting Mayan numerals is made by counting dots and bars symbols on each rows and treat it as base 20 writing, before converting it to base 10. For numbers that are greater than or equal to 360, be sure to apply the modified vigesimal system if necessary.

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