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Central America: 350 A.D.

The Mayans, native inhabitants of Central America, were highly skilled mathematicians, astronomers, artists and architects. They had a very complex calendar system and the need to hold a place in their elborate date system lead to their invention of zero--600 years and 12,000 miles removed from the Babylonians.

The Mayans had several calendars. There was a 365 day civil year, a 260 day religious year and the complicated Long Count calendar which measured time from the start of the Mayan civilization (August 12, 3113 B.C.).

kin

day

 
unial

month

20 days

tun

year

360 days (18 months)

katun

20 tuns

7200 days (20 years)

baktun

20 katuns

144,000 days (400 years)

pictun

20 baktuns

2,880,000 days (8,000 years)

calabtun

20 pictuns

57,600,000 days (160,000 years)

kinchiltun

20 calabtuns

1,152,000,000 days (3,200,000 years)

alautun

20 kinchiltuns

23,040,000,000 days (64 million years)

It is the formal Long Count calendar that brought about the zero. The Mayan numerals were very complex in formal use--painted or carved heads or even full figures were used to represent numbers. When using these ornate carvings on a stelae, or stone tablet, the Mayans had a rather rigid graphic layout; each period of time had a space and all the spaces needed to be filled in. So a date that was 8 baktuns, 14 katuns, 3 tuns, 0 unials and 12 kins had to have one figure for each place. The zero was often represented by a shell shape.

Despite the use of zero in the place value system, it was never used for calculations. Once again, this stems back to the calendar. You may have noticed that a 360 day year is 18 months (20 days to a month). This irregularity messed up an otherwise tidy vegisimal (base 20) system.

Decimal 10 is (1 x 10) + (0 x 1) = 10
Vegisimal 10 is (1 x 20) + (0 x 1) = 20
Mayan 10 is (1 x 20) + (0 x 1) = 20

Decimal 100 is (1 x 10exp2) + (0 x 10) + (0 x 1) = 100
Vegisimal 100 is (1 x 20exp2) + (0 x 20) + (0 x 1) = 400
Mayan 100 is (1 x (18x20)) + (0 x 20) + (0 x 1) = 360

Decimal 1000 is (1 x 10exp3) + (0 x 10exp2) + (0 x 10) + (0 x 1) = 1000
Vegisimal 1000 is (1 x 20exp3) + (0 x 20exp2) + (0 x 20) + (0 x 1) = 8000
Mayan 1000 is (1 x (18x20exp2)) + (0 x (18x20)) + (0 x 20) + (0 x 1) = 7200

The Mayans, for all their high level mathematical and astronomical skills, failed to make other key discoveries and inventions that might have helped their culture survive. They never used the plow or metal tools.


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