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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