- WELCOME TO THE FIRST LESSON ON THE MAYAN NUMBER SYSTEM.
IN THIS LESSON WE'LL FOCUS ON CONVERTING MAYAN NUMBERS
TO BASE 10 NUMBERS.
THERE WERE TWO NUMERICAL SYSTEMS DEVELOPED BY THE MAYANS.
ONE FOR THE COMMON PEOPLE AND ONE FOR THE PRIESTS.
NOT ONLY DID THE TWO SYSTEMS USE DIFFERENT SYMBOLS,
THEY ALSO USED DIFFERENT BASE SYSTEMS.
FOR THE PRIESTS, THE NUMBER SYSTEM WAS GOVERNED BY RITUAL.
THE DAYS OF THE YEAR WERE THOUGHT TO BE GODS
SO THE FORMAL SYMBOLS FOR THE DAYS
WERE DECORATED HEADS LIKE THE SAMPLE BELOW.
SINCE THE BASIC CALENDAR WAS BASED ON 360 DAYS,
THE PRIESTLY NUMERICAL SYSTEM,
THE PRIESTLY NUMERAL SYSTEM USED A MIXED BASE SYSTEM
EMPLOYING MULTIPLES OF 20 AND 360.
THIS MAKES FOR A CONFUSING SYSTEM
WHICH WILL NOT BE DISCUSSED IN THIS LESSON.
INSTEAD WE WILL FOCUS ON THE NUMBER SYSTEM
OF THE COMMON PEOPLE
WHICH USED THE MORE CONSISTENT BASED SYSTEM.
AS WE STATED EARLIER,
THE MAYANS USED A BASE 20 SYSTEM CALLED THE VIGESIMAL SYSTEM.
LIKE OUR SYSTEM, IT IS POSITIONAL
MEANING THAT THE POSITION OF THE NUMERIC SYMBOL
INDICATES ITS PLACE VALUE.
IN THE FOLLOWING TABLE YOU CAN SEE THE PLACE VALUE
IN ITS VERTICAL FORMAT.
AND THE MAYANS DID USE VERTICAL FORMAT STARTING AT THE BOTTOM.
NOTICE HOW WE CAN DETERMINE THE PLACE VALUE
STARTING WITH 20 TO THE ZERO WHICH IS THE ONE'S PLACE VALUE
AND THEN INCREASING THE EXPONENT BY ONE
AS THEY MOVE UP VERTICALLY.
SO 20 TO THE FIRST WOULD BE THE 20'S PLACE VALUE,
20 TO THE SECOND WOULD BE THE 400'S PLACE VALUE AND SO ON.
IN ORDER TO WRITE NUMBERS DOWN,
THERE WERE ONLY THREE SYMBOLS USED IN THIS SYSTEM.
A HORIZONTAL BAR REPRESENTED THE QUANTITY FIVE.
A DOT REPRESENTED THE QUANTITY ONE,
AND A SPECIAL SYMBOL THOUGHT TO BE A SHELL PICTURED HERE
REPRESENTED ZERO.
THE MAYAN SYSTEM MAY HAVE BEEN THE FIRST TO MAKE USE OF ZERO
AS A PLACE HOLDER OR NUMBER.
THE FIRST 20 NUMBERS ARE SHOWN IN THE TABLE TO THE RIGHT.
SO YOU MAY WANT TO PAUSE THE VIDEO
SO YOU CAN LOOK OVER THIS TABLE.
NOTICE HOW ONE THROUGH FOUR ARE JUST ONE THROUGH FOUR DOTS,
FIVE IS THE HORIZONTAL BAR,
SIX IS THE HORIZONTAL BAR WITH A DOT,
AND THEN NOTICE WHEN WE REACH 10,
WE HAVE TWO HORIZONTAL BARS AND SO ON.
BEFORE WE LOOK AT OUR EXAMPLES,
LET'S TALK ABOUT WRITING MAYAN NUMBERS.
NUMBER ONE, WHERE NUMBERS ARE WRITTEN IN VERTICAL FORM,
THERE SHOULD NEVER BE MORE THAN FOUR DOTS IN A SINGLE PLACE.
TWO, WHEN WRITING MAYAN NUMBERS,
EVERY GROUP OF FIVE DOTS BECOMES ONE BAR,
AND THREE, THERE SHOULD NEVER BE MORE THAN THREE BARS
IN A SINGLE PLACE.
FOUR BARS WOULD BE CONVERTED TO ONE DOT IN THE NEXT PLACE UP.
IT'S THE SAME AS 10 GETTING CONVERTED TO ONE
IN THE NEXT PLACE UP
WHEN WE CARRY DURING ADDITION IN BASE 10.
BUT AGAIN THE FOCUS OF THIS LESSON
IS CONVERTING MAYAN NUMBERS TO BASE 10 NUMBERS.
SO LET'S TAKE A LOOK AT SOME EXAMPLES.
AGAIN OUR GOAL HERE IS TO CONVERT THE MAYAN NUMBER
TO BASE 10.
NOTICE HOW THE MAYAN NUMBER IS WRITTEN VERTICALLY
AND THERE ARE THREE PLACES.
AND THEREFORE WE KNOW THE PLACE VALUES
WILL BE HERE, HERE, AND HERE FROM THE BOTTOM UP.
SO THIS IS THE 20 TO THE ZERO OR ONE'S PLACE VALUE.
THIS IS A 20 TO THE FIRST OR 20'S PLACE VALUE
AND THIS IS THE 20 TO THE SECOND OR 400'S PLACE VALUE.
STARTING AT THE BOTTOM, THIS HORIZONTAL BAR IS FIVE,
THE DOT IS ONE,
SO THIS REPRESENTS 6 x THE PLACE VALUE OF ONE.
HERE WE HAVE TWO HORIZONTAL BARS, THAT'S 5 + 5 OR 10,
PLUS TWO DOTS, THAT'S 12,
SO THIS REPRESENTS 12 x THE PLACE VALUE OF 20 TO THE FIRST
OR 20
AND HERE WE HAVE THREE DOTS
THAT MEANS 3 x 20 TO THE SECOND OR 400.
AND WE'LL FIND THESE PRODUCTS AND THEN FIND THE SUM
TO DETERMINE THE MAYAN NUMBER IN BASE 10.
SO 3 x 400 IS 1,200, 12 x 20 IS 240 AND 6 x 1 OF COURSE IS 6.
1,200 + 240 + 6 = 1,446.
SO THIS MAYAN NUMBER REPRESENTS 1,446 IN BASE 10.
TO INDICATE BASE 10, WE CAN PUT A SUBSCRIPT HERE OF 10
TO AVOID ANY CONFUSION.
LET'S TAKE A LOOK AT A SECOND EXAMPLE.
NOTICE HERE WE HAVE ONE, TWO, THREE, FOUR PLACES OR FOUR ROWS.
SO WE'LL BE USING THESE FOUR PLACE VALUES
STARTING FROM THE BOTTOM UP.
SO HERE WE HAVE TWO DOTS,
THAT MEANS TWO SO THIS WOULD BE 2 x THE PLACE VALUE OF ONE.
HERE WE HAVE FIVE, 10, 15 + 1 IS 16.
SO WE'D HAVE 16 x THE PLACE VALUE OF 20
TO THE FIRST OUR JUST 20.
HERE WE HAVE 5, 10 + 3 THAT'S 13
x THE PLACE VALUE OF 20 TO THE SECOND WHICH IS 400
AND THEN HERE WE HAVE ONE BAR,
THAT'S 5 x THE PLACE VALUE OF 20 TO THE THIRD
WHICH IS THE 8,000 PLACE VALUE.
SO NOW WE'LL FIND THESE PRODUCTS AND THEN FIND THE SUM.
SO HERE WE HAVE 40,000.
HERE WE HAVE 13 x 400, THAT'S 5,200, 16 x 20 IS 320,
AND 2 x 1 IS 2.
40,000 + 5,200 + 320 + 2 = 45,522
AND AGAIN THIS IS BASE 10
WHICH IS THE VALUE OF THE GIVEN MAYAN NUMBER IN BASE 10.
IN OUR NEXT LESSON, WE'LL TAKE A GIVEN NUMBER IN BASE 10
AND WRITE IT AS A BASE 20 NUMBER AS WELL AS A MAYAN NUMBER.
I HOPE YOU FOUND THIS HELPFUL.