- 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.
