The Mayan Numeration System

The Mayan Numeration System

1. The Mayan numeration system

2. The Maya Civilization Around 2600 B.C-XVI in Central America Pre-Columbian Civilization Southeast of Mexico West of Honduras and Salvador North of Belize and Guatemala

3. What have they done ?

4. Writing They were the first to implant a writing system that represents the spoken language of their community.

5. Agriculture Economy based on Agriculture Maya means : those who cultivate the corn No metal tools

6. Science Astronomy development Development of Matematics tools to calculate the movement in the sky notably the moon and sun . Master the 0 numeral Solar year very precised times is counted in days , period of 20 days , in years of 360 days

7. The numeration

8. THE MAYAN NUMERATION Pure Vigesimal system for counting objects Modified Vigesimal system for days  3 signs are used to write the numbers • 1 5

9. • • 2

10. •• 7

11. Numeration is additive from 1 to 19

12. 2 ways of writing it…

13. Counting from 20 20…

14. NO SPECIFIC SYMBOLS FOR NUMBER GREATER THAN 19 INSTEAD… SYSTEM OF POSITION

15. The Maya were not using the same system to count objects and numbers…. Objects Unit of Time 20x20x20x20 20x20x20 20x20 20 1 20x18x20x20 20x18x20 20x18 20 1

16. Counting from 20… Numeration is one of POSITION Every number more than 20 needs to be decomposed into the sum of powers of 20 EX : 21= 20x1 +1 79=20x3+19 If a number is more than 20 than we need to write it on a vertical column. The position of the number determined its value We read the number from top to bottom and the power of 20 decreases.

17. Think of floors The 2 nd floor is a multiple of 20 First floor Second Floor

18. • • 1 x 20 1 1 x 20 + 1 = 21

19. •••• ••• 3 x20 19 79 3 x 20 + 19 =

20. The 3 rd floor is a multiple of 360 (18x20)=360 12 x 18 x 20 0 x 20 5 12 x 18 x 20 + (0 x 20) + 5 = 4325

21. The 4 th floor or a multiple of 18x20x20=7200 15x18x20x20=108000 4x18x20=1440 7x20=140 10 109590

22. Quizz !!! Convert 25 into the Mayan System 25

23. Quizz !!! Convert 25 into the Mayan System 25 •

24. 2) Convert the following Maya number into a normal number • • ?

25. 2) Convert the following Maya number into a normal number • • 350

26. 3) Convert the number into a Mayan Number 19578

27. 19578=14400 +5040+120+18 =(2 x 7200 )+ (14 x 360 ) +(6x 20 ) +18 4 th Floor 3th Floor 2th Floor 1th Floor

28. 19578=14400 +5040+120+18 =(2 x 7200 )+ (14 x 360 ) +(6x 20 ) +18 • • • • • • • 18 6x 20 14x 18x20 2x 18x20x20 • • •