Mathematics of Maya by P3y0f4E3

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									Mathematics of Maya

    By Patty Smak
    May 31, 2007
   Mayan Mathematics
 Discussion focused on:

Location
Time frame
Type and description of system
Calculation examples
Importance of numerical system
Applying Mayan math in classroom
    Where Did the Mayans Live?

• Mexico and upper
  Central America

• 16 ancient city ruins
  are found in the
  Yucatan Peninsula
  Why Develop a Mathematical
          System?
• To create an accurate   • To study astronomy
  calendar
        Mayan Math System
• Used dots, bars and shells to denote
  quantities in a base 20 or vigesimal system
            Why Base 20?
• Mayans used fingers and toes
• Twenty represented a whole person
              Representation
• a thick dot or circle (a grain)
  represented the units
                                    1

• a dash or bar (a stick)
  represented 5
                                    5
• a shell, indicated emptiness or
  completion, equivalent of our
  zero notion.
                                    0
      Mayan Counting


hun    ca      ox     can     ho




uac     uuc   uaxac   bolon   lahun
           Mayan Counting


 buluc      lahca       oxlahun     canlahun     holahun




uaclahun                            bolonlahun
            uuclahun   uaxaclahun
  Mayan Zero
• Symbol is a shell
• Advanced for time
• Advantage of zero
Mayan Twenty
             Tiered System
• The Mayan numeral system was written
  vertical instead of horizontal.
 Example of Tiered Numbers
     2
20

 1
20


     0
20

         21   77   500   855
                    Addition
• Add 43 plus 67


Arabic base 10 system            Mayan base 20 system



         43
                         1
                        20
    +    67                             +
                             0
                                                  =
        110             20
            Multiplication

• Multiplication is possible
• No concrete evidence it was used, but
  referred to in Dresden Codex
• Mayans could have used repeated addition
             Example of Mayan
               Multiplication
• Multiply 7 X 166

     2
20
   1
20
     0
20

         7     X   166
     Multiply Partial Products
• Multiply       x           =

             7   x       6   =   42


        x            =

         x           =

         x           =
         x           =
     Multiply Partial Products
• Multiply           x         =


             7       x   160   =   1120


                 x        =
                 x        =

                 x        =


                 x        =
Add Partial Products


      +          =




42    +     1120 =     1162
   Number System for Calendar
• The long-count was               8725
  used to calculate the
                          20 x 20 x20 x 20
  days of the calendar
                          18 x 20 x 20
• Every third position
  used 18 instead of 20   20 x 20
• Ingenious way to        20 x 1
  calculate 360 days!     1
 Number System for Astronomy
• Dresden Codex
  showed how
  numerical system used
  for astronomy
• Predictions of Venus,
  the Sun, the Moon,
  and the Ecliptic.
    Importance of Mayan Number
              System
•   Use of zero
•   Positional system
•   Ability to calculate
•   Adaptability
    Benefit of students learning
     Mayan Number System
• Learning/reinforcing place value
• Reinforcing number sense
    Example of classroom Applications
                    Mayan Numeral Exercises
Write the following Mayan numerals in decimal notation (base 10).
1.                     2.                         3.



Add the following (without converting to decimal form).
4.                 5.                        6.



Subtract the following (without converting to decimal form).
7.                       8.                         9.


Write the following in Mayan numerals.
10. 238                  11. 1280                     12. 239 836
                             References
http://www-history.mcs.st-andrews.ac.uk/HistTopics/Mayan_mathematics.html

http://mathcentral.uregina.ca/mayannumerals.html

JB Lambert, B. Ownbey-McLaughlin, C.D. McLaughlin, Maya Arithmetic in
American Scientist, Vol 68 (May-June 1980). PP249-255.
McNeill, Sheila A. The Mayan Zeros, Mathematics Teacher, vol 94, no 7,
October, 2001.
Whitlock, Ralph (1976). Everyday Life of the Maya. Dorset Press, New York, New
York. Pp 106-109.

								
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