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
Mayan Twenty
Tiered System
• The Mayan numeral system was written
Example of Tiered Numbers
2
20

1
20

0
20

21   77   500   855

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        =

+          =

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
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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