Exploring Maya Math by Jackie Belize https://padlet.com/jackie_pekar/h5r2u5w0zwom by Jacquelyn Pekar May 2018 en-us 2018-04-12 18:44:31 UTC 2023-05-22 15:13:31 UTC hello@padlet.com WHO... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251705617 ...were the Ancient Maya people? The Maya civilization developed as a Mesoamerican peoples who arose around 1800 B.C. Their civilization developed into a very rich and complicated one with great strides in astronomy, art, agriculture, religion, politics and most notably, for the purposes of this presentation, mathematics.]]> 2018-04-13 19:11:44 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251705617 WHERE... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251709317 ...were these people living? The Maya people lived in Central America throughout the Yucatan peninsula.  Their kingdoms spread through what is now known as Belize, Honduras, El Salvador, Guatemala, and five states in southern Mexico. At its height, there existed over forty cities each housing between 5,000 and 50,000 people. At its peak, the numbers may have reached 2,000,000. Some of those cities included Tikal, Uaxatun, Palenque, Xunantunich, and Caracol.  Many are shown on the map below. ]]> 2018-04-13 19:21:01 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251709317 WHAT... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251709945 ...about mathematics?  My first instinct was to find out how the Maya people used mathematics to build their incredible cities.  Well, they didn't!  Their use of mathematics was for market purchasing and merchant exchange and in their amazing calendar system of measuring time. It is the calendar Long Count that we will explore. The Maya based their number system on 20 instead of the base-10 system that we use today. While they only used stones and sticks (and later a shell for zero) their number system was accurate and useful. Below is the very simple example of the system zero to 19.]]> 2018-04-13 19:22:52 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251709945 WHEN... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251710295 ...did this happen? There are three time periods in classifying the ancient Maya civilization.  The first was the Preclassic period or Formative Period.  Lasting from about 1800 B. C. to A. D. 250, these early Maya developed agriculture and grew corn, beans, squash and cassava. The Middle Preclassic Period lasted until 300 A. D. and during this period we see the development of religious and cultural traits as well as the number system we will explore. This is also the period when their famous calendar was created.  A simplified example is shown below.  The Classic period was from A. D. 250-900 and this was the rise of the great stone cities with their elegant temples and ball courts.  Shortly after A. D. 900, the great cities were abandon one by one and the Maya civilization crumbled.]]> 2018-04-13 19:23:52 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251710295 WHY... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251712833 ...is this important? The ancient Maya were one of the first civilizations to create the zero. The development of their mathematics helped them create the calendar for religious, daily, and astronomical use.  Their culture depended on this use and we have reaped the benefits of having that famous zero.  ]]> 2018-04-13 19:32:50 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251712833 HOW... jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251713086 ...did they do it? The Maya Long Count is an extremely sophisticated calendar system. Like our own system they had a cyclical rotation of days, months and years. Although, their days numbered 20, they had 18 months and 365 days in their year. "Our own calendar is comparable: the days of the week form a repeating cycle of seven, Sunday to Saturday, followed again by Sunday; the days of the month form another repeating cycle from one to thirty-one (or 30, or 28/29 in February), after which the next month begins with one again; and the months of the year form a third cycle, from January to December and back to January"(Hammond). As you can see below in the drawing of the Maya calendar, it is far easier to figure out than at first glance. Further illustrations will follow.]]> 2018-04-13 19:33:54 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251713086 THE LONG COUNT jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251820190 This is the calendar they used to count long periods of time for astronomical purposes. Their regular calendar was called The Haab and their divine calendar was called The Tzolkin. More on those will be discussed further.
Our base date of the Gregorian calendar that we use begins counting years from the birth of Jesus Christ.  The Maya calendar begins from a base date of August 3114 B. C.  You will notice that this is far earlier than the Maya people existed.  However, the Maya people got this date from their own creation story.  From our base date to now, we count two millennium of 1,000 years, no (or zero!) centuries of 100 years, no (or zero!) scores of 20 years each, 18 single years of 365 days each, three months of 28-31 days, and 14 days of the fourth month (as of this writing)...and counting!]]> 2018-04-14 19:43:59 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251820190 THE LONG COUNT (cont.) jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251822429 Looking at how the Maya counted their time, we see that they used a similar cyclic pattern. Maya had two cycles of days: the Sacred Round of 260 days and the solar year of 365 days. There were 20 days of 18 months and one month of 5 days only. The name of the day changed as ours does along with the number. For example, Monday the 1st, Tuesday the 2nd, etc. Maya time would be called 1 Imix, 2 Ik, 3 Akbal, etc. with the cycle of numbers being 1-13 instead of 20. So, you had 13x20 or 260 days of the Sacred Round Calendar. More on this further. Back to understanding the Long Count...Time begins with their creation date and time was counted forward from that and divided into periods of varying length. The Maya used multiples of 20 which is a vigesimal, not a decimal system of numeration (Hammond 109).]]> 2018-04-14 20:27:03 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251822429 THE HAAB jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251823609 The solar calendar was the 365 day civil calendar. This one had 18 months of 20 days each with one extra month of only 5 days. The Haab and the Tzolkin measured days and months but not years.]]> 2018-04-14 20:47:24 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251823609 THE TZOLKIN jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251823621 The Divine calendar also known as The Sacred Round is the 260 day calendar. it had 20 periods of 13 days used to determine religious and ceremonial events.]]> 2018-04-14 20:47:44 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251823621 SETTING A DATE jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251904336 Both the Haab and the Tzolkin wheels were used simultaneously along with the Long Count calendar. The wheels of the Haab and the Tzolkin moved in opposite directions as illustrated  in the previous picture.   The entire cycle takes about 52 years to complete.  The smallest wheel has 260 teeth and the larger one has 365 teethwith  the name of each of the positions of the Haab year. As both wheels rotate, the name of the Tzolkin day corresponds to each Haab position. The date is identified by counting the number of days from their creation date. The Long Count works along with these two calendars and the corresponding names are illustrated in the first picture under that title (TimeandDate.com)

]]> 2018-04-15 16:36:38 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251904336 WHEN'S MY BIRTHDAY? jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907329 Here is a fun Maya date converter to engage your curiosity and have fun learning more!

https://maya.nmai.si.edu/calendar/maya-calendar-converter]]> 2018-04-15 17:02:15 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907329 WHAT ABOUT THOSE STICKS AND STONES? jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907652 The simple way of creating a counting system using stones and sticks must have originated with counting on their fingers and toes.  Using a vigesimal system based on the number twenty, the Maya could count into the millions!  Their numbers were written from top to bottom rather than left to right.  So while we would put a 3 to the left of a 4 for 34, the Maya would put one stone at the top, a space and then four stones close to two sticks below. This is illustrated below in the window next to this one.

Here is a simple video that explains it in the easiest terms.
https://youtu.be/VmZjPVT2M20]]> 2018-04-15 17:04:41 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907652 MORE FUN GAMES jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907744 Some of the most fun I have had with exploring Maya math has been this site.  I hope you enjoy it!
https://maya.nmai.si.edu/maya-sun/maya-math-game

For more interesting calendar conversions so here...
https://www.maa.org/press/periodicals/convergence/maya-calendar-conversions-introduction]]> 2018-04-15 17:05:35 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907744 WORKS CITED jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907751 “Calendar.” - Sun, Corn and the Calendar, Smithsonian Institution, 2018, maya.nmai.si.edu/. https://maya.nmai.si.edu/site-credits

Catepillan, Ximena, and Waclaw Szymanski. “Maya Calendar Conversions.” Homepage | Mathematical Association of America, Mathematical Association of America, 2018, www.maa.org/.

Hammond, Norman. Ancient Maya Civilization. Rutgers University Press, 1994.

Mackillop, Heather. The Ancient Maya: New Perspectives. W.W. Norton, 2006.

Sharer, Robert J., and Loa P. Traxler. The Ancient Maya. Sixth ed., Stanford University Press, 2005.

Voelkel, Jon and Pamala. “Maya Math.” Home, jaguarstones.com/maya/index.html. 
]]> 2018-04-15 17:05:43 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907751 SPECIAL THANKS jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907781 A very special thanks goes to Dr. Antonio Beardall, Archaeologist at the Institute of Archaeology in Belmopan, Belize and Paul Smith, his assistant for the invaluable resources they made in the form of books, maps and time spent to help me ]]> 2018-04-15 17:05:59 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/251907781 jackie_pekar https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/253868871 2018-04-20 15:12:22 UTC https://padlet.com/jackie_pekar/h5r2u5w0zwom/wish/253868871