MONT 109N – Mathematics Across Cultures Midterm Exam March 25, 2011

Your Name:

Directions: Do all work on these sheets. You may use the backs of the page if you need more space. Note the table of information provided on the accompanying sheet. There are 100 total points.

I. In the Mayan calendar system, today is the day 4 Akbal 16 Cumku in the Calendar Round and 12.19.18.4.3 (in baktuns, katuns, tuns, uinals, days) in the Long Count.

A. (15) What day will it be three of our weeks from today (on Friday, April 15)? Show all calculations needed to determine this.

B. (10) What will the Long Count date be three weeks from today?

II. (15) Suppose you are playing mancala and it is your turn. Your 6 pits contain numbers of stones left to right as follows: 0,5,3,0,0,0. Is it possible to get all 8 stones to your store before the other player gets to play? If so, show how to do it, step by step. If not, explain why not.

IV. Short Answer (choose any 6 for 30 total points – if you answer more than 6, only the best 6 scores will be used).

A. (5) What base did the Maya use in their number system? How would a Classic Maya scribe have represented the number 151?

B. (5) The role of mancala games in African cultures is often compared to the role of what game in European cultures? In what ways could it be said that these games are similar?

C. (5) What was the actual information represented in the mettang “stick charts” used by the Marshall Islanders in their culture? Were they maps in our sense?

D. (5) What is the name of the medieval palace in Spain whose decorations stimulated M.C. Escher’s interest in periodic patterns and near which city is it located?

E. (5) In what modern-day countries are most of the sites of Classic Maya cities located? Approximately when did the collapse of the Classic Maya civilization occur?

F. (5) What are some of the common features shared by the Classic Maya collapse and the collapse of the Easter Island culture?

G. (5) What was the meaning of the numerical information in the section of the Maya Dresden Codex that we studied in Problem Set 1?

H. (5) Give two examples of transformations that are symmetries of the pattern in the Escher drawing reproduced on the next page. (Imagine the pattern extended to fill out the whole plane of that sheet.) Are you taking the shading (coloring) into account? Explain.

IV. Essay. (30) What is the mathematical meaning of symmetry? What examples of symmetry transformations have we used in discussing examples from visual art in this course? What is the mathematical concept of a group and why is it important for the study of symmetries? Describe how symmetry groups can be used to classify plane periodic patterns. In what sense are two patterns of the same type similar? In what ways can they be different?

The “Months” in the Maya Sacred Round

1. Imix  11. Chuen
2. Ik  12. Eb
3. Akbal  13. Ben
4. Kan  14. Ix
5. Chicchan 15. Men
6. Cimi  16. Cib
7. Manik  17. Caban
8. Lamat  18. Etznab
9. Muluc  19. Ahab
10. Oc  20. Ahau

The “Months” in the Maya Vague Year

1. Pop  10. Yax
2. Uo  11. Zak
3. Zip  12. Ceh
4. Zotz  13. Mac
5. Zec  14. Kankin
6. Xul  15. Muan
7. Yaxkin 16. Pax
8. Mol  17. Kayab
9. Chen 18. Cumku
19. Uayeb