Topics in Mathematics: Math and Music

MATH 110   Homework Assignment #7 (Last One!)

Due Thursday, April 26, start of class


Homework should be turned in at the START OF CLASS. All problem numbers refer to From Music to Mathematics: Exploring the Connections. Unless otherwise indicated, all parts of a problem (e.g., a., b., c., etc.) should be completed. You are encouraged to work on these problems with other classmates, and it is ok to use internet sources for help if it's absolutely necessary; however, the solutions you turn in should be YOUR OWN WORK and written in YOUR OWN WORDS. Be sure to cite any references, websites, Internet sources, etc. that you may have used for assistance with the assignment.

Important: Please list the names of any students you worked with on the top of your assignment.


[I]t should be frankly admitted that in some plants the numbers do not belong to the sequence of f's [Fibonacci numbers] but to the sequence of g's [Lucas numbers] or even to the still more anomalous sequences

3, 1, 4, 5, 9, ... or 5, 2, 7, 9, 16, ... .

Thus we must face the fact that [Fibonacci] phyllotaxis is really not a universal law but only a fascinatingly prevalent tendency.

— H. S. M. Coxeter, from Introduction to Geometry (1961, Wiley, p. 172)

Section 5.2 (pp. 189–190)
Problems:   1, 2, 3, 5, 6

Note: For #3, don't worry about the last part of the question (the part about why you have to round off more with 150 than 144).

In addition to the problems listed above, listen to CD #4: Mathematical Composers, available on Moodle. This CD features the music of Bartok, Reich, Philip Glass, Arnold Schoenberg, Peter Maxwell Davies, and Xenakis. We will not have enough time to discuss all of these "mathematical" composers, but you may find information about them and the pieces on the CD in Chapters 7 and 8 of the course textbook.